127.0.0.1:9200<br>URL: http://127.0.0.1:9200/likecs_art_db/_search<br>REQUEST:<pre>Array
(
    [query] => Array
        (
            [match] => Array
                (
                    [text] => Array
                        (
                            [query] => 决策模型(二)：风险决策法
                        )

                )

        )

    [highlight] => Array
        (
            [fields] => Array
                (
                    [text] => stdClass Object
                        (
                        )

                )

            [pre_tags] => #em#
            [post_tags] => #/em#
        )

    [size] => 8
    [from] => 0
)
</pre>RESPONSE:<pre>string(7255) "{"took":20,"timed_out":false,"_shards":{"total":1,"successful":1,"skipped":0,"failed":0},"hits":{"total":{"value":10000,"relation":"gte"},"max_score":55.54028,"hits":[{"_index":"likecs_art_db","_type":"_doc","_id":"40699","_score":55.54028,"_source":{"id":"40699","text":"\u51b3\u7b56\u6a21\u578b(\u4e8c)\uff1a\u98ce\u9669\u51b3\u7b56\u6cd5","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"dmego","tagsname":"\u5b66\u4e60\u7b14\u8bb0","tagsid":"[\"463\"]","catesname":"\u8fd0\u7b79\u51b3\u7b56","catesid":"[5653]","createtime":"1542707333"},"highlight":{"text":["#em#决#/em##em#策#/em##em#模#/em##em#型#/em#(#em#二#/em#)：#em#风#/em##em#险#/em##em#决#/em##em#策#/em##em#法#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"164997","_score":34.17326,"_source":{"id":"164997","text":"\u51b3\u7b56\u6811\u6a21\u578b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"tinglele527","tagsname":"","tagsid":"","catesname":null,"catesid":"","createtime":"1627804695"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"203299821","_score":34.17326,"_source":{"id":"203299821","text":"\u51b3\u7b56\u6811\u6a21\u578b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"","tagsname":null,"tagsid":"","catesname":null,"catesid":"","createtime":"1624415959"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"203299823","_score":34.17326,"_source":{"id":"203299823","text":"\u51b3\u7b56\u6811\u6a21\u578b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"","tagsname":null,"tagsid":"","catesname":null,"catesid":"","createtime":"1617200845"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"203299827","_score":34.17326,"_source":{"id":"203299827","text":"\u51b3\u7b56\u6811\u6a21\u578b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"","tagsname":null,"tagsid":"","catesname":null,"catesid":"","createtime":"1627996668"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"203299834","_score":32.750984,"_source":{"id":"203299834","text":"\u6811\u6a21\u578b-\u51b3\u7b56\u6811","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"","tagsname":null,"tagsid":"","catesname":null,"catesid":"","createtime":"1621948333"},"highlight":{"text":["树#em#模#/em##em#型#/em#-#em#决#/em##em#策#/em#树"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"412123","_score":31.442368,"_source":{"id":"412123","text":"\u591a\u5c5e\u6027\u51b3\u7b56\u6a21\u578b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"lilei0128","tagsname":"","tagsid":"","catesname":null,"catesid":"","createtime":"1632982650"},"highlight":{"text":["多属性#em#决#/em##em#策#/em##em#模#/em##em#型#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"203299817","_score":31.442368,"_source":{"id":"203299817","text":"\u51b3\u7b56\u6811\u6a21\u578b\u7406\u89e3","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"","tagsname":null,"tagsid":"","catesname":null,"catesid":"","createtime":"1635631870"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#理解"]}}]}}"
</pre>127.0.0.1:9200<br>URL: http://127.0.0.1:9200/likecs_art_db/_search<br>REQUEST:<pre>Array
(
    [query] => Array
        (
            [match] => Array
                (
                    [text] => Array
                        (
                            [query] => 决策模型(二)：风险决策法
                        )

                )

        )

    [highlight] => Array
        (
            [fields] => Array
                (
                    [text] => stdClass Object
                        (
                        )

                )

            [pre_tags] => #em#
            [post_tags] => #/em#
        )

    [size] => 8
    [from] => 8
)
</pre>RESPONSE:<pre>string(7601) "{"took":21,"timed_out":false,"_shards":{"total":1,"successful":1,"skipped":0,"failed":0},"hits":{"total":{"value":10000,"relation":"gte"},"max_score":55.54028,"hits":[{"_index":"likecs_art_db","_type":"_doc","_id":"203299829","_score":31.442368,"_source":{"id":"203299829","text":"\u51b3\u7b56\u6811\u6a21\u578b\u603b\u7ed3","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"","tagsname":null,"tagsid":"","catesname":null,"catesid":"","createtime":"1630845586"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#总结"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"474159","_score":30.826263,"_source":{"id":"474159","text":"\u98ce\u9669\u5e94\u5bf9\u7b56\u7565","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"nygfcn1234","tagsname":"","tagsid":"","catesname":null,"catesid":"","createtime":"1634217853"},"highlight":{"text":["#em#风#/em##em#险#/em#应对#em#策#/em#略"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"1021962","_score":30.082977,"_source":{"id":"1021962","text":"\u5206\u7c7b\u2014\u2014\u51b3\u7b56\u6811\u6a21\u578b\uff08\u9644\u6709\u51b3\u7b56\u6811\u751f\u6210\u6b65\u9aa4\uff09","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"lgbdbky","tagsname":"","tagsid":"","catesname":"","catesid":"","createtime":"1641357682"},"highlight":{"text":["分类——#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#（附有#em#决#/em##em#策#/em#树生成步骤）"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"786065","_score":29.62156,"_source":{"id":"786065","text":"\u7b2c\u4e03\u7ae0\u3001\u98ce\u9669\u5206\u6790\u4e0e\u51b3\u7b56 - \u6b22\u7b11\u4e00\u58f0","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"wuhuixuri","tagsname":"","tagsid":"","catesname":null,"catesid":"","createtime":"1636848208"},"highlight":{"text":["第七章、#em#风#/em##em#险#/em#分析与#em#决#/em##em#策#/em# - 欢笑一声"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"477493","_score":29.15716,"_source":{"id":"477493","text":"\u6570\u5b66\u5efa\u6a21\u65b9\u6cd5-\u591a\u5c5e\u6027\u51b3\u7b56\u6a21\u578b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"Qling","tagsname":null,"tagsid":"","catesname":"","catesid":"","createtime":"1635804820"},"highlight":{"text":["数学建#em#模#/em#方#em#法#/em#-多属性#em#决#/em##em#策#/em##em#模#/em##em#型#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"331773","_score":29.15716,"_source":{"id":"331773","text":"\u6570\u5b66\u5efa\u6a21\u65b9\u6cd5-\u591a\u5c5e\u6027\u51b3\u7b56\u6a21\u578b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"Qling","tagsname":null,"tagsid":"","catesname":"","catesid":"","createtime":"1633058121"},"highlight":{"text":["数学建#em#模#/em#方#em#法#/em#-多属性#em#决#/em##em#策#/em##em#模#/em##em#型#/em#"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"10035","_score":29.115644,"_source":{"id":"10035","text":"\u51b3\u7b56\u6811\u6a21\u578b\u4e0e\u5b66\u4e60\u300a\u4e00\u300b","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"George1994","tagsname":"","tagsid":"[]","catesname":"Machine Learning","catesid":"[\"99\"]","createtime":"1520736130"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#与学习《一》"]}},{"_index":"likecs_art_db","_type":"_doc","_id":"203253419","_score":29.115644,"_source":{"id":"203253419","text":"\u51b3\u7b56\u6811\u6a21\u578b-\u7406\u8bba\u57fa\u7840","intro":"\u76ee\u5f55\n\nECharts\n\u5f02\u6b65\u52a0\u8f7d\n\n\n\nECharts\r\n\u6570\u636e\u53ef\u89c6\u5316\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u8fdb\u5c55\u3002\u5f00\u53d1\u4eba\u5458\u5bf9\u53ef\u89c6\u5316\u4ea7\u54c1\u7684\u671f\u671b\u4e0d\u518d\u662f\u7b80\u5355\u7684\u56fe\u8868\u521b\u5efa\u5de5\u5177\uff0c\u800c\u662f\u5728\u4ea4\u4e92\u3001\u6027\u80fd\u3001\u6570\u636e\u5904\u7406\u7b49\u65b9\u9762\u6709\u66f4\u9ad8\u7684\u8981\u6c42\u3002\r\nchart.setOption({\r\n    color: [\r\n        ","username":"","tagsname":null,"tagsid":"","catesname":null,"catesid":"","createtime":"1632244229"},"highlight":{"text":["#em#决#/em##em#策#/em#树#em#模#/em##em#型#/em#-理论基础"]}}]}}"
</pre>127.0.0.1:9200<br>URL: http://192.168.101.128/searchcore/index.php/cihere_cn_db/_search<br>REQUEST:<pre>Array
(
    [query] => Array
        (
            [match] => Array
                (
                    [title] => Array
                        (
                            [query] => 决策模型(二)：风险决策法
                        )

                )

        )

    [highlight] => Array
        (
            [fields] => Array
                (
                    [title] => stdClass Object
                        (
                        )

                )

            [pre_tags] => #em#
            [post_tags] => #/em#
        )

    [from] => 0
)
</pre>RESPONSE:<pre>bool(false)
</pre>127.0.0.1:9200<br>URL: http://127.0.0.1:9200/likecs_down_db/_search<br>REQUEST:<pre>Array
(
    [query] => Array
        (
            [bool] => Array
                (
                    [must] => Array
                        (
                            [0] => Array
                                (
                                    [match] => Array
                                        (
                                            [title] => Array
                                                (
                                                    [query] => 决策模型(二)：风险决策法
                                                )

                                        )

                                )

                        )

                    [must_not] => Array
                        (
                            [0] => Array
                                (
                                    [term] => Array
                                        (
                                            [cate1] => 电子书籍
                                        )

                                )

                        )

                )

        )

    [highlight] => Array
        (
            [fields] => Array
                (
                    [title] => stdClass Object
                        (
                        )

                )

            [pre_tags] => #em#
            [post_tags] => #/em#
        )

    [size] => 5
    [from] => 0
)
</pre>RESPONSE:<pre>string(3137) "{"took":7,"timed_out":false,"_shards":{"total":1,"successful":1,"skipped":0,"failed":0},"hits":{"total":{"value":2814,"relation":"eq"},"max_score":24.674414,"hits":[{"_index":"likecs_down_db","_type":"_doc","_id":"40134","_score":24.674414,"_source":{"id":"40134","title":"PHPstat\u7f51\u7ad9\u51b3\u7b56\u652f\u6301\u5206\u6790\u7cfb\u7edf v1.0 \u4fee\u6539\u7248","spidertime":"1623038547","contenttime":"1671192533","tag":"PHPstat|\u7f51\u7ad9|\u51b3\u7b56\u652f\u6301|\u5206\u6790\u7cfb\u7edf|v1.0|\u4fee\u6539\u7248","cate1":"\u6e90\u7801\u4e0b\u8f7d","cate2":"php\u6e90\u7801","cate3":"\u8ba1\u6570\u7edf\u8ba1","attr1":"1.79MB"},"highlight":{"title":["PHPstat网站#em#决#/em##em#策#/em#支持分析系统 v1.0 修改版"]}},{"_index":"likecs_down_db","_type":"_doc","_id":"98306","_score":24.674414,"_source":{"id":"98306","title":"PHPstat\u7f51\u7ad9\u51b3\u7b56\u652f\u6301\u5206\u6790\u7cfb\u7edf v1.0 \u4fee\u6539\u7248","spidertime":"1623216396","contenttime":"1678336501","tag":"PHPstat|\u7f51\u7ad9|\u51b3\u7b56\u652f\u6301|\u5206\u6790\u7cfb\u7edf|v1.0|\u4fee\u6539\u7248","cate1":"\u6e90\u7801\u4e0b\u8f7d","cate2":"php\u6e90\u7801","cate3":"\u8ba1\u6570\u7edf\u8ba1","attr1":"1.79MB"},"highlight":{"title":["PHPstat网站#em#决#/em##em#策#/em#支持分析系统 v1.0 修改版"]}},{"_index":"likecs_down_db","_type":"_doc","_id":"40136","_score":22.169754,"_source":{"id":"40136","title":"PHPstat\u7f51\u7ad9\u51b3\u7b56\u652f\u6301\u5206\u6790\u7cfb\u7edf v1.0 GBK\u7b80\u4f53\u4e2d\u6587\u7248","spidertime":"1623038549","contenttime":"1675848509","tag":"PHPstat|\u7f51\u7ad9|\u51b3\u7b56|\u652f\u6301|\u5206\u6790|\u7cfb\u7edf|v1.0|GBK\u7b80\u4f53\u4e2d\u6587\u7248","cate1":"\u6e90\u7801\u4e0b\u8f7d","cate2":"php\u6e90\u7801","cate3":"\u8ba1\u6570\u7edf\u8ba1","attr1":"1.84MB"},"highlight":{"title":["PHPstat网站#em#决#/em##em#策#/em#支持分析系统 v1.0 GBK简体中文版"]}},{"_index":"likecs_down_db","_type":"_doc","_id":"40137","_score":22.169754,"_source":{"id":"40137","title":"PHPstat\u7f51\u7ad9\u51b3\u7b56\u652f\u6301\u5206\u6790\u7cfb\u7edf v1.0 BIG5\u7e41\u4f53\u4e2d\u6587\u7248","spidertime":"1623038553","contenttime":"1671368954","tag":"PHPstat|\u7f51\u7ad9|\u51b3\u7b56|\u652f\u6301|\u5206\u6790\u7cfb\u7edf|v1.0|BIG5\u7e41\u4f53\u4e2d\u6587\u7248","cate1":"\u6e90\u7801\u4e0b\u8f7d","cate2":"php\u6e90\u7801","cate3":"\u8ba1\u6570\u7edf\u8ba1","attr1":"1.84MB"},"highlight":{"title":["PHPstat网站#em#决#/em##em#策#/em#支持分析系统 v1.0 BIG5繁体中文版"]}},{"_index":"likecs_down_db","_type":"_doc","_id":"98308","_score":22.169754,"_source":{"id":"98308","title":"PHPstat\u7f51\u7ad9\u51b3\u7b56\u652f\u6301\u5206\u6790\u7cfb\u7edf v1.0 GBK\u7b80\u4f53\u4e2d\u6587\u7248","spidertime":"1623216399","contenttime":"1677194773","tag":"PHPstat|\u7f51\u7ad9|\u51b3\u7b56|\u652f\u6301|\u5206\u6790|\u7cfb\u7edf|v1.0|GBK\u7b80\u4f53\u4e2d\u6587\u7248","cate1":"\u6e90\u7801\u4e0b\u8f7d","cate2":"php\u6e90\u7801","cate3":"\u8ba1\u6570\u7edf\u8ba1","attr1":"1.84MB"},"highlight":{"title":["PHPstat网站#em#决#/em##em#策#/em#支持分析系统 v1.0 GBK简体中文版"]}}]}}"
</pre><!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="utf-8" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta http-equiv="content-language" content="zh-CN" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" /> 
    <title>决策模型(二)：风险决策法 - 爱码网</title>
     
<meta name="keywords" content="学习笔记 运筹决策" />
<meta name="description" content="目录ECharts异步加载ECharts
数据可视化在过去几年中取得了巨大进展。开发人员对可视化产品的期望不再是简单的图表创建工具，而是在交互、性能、数据处理等方面有更高的要求。
chart.setOption({
    color: [" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<link rel="stylesheet" type="text/css" href="/statics/css/base.css?v=2.7" />
<script src="/statics/js/detail.min.js?v=2.2"></script>   
<script>
   $(document).ready(function () { 
		$("img").error(function () {
			$(this).hide();
		}); 
	}); 
</script>
</head>
<body class="home-template dtpg">
<nav class="main-nav clearfix">
    <div class="inner">
        <ul class="nav">
            <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/" title="爱码网">首页</a></li>
                        <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/nav/1.html" title="前端技术">前端技术</a></li>
                        <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/nav/9.html" title="编程语言">编程语言</a></li>
                        <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/nav/31.html" title="人工智能">人工智能</a></li>
                        <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/nav/41.html" title="运维知识">运维知识</a></li>
                        <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/nav/52.html" title="资源下载">资源下载</a></li>
                        <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/nav/68.html" title="常用小工具">常用小工具</a></li>
                        <li class="menu-item menu-item-type-custom menu-item-object-custom current-menu-item current_page_item menu-item-home menu-item-886"><a href="/nav/72.html" title="技术问答">技术问答</a></li>
                    </ul>            
	 
    </div>
</nav><div class="site-wrapper">
 
    <header style="height: auto;padding: 10px 0px;" class="main-header">
        <div style="max-width:910px" class="main-header-content inner">
                        <h1 class="page-title"><a href="/show-40699.html" title="决策模型(二)：风险决策法">决策模型(二)：风险决策法</a></h1>
            
        </div>

    </header>
    <main class="content" role="main">
	

        <div class="leftbox">
    <article class="post tag-uifont tag-webview">
        <header class="post-header">
            <footer class="tc"> dmego 
                <time class="post-date" datetime="2018-11-20">2018-11-20</time>
            </footer>
        </header>
        <section class="post-content">
            <div class="contentbef">  
                  
                              </div>

            
                                    
<!--done-->
<div id="topics">
	<div class="post">
		
		
		<div class="postBody">
			<div id="likecs_post_body" class="blogpost-body cnblogs-markdown">
<p><br><br></p>
<center><img src="/default/index/img?u=L2RlZmF1bHQvaW5kZXgvaW1nP3U9YUhSMGNITTZMeTlwYldjeU1ERTRMbU51WW14dlozTXVZMjl0TDJKc2IyY3ZNVEF5TmpnMk5pOHlNREU0TVRFdk1UQXlOamcyTmkweU1ERTRNVEV5TURFM05EWTBOakkyTlMwME1qVXpNVGMwTmpVdWNHNW4=" width="200px"></center>
<p></p>
<h3 id="前言">前言</h3>
<p>风险决策法是指决策者对客观情况不了解，但是对将发生各事件的概率是已知的。决策者往往通过调查，根据过去的经验或主观估计等途径获得这些概率。在风险决策中一般采用期望值作为决策准则，常用的有最大期望收益决策准则（EMV）和最小机会损失决策准则（EOL）。</p>
<p>风险型决策问题一般具有以下特点:</p>
<ul>
<li>决策具有明确目标: 获得最大收益（利润）或最小损失；</li>
<li>存在两个以上可供选择的行动方案</li>
<li>存在两个或两个以上不以决策者主观意志为转移的自然状态，但决策者根据过去的经验，主观估计或科学理论等可预先估算出这些状态出现的概率值；</li>
<li>各行动方案在确定状态下的损益值可以计算出来；</li>
</ul>
<p>下面接着上一篇博文，对文中的例子做风险决策分析，决策矩阵如下：</p>
<table>
<thead><tr class="header">
<th>（策略\事件）</th>
<th>E<sub>1</sub> = 0</th>
<th>E<sub>2</sub> = 10</th>
<th>E<sub>3</sub> = 20</th>
<th>E<sub>4</sub> = 30</th>
<th>E<sub>5</sub> = 40</th>
</tr></thead>
<tbody>
<tr class="odd">
<td><strong>事件概率（p<sub>j</sub>）</strong></td>
<td>0.1</td>
<td>0.2</td>
<td>0.4</td>
<td>0.2</td>
<td>0.1</td>
</tr>
<tr class="even">
<td><strong>S<sub>1</sub> = 0</strong></td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td><strong>S<sub>2</sub> = 10</strong></td>
<td>-10</td>
<td>50</td>
<td>50</td>
<td>50</td>
<td>50</td>
</tr>
<tr class="even">
<td><strong>S<sub>3</sub> = 20</strong></td>
<td>-20</td>
<td>40</td>
<td>100</td>
<td>100</td>
<td>100</td>
</tr>
<tr class="odd">
<td><strong>S<sub>4 </sub>= 30</strong></td>
<td>-30</td>
<td>30</td>
<td>90</td>
<td>150</td>
<td>150</td>
</tr>
<tr class="even">
<td><strong>S<sub>5</sub> = 40</strong></td>
<td>-40</td>
<td>20</td>
<td>80</td>
<td>140</td>
<td>200</td>
</tr>
</tbody>
</table>
<p>(注：记各自然状态发生的概率为<span class="math inline">\(p_j\)</span>，采用第 i 种方案在发生第 j 自然状态下的损益值为 <span class="math inline">\(a_{ij}\)</span>)</p>
<h3 id="最大期望收益决策准则emv">最大期望收益决策准则（EMV）</h3>
<h5 id="定义">定义</h5>
<p>最大期望收益决策，显而易见，就是计算出每个方案期望收益值，然后选取最大期望值对应的方案即为最优方案。</p>
<h5 id="计算步骤">计算步骤</h5>
<p>先根据各事件发生的概率 <span class="math inline">\(p_j\)</span>，求出各个策略的期望收益值。然后从这些期望收益值中选择最大者，它对应的策略为决策应选策略。</p>
<h5 id="计算公式">计算公式</h5>
<blockquote>
<p>S<sup>*</sup><sub>k</sub><span class="math inline">\(\rightarrow\)</span> max <span class="math inline">\(\sum_{j} p_ja_{ij}\)</span></p>
</blockquote>
<h5 id="计算结果">计算结果</h5>
<table>
<thead><tr class="header">
<th>（策略\事件）</th>
<th>E<sub>1</sub> = 0</th>
<th>E<sub>2</sub> = 10</th>
<th>E<sub>3</sub> = 20</th>
<th>E<sub>4</sub> = 30</th>
<th>E<sub>5</sub> = 40</th>
<th>EMV</th>
</tr></thead>
<tbody>
<tr class="odd">
<td><strong>事件概率（p<sub>j</sub>）</strong></td>
<td>0.1</td>
<td>0.2</td>
<td>0.4</td>
<td>0.2</td>
<td>0.1</td>
<td></td>
</tr>
<tr class="even">
<td><strong>S<sub>1</sub> = 0</strong></td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td><strong>S<sub>2</sub> = 10</strong></td>
<td>-10</td>
<td>50</td>
<td>50</td>
<td>50</td>
<td>50</td>
<td>44</td>
</tr>
<tr class="even">
<td><strong>S<sub>3</sub> = 20</strong></td>
<td>-20</td>
<td>40</td>
<td>100</td>
<td>100</td>
<td>100</td>
<td>76</td>
</tr>
<tr class="odd">
<td><strong>S<sub>4 </sub>= 30</strong></td>
<td>-30</td>
<td>30</td>
<td>90</td>
<td>150</td>
<td>150</td>
<td>84 <span class="math inline">\(\longleftarrow\)</span> max</td>
</tr>
<tr class="even">
<td><strong>S<sub>5</sub> = 40</strong></td>
<td>-40</td>
<td>20</td>
<td>80</td>
<td>140</td>
<td>200</td>
<td>80</td>
</tr>
</tbody>
</table>
<p>根据 EMV 决策准则有</p>
<blockquote>
<p>max (0 , 44 , 76, 84, 80) = 84</p>
</blockquote>
<p>对应的决策策略为 S<sub>4</sub>，为决策者选择的策略。</p>
<p>EMV 决策准则适用于一次决策多次重复进行生产的情况，所以它是平均意义下的最大收益。</p>
<h5 id="计算代码">计算代码</h5>
<pre class="java"><code>private static int row = 4; //行
private static int col = 3; //列
private static double t =2; //效用曲率系数

private static double[][] matrix = {//决策矩阵
     //事件     1   2   3
            {0.2,0.5,0.3},  //事件概率
            {140,120, 80},  //策略
            {200,150, 40},  //策略
            {340,140,-20},  //策略
    };

/**
 * 最大期望收益决策准则(EMV)
 * @param matrix
 * @param row
 * @param col
 */
private static void EMV(double[][] matrix, int row, int col){
    double[] maxMar = new double[row+1]; //记录每种行动方案的结果，第一行是自然状态概率
    double max = 0.0; //最优结果
    double temp = 0.0;
    double chance = 0.0; //概率
    int maxIndex = 0; //最优结果下标
    //因为第一行是自然状态概率，所以从第二行开始，实际的行数比 row 多一行
    for (int i = 1; i &lt;= row; i++) {
        for (int j = 0; j &lt; col; j++) {
            chance =  matrix[0][j]; //自然概率
            temp = (j != 0) ? (temp + matrix[i][j]*chance) : (matrix[i][j]*chance);
        }
        maxMar[i] = temp;
        if(i == 1){ // 当 i=1时，为 max 与 maxIndex 赋初值
            max = temp;
            maxIndex = 1;
        }else if(temp &gt; max){
            max = temp;
            maxIndex = i;
        }
    }
    System.out.println(Arrays.toString(maxMar));
    System.out.println(max+"--"+maxIndex);
}</code></pre>
<h3 id="最小机会损失决策准则eol">最小机会损失决策准则（EOL）</h3>
<h5 id="定义-1">定义</h5>
<p>最小机会损失决策与不确定型决策法里的<code>最小机会损失决策准则</code>相类似，都是先将收益矩阵的中各元素变换为机会损失值。将各自然状态下的最大收益值定为理想目标，并将该状态中的其他值与最高值之差称为机会损失值。然后求这些机会损失值的期望损失值，最后从中选取最小的期望损失值，对应的策略即为决策者所选的策略。</p>
<h5 id="计算步骤-1">计算步骤</h5>
<p>首先计算出当发生 j 事件后，各策略的收益最大值</p>
<blockquote>
<p>a<sub>i</sub><sub>j</sub> = max ( a<sub>i</sub><sub>j</sub> )</p>
</blockquote>
<p>这时各策略的机会损失值为</p>
<blockquote>
<p><span class="math inline">\(a'_{ij}\)</span> = { max ( a<sub>i</sub><sub>j</sub> ) - a<sub>i</sub><sub>j</sub> }</p>
</blockquote>
<p>然后求这些机会损失值的期望损失值，最后从中选取最小的期望损失值</p>
<blockquote>
<p>min <span class="math inline">\(\sum_{j} p_ja'_{ij}\)</span></p>
</blockquote>
<h5 id="计算公式-1">计算公式</h5>
<blockquote>
<p>S<sup>*</sup><sub>k</sub><span class="math inline">\(\rightarrow\)</span> min <span class="math inline">\(\sum_{j} p_ja'_{ij}\)</span></p>
</blockquote>
<h5 id="计算结果-1">计算结果</h5>
<table>
<thead><tr class="header">
<th>（策略\事件）</th>
<th>E<sub>1</sub> = 0</th>
<th>E<sub>2</sub> = 10</th>
<th>E<sub>3</sub> = 20</th>
<th>E<sub>4</sub> = 30</th>
<th>E<sub>5</sub> = 40</th>
<th>EOL</th>
</tr></thead>
<tbody>
<tr class="odd">
<td><strong>事件概率（p<sub>j</sub>）</strong></td>
<td>0.1</td>
<td>0.2</td>
<td>0.4</td>
<td>0.2</td>
<td>0.1</td>
<td></td>
</tr>
<tr class="even">
<td><strong>S<sub>1</sub> = 0</strong></td>
<td>0</td>
<td>50</td>
<td>100</td>
<td>150</td>
<td>200</td>
<td>100</td>
</tr>
<tr class="odd">
<td><strong>S<sub>2</sub> = 10</strong></td>
<td>10</td>
<td>0</td>
<td>50</td>
<td>100</td>
<td>150</td>
<td>56</td>
</tr>
<tr class="even">
<td><strong>S<sub>3</sub> = 20</strong></td>
<td>20</td>
<td>10</td>
<td>0</td>
<td>50</td>
<td>100</td>
<td>24</td>
</tr>
<tr class="odd">
<td><strong>S<sub>4 </sub>= 30</strong></td>
<td>30</td>
<td>20</td>
<td>10</td>
<td>0</td>
<td>50</td>
<td>16 <span class="math inline">\(\longleftarrow\)</span> max</td>
</tr>
<tr class="even">
<td><strong>S<sub>5</sub> = 40</strong></td>
<td>40</td>
<td>30</td>
<td>20</td>
<td>10</td>
<td>0</td>
<td>20</td>
</tr>
</tbody>
</table>
<p>根据 EOL 决策准则有</p>
<blockquote>
<p>min (100, 56 , 24, 16, 20) = 16</p>
</blockquote>
<p>对应的决策策略为 S<sub>4</sub>，为决策者选择的策略。</p>
<p>从本质上讲 EMV 与 EOL 决策准则是一样的。所以决策时这两个决策结果是一样的。</p>
<h5 id="计算代码-1">计算代码</h5>
<pre class="java"><code>/**
 * 最小机会损失决策准则(EOL)
 * @param matrix
 * @param row
 * @param col
 */
private static void EOL(double[][] matrix, int row, int col){
    //先求损失矩阵
    double[][] loss = new double[row+1][col];
    for (int j = 0; j &lt; col; j++) {
        loss[0][j] = matrix[0][j]; //将自然概率复制到损失矩阵的第一行中
        double max = matrix[1][j]; //先定每一列的第一个最大
        for (int i = 1; i &lt;= row; i++) {
            if(matrix[i][j] &gt; max){
                max = matrix[i][j];
            }
        }
        //此时已经求出该列的最大值
        //损失矩阵中对应位置的值 = 决策矩阵中列最大值 - 决策矩阵中对应位置值
        for (int i = 1; i &lt;= row; i++) {
            loss[i][j] = max - matrix[i][j];
        }
    }

    //然后再求 EOL 决策
    double[] maxMar = new double[row+1];
    double min = 0.0;
    double temp = 0.0;
    int minIndex = 0;
    double chance = 0.0;
    for (int i = 1; i &lt;= row; i++) {
        for (int j = 0; j &lt; col; j++) {
            chance =  loss[0][j]; //自然概率
            temp = (j != 0) ? (temp + loss[i][j]*chance) : (loss[i][j]*chance);
        }
        maxMar[i] = temp;
        if(i == 1){
            min = temp;
            minIndex = 1;
        } else if(temp &lt; min){
            min = temp;
            minIndex = i;
        }
    }
    
    System.out.println(Arrays.toString(maxMar));
    System.out.println(min+"--"+minIndex);
}</code></pre>
<h3 id="全情报的价值evpi">全情报的价值（EVPI）</h3>
<h5 id="定义-2">定义</h5>
<p>当决策者耗费了一定经费进行调研，获得了各事件发生概率的信息，应采用 ”随机应变“ 的战术，这时所得的期望收益称为全情报的期望收益，记做 EPPI，这个收益应当大于至少等于最大期望收益，即 EPPI &gt;= max（EMV），则有EVPI = EPPL - max(EMV)，EVPI 称为全情报的价值，这就说明获得情报的费用不能超过 EVPI 值，否则就没有增加收入。</p>
<h5 id="计算步骤-2">计算步骤</h5>
<p>先进行 EMV 决策法计算，求得最大期望收益值</p>
<blockquote>
<p>max <span class="math inline">\(\sum_{j} p_ja_{ij}\)</span></p>
</blockquote>
<p>然后求全情报期望收益，先得求收益矩阵中每行的最大值然后求期望，最后将每行最大值的期望相加，得到全情报期望收益。</p>
<blockquote>
<p><span class="math inline">\(\sum_{j} p_jmax(a_{i})\)</span> ; <span class="math inline">\(max(a_{i})\)</span> 是 i 行的最大值</p>
</blockquote>
<p>全情报期望收益减去最大期望收益即为全情报价值 EVPI</p>
<blockquote>
<p>EVPI = <span class="math inline">\(\sum_{j} p_jmax(a_{i})\)</span> - max <span class="math inline">\(\sum_{j} p_ja_{ij}\)</span></p>
</blockquote>
<h5 id="计算公式-2">计算公式</h5>
<blockquote>
<p>EVPI = <span class="math inline">\(\sum_{j} p_jmax(a_{i})\)</span> - max <span class="math inline">\(\sum_{j} p_ja_{ij}\)</span></p>
</blockquote>
<h5 id="计算结果-2">计算结果</h5>
<table>
<thead><tr class="header">
<th>（策略\事件）</th>
<th>E<sub>1</sub> = 0</th>
<th>E<sub>2</sub> = 10</th>
<th>E<sub>3</sub> = 20</th>
<th>E<sub>4</sub> = 30</th>
<th>E<sub>5</sub> = 40</th>
<th>EMV</th>
<th>期望收益</th>
<th>EVPI</th>
</tr></thead>
<tbody>
<tr class="odd">
<td><strong>事件概率（p<sub>j</sub>）</strong></td>
<td>0.1</td>
<td>0.2</td>
<td>0.4</td>
<td>0.2</td>
<td>0.1</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>S<sub>1</sub> = 0</strong></td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><strong>S<sub>2</sub> = 10</strong></td>
<td>-10</td>
<td>50</td>
<td>50</td>
<td>50</td>
<td>50</td>
<td>44</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>S<sub>3</sub> = 20</strong></td>
<td>-20</td>
<td>40</td>
<td>100</td>
<td>100</td>
<td>100</td>
<td>76</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><strong>S<sub>4 </sub>= 30</strong></td>
<td>-30</td>
<td>30</td>
<td>90</td>
<td>150</td>
<td>150</td>
<td>84 <span class="math inline">\(\longleftarrow\)</span> max</td>
<td>100</td>
<td>16</td>
</tr>
<tr class="even">
<td><strong>S<sub>5</sub> = 40</strong></td>
<td>-40</td>
<td>20</td>
<td>80</td>
<td>140</td>
<td>200</td>
<td>80</td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p>根据 EMV 决策准则有</p>
<blockquote>
<p>max (0, 44, 76 , 84, 80) = 84</p>
</blockquote>
<p>得到最大的期望收益值为 84 , 再求得全情报期望收益 = 100 ,最后可得全情报价值EVPI = 16, 对应的决策策略为 S<sub>4</sub>，为决策者选择的策略。</p>
<h5 id="计算代码-2">计算代码</h5>
<pre class="java"><code> /**
  * 全情报价值(EVPI)
  * @param matrix
  * @param row
  * @param col
  */
private static void EVPI(double[][] matrix, int row, int col){
    double[] maxMar = new double[row+1]; //记录每种行动方案的结果，第一行是自然状态概率
    double max = 0.0; //最优结果
    double temp = 0.0;
    double chance = 0.0; //概率
    int maxIndex = 0; //最优结果下标
    //因为第一行是自然状态概率，所以从第二行开始，实际的行数比 row 多一行
    for (int i = 1; i &lt;= row; i++) {
        for (int j = 0; j &lt; col; j++) {
            chance =  matrix[0][j]; //自然概率
            temp = (j != 0) ? (temp + matrix[i][j]*chance) : (matrix[i][j]*chance);
        }
        maxMar[i] = temp;
        if(i == 1){ // 当 i=1时，为 max 与 maxIndex 赋初值
            max = temp;
            maxIndex = 1;
        }else if(temp &gt; max){
            max = temp;
            maxIndex = i;
        }
    }

    double rowMax = 0.0;
    double expect = 0.0;
    double chance = 0.0;
    double value = 0.0;

    //计算全情报价值收益
    for (int i = 0; i &lt; col; i++) {
        chance =  matrix[0][i]; //自然概率
        for (int j = 1; j &lt;= row; j++) {
            if(j == 1){ //初始化第一行第一个为该行最大的收益值
                rowMax = matrix[j][i];
            }else if (matrix[j][i] &gt; rowMax){
                rowMax = matrix[j][i];
            }
        }
        expect += rowMax * chance;
    }
    
    except = new BigDecimal(expect).setScale(2, BigDecimal.ROUND_HALF_UP).doubleValue();
    value = new BigDecimal(expect - max).setScale(2, BigDecimal.ROUND_HALF_UP).doubleValue();
    
    System.out.println("全情报期望收益:"+except);
    System.out.println("全情报价值EVPI:"+value);
}
</code></pre>
<h3 id="效用曲线拟合euv">效用曲线拟合（EUV）</h3>
<h5 id="定义-3">定义</h5>
<p>效用概念首先是由贝努里提出的,他认为人们对其钱财的真实价值的考虑与他的钱财拥有量有对数关系。经济管理学家将效用作为指标，用它来衡量人们对某些事物的主观价值，态度，偏爱，倾向等。例如在风险情况下进行决策，决策者对风险的态度是不同的，用效用指标来量化决策者对待风险的态度，可以给每一个决策者测定他对待风险的态度的效用曲线函数。这里还有一个概率是效用曲线系数，效用曲线系数的取值范围为（0,∞）。</p>
<p><img src="/default/index/img?u=L2RlZmF1bHQvaW5kZXgvaW1nP3U9YUhSMGNITTZMeTlwYldjeU1ERTRMbU51WW14dlozTXVZMjl0TDJKc2IyY3ZNVEF5TmpnMk5pOHlNREU0TVRFdk1UQXlOamcyTmkweU1ERTRNVEV5TURFM05EY3pOVFkwTVMweE5ERTRNemN3TlRZMExuQnVadz09" alt="效用曲线函数"></p>
<h5 id="计算步骤-3">计算步骤</h5>
<p>先建立效用曲线函数，将矩阵中的收益值装化为效用值，其中 t 为效用曲线系数，b=max{x1,x2,x3,⋯,xn} ，a=min{x1,x2,x3,⋯,xn}) ；</p>
<blockquote>
<p>U(x) = <span class="math inline">\(\left\{\begin{matrix} &amp;0, &amp; x\leq a &amp; \\ &amp;(\frac{x-a}{b-a})^t, &amp; a\leq x\leq b \\ &amp;1, &amp;x\geq b \end{matrix}\right.\)</span></p>
</blockquote>
<p>然后计算期望效用值,结果为期望效用的最大值</p>
<blockquote>
<p>EUV<sub>i</sub> = <span class="math inline">\(\sum_{j} p_ju_{ij}\)</span></p>
</blockquote>
<h5 id="计算公式-3">计算公式</h5>
<blockquote>
<p>S<sup>*</sup><sub>k</sub><span class="math inline">\(\rightarrow\)</span> max <span class="math inline">\(\sum_{j} p_ju_{ij}\)</span></p>
</blockquote>
<h5 id="计算结果-3">计算结果</h5>
<table>
<thead><tr class="header">
<th>（策略\事件）</th>
<th>E<sub>1</sub> = 0</th>
<th>E<sub>2</sub> = 10</th>
<th>E<sub>3</sub> = 20</th>
<th>E<sub>4</sub> = 30</th>
<th>E<sub>5</sub> = 40</th>
<th>EUV（t=2）</th>
</tr></thead>
<tbody>
<tr class="odd">
<td><strong>事件概率（p<sub>j</sub>）</strong></td>
<td>0.1</td>
<td>0.2</td>
<td>0.4</td>
<td>0.2</td>
<td>0.1</td>
<td></td>
</tr>
<tr class="even">
<td><strong>S<sub>1</sub> = 0</strong></td>
<td>0.03</td>
<td>0.03</td>
<td>0.03</td>
<td>0.03</td>
<td>0.03</td>
<td>0.03</td>
</tr>
<tr class="odd">
<td><strong>S<sub>2</sub> = 10</strong></td>
<td>0.02</td>
<td>0.14</td>
<td>0.14</td>
<td>0.14</td>
<td>0.14</td>
<td>0.128</td>
</tr>
<tr class="even">
<td><strong>S<sub>3</sub> = 20</strong></td>
<td>0.01</td>
<td>0.11</td>
<td>0.34</td>
<td>0.34</td>
<td>0.34</td>
<td>0.261</td>
</tr>
<tr class="odd">
<td><strong>S<sub>4 </sub>= 30</strong></td>
<td>0.0</td>
<td>0.09</td>
<td>0.29</td>
<td>0.63</td>
<td>0.63</td>
<td>0.323</td>
</tr>
<tr class="even">
<td><strong>S<sub>5</sub> = 40</strong></td>
<td>0.0</td>
<td>0.06</td>
<td>0.25</td>
<td>0.56</td>
<td>1.0</td>
<td>0.324 <span class="math inline">\(\longleftarrow\)</span> max</td>
</tr>
</tbody>
</table>
<p>根据 EUV决策准则有</p>
<blockquote>
<p>max (0.03, 0.128 , 0.261, 0.323, 0.324) = 0.324</p>
</blockquote>
<p>对应的决策策略为 S<sub>5</sub>，为决策者选择的策略。</p>
<h5 id="计算代码-3">计算代码</h5>
<pre class="java"><code>/**
 * 效用曲线拟合(EUV)
 * @param matrix
 * @param row
 * @param col
 */
private static void EUV(double[][] matrix, double a, int row, int col){
    //先求出收益矩阵中的最大值与最小值
    double min = matrix[1][0];
    double max = matrix[1][0];
    for (int i = 2; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
            if(matrix[i][j] &gt; max){
                max = matrix[i][j];
            }
            if(matrix[i][j] &lt; min){
                min = matrix[i][j];
            }
        }
    }
    System.out.println("min="+min+"max="+max);
    //然后求出效用值矩阵
    /*计算方法
           小于最小值(a) =&gt; 0
           大于最大值(b) =&gt; 1
           介于之间=&gt; (x-a/b-a)^t,其中t为效用曲线系数
         */
    double[][] avail = new double[row+1][col];
        for (int i = 1; i &lt;= row; i++) {
            for (int j = 0; j &lt; col; j++) {
                avail[0][j] = matrix[0][j]; //将自然状态概率复制到第一行中
                if(matrix[i][j] &lt;= min){
                    avail[i][j] = 0.0;
                }else if(matrix[i][j] &gt;= max){
                    avail[i][j] = 1.0;
                }else {
                    double pow = Math.pow((matrix[i][j] - min) / (max - min), t);
                    avail[i][j] = new BigDecimal(pow).setScale(2, BigDecimal.ROUND_HALF_UP).doubleValue();
                }
            }
        }

    for (int i = 0; i &lt; row; i++) {
        System.out.println(Arrays.toString(avail[i]));
    }

    //再求期望效用值
     double[] maxMar = new double[row+1];
        double availMax = 0.0; //效用期望最大值
        int maxIndex = 0;
        double temp = 0.0;
        double chance = 0.0;
        for (int i = 1; i &lt;= row; i++) {
            for (int j = 0; j &lt; col; j++) {
                chance =  avail[0][j]; //自然概率
                temp = (j != 0) ? (temp + avail[i][j]*chance) : (avail[i][j]*chance);
            }
            double value =new BigDecimal(temp).setScale(3, BigDecimal.ROUND_HALF_UP).doubleValue();
            maxMar[i] = value;
            if(i == 1){
                availMax = value;
                maxIndex = 1;
            } else if(value &gt; availMax){
                availMax = value;
                maxIndex = i;
            }
        }
    System.out.println(Arrays.toString(maxMar));
    System.out.println(availMax+"--"+maxIndex);

}</code></pre>
<h3 id="总结">总结</h3>
<p>至此，决策模型模块的所有算法模型都分析，建立并实现完成。</p>
<h3 id="参考">参考</h3>
<ul>
<li><a href="http://www.tup.tsinghua.edu.cn/booksCenter/book_04835901.html" rel="nofollow" target="_blank">运筹学（第4版）本科版</a></li>
</ul>
</div>




		</div>
		
	</div>
	</div>
<!--end: topics 文章、评论容器-->
 
                    
            
                <div style="margin-top: 10px;">
                  </div> 
        </section>
	 
        <footer class="post-footer">
            <section class="author">
                                <p>分类：</p> 
                                <a class="cateclass" href="/default/index/cates?cid=5653&cname=%E8%BF%90%E7%AD%B9%E5%86%B3%E7%AD%96" title="运筹决策">运筹决策</a>
                                                                <p>技术点：</p>
                                <a class="cateclass" href="/default/index/tags?cid=463&cname=%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0" title="学习笔记">学习笔记</a>
                                            </section>
        </footer>
        <p class="mt10">相关文章：</p>
        <div style="width: 100%;" class="contentcard">
      
            <div style="width: 100%;height: auto;" class="carditem litem clearfix"> 
                    <ul style="padding-left: 0rem;" class="cardcont">
                                                    <li>
                                <a  title="决策树模型总结" href='/show-203299829.html' target="_blank"></a> 
                                <span>2021-09-05</span>
                            </li>
                                                        <li>
                                <a  title="风险应对策略" href='/show-474159.html' target="_blank"></a> 
                                <span>2021-10-14</span>
                            </li>
                                                        <li>
                                <a  title="分类——决策树模型（附有决策树生成步骤）" href='/show-1021962.html' target="_blank"></a> 
                                <span>2022-01-05</span>
                            </li>
                                                        <li>
                                <a  title="第七章、风险分析与决策 - 欢笑一声" href='/show-786065.html' target="_blank"></a> 
                                <span>2021-11-14</span>
                            </li>
                                                        <li>
                                <a  title="数学建模方法-多属性决策模型" href='/show-477493.html' target="_blank"></a> 
                                <span>2021-11-02</span>
                            </li>
                                                        <li>
                                <a  title="决策树模型与学习《一》" href='/show-10035.html' target="_blank"></a> 
                                <span>2018-03-11</span>
                            </li>
                                                        <li>
                                <a  title="决策树模型-理论基础" href='/show-203253419.html' target="_blank"></a> 
                                <span>2021-09-22</span>
                            </li>
                                                </ul>
               </div>   
         </div>
    </article>

  

</div>

<div class="rigthbox contentcard mt10">
 
          <div style="height: auto;" class="carditem litem">
    <div class="cardtit">猜你喜欢 </div>
        <ul class="cardcont">
                                 <li>
                    <a title="决策树模型" href="/show-164997.html" target="_blank"></a> 
                    <span>2021-08-01</span>
                </li>
                                     <li>
                    <a title="树模型-决策树" href="/show-203299834.html" target="_blank"></a> 
                    <span>2021-05-25</span>
                </li>
                                     <li>
                    <a title="多属性决策模型" href="/show-412123.html" target="_blank"></a> 
                    <span>2021-09-30</span>
                </li>
                                     <li>
                    <a title="决策树模型理解" href="/show-203299817.html" target="_blank"></a> 
                    <span>2021-10-31</span>
                </li>
                            </ul>
   </div> 

<div style="height: auto;" class="carditem litem">
    <div class="cardtit">相关资源 </div>
        <ul class="cardcont">
              
                                         <li>
                        <a title="PHPstat网站决策支持分析系统 v1.0 修改版下载" href="/down-40134.html" target="_blank">下载</a> 
                        <span>2022-12-16</span>
                    </li>
                                             <li>
                        <a title="PHPstat网站决策支持分析系统 v1.0 GBK简体中文版下载" href="/down-40136.html" target="_blank">下载</a> 
                        <span>2023-02-08</span>
                    </li>
                                             <li>
                        <a title="PHPstat网站决策支持分析系统 v1.0 BIG5繁体中文版下载" href="/down-40137.html" target="_blank">下载</a> 
                        <span>2022-12-18</span>
                    </li>
                                </ul>
   </div>
   
    <div style="height: auto;" class="carditem litem">
     <div class="cardtit">相似解决方案 </div>
         <ul class="cardcont">
                          </ul>
    </div>
  
   <div style="height: auto;background-color: #ddd;text-align: center;" class="carditem litem">
    <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-5446233687289962" data-ad-slot="2607637140"  data-ad-format="auto"  data-full-width-responsive="true"></ins><script>(adsbygoogle = window.adsbygoogle || []).push({});</script>
</div> 
   <div  style="height: auto;" class="carditem litem mt20">
    <div class="cardtit">热门标签  </div>
    <div class="tagbox">
                    <a target="_blank" title="Java" href="/default/index/tags?cid=164&cname=Java" >Java</a>
                        <a target="_blank" title="Python" href="/default/index/tags?cid=367&cname=Python" >Python</a>
                        <a target="_blank" title="linux" href="/default/index/tags?cid=274&cname=linux" >linux</a>
                        <a target="_blank" title="javascript" href="/default/index/tags?cid=169&cname=javascript" >javascript</a>
                        <a target="_blank" title="Mysql" href="/default/index/tags?cid=237&cname=Mysql" >Mysql</a>
                        <a target="_blank" title="C#" href="/default/index/tags?cid=187&cname=C%23" >C#</a>
                        <a target="_blank" title="Docker" href="/default/index/tags?cid=243&cname=Docker" >Docker</a>
                        <a target="_blank" title="算法" href="/default/index/tags?cid=344&cname=%E7%AE%97%E6%B3%95" >算法</a>
                        <a target="_blank" title="前端" href="/default/index/tags?cid=160&cname=%E5%89%8D%E7%AB%AF" >前端</a>
                        <a target="_blank" title="SpringBoot" href="/default/index/tags?cid=168&cname=SpringBoot" >SpringBoot</a>
                        <a target="_blank" title="Redis" href="/default/index/tags?cid=227&cname=Redis" >Redis</a>
                        <a target="_blank" title="Vue" href="/default/index/tags?cid=236&cname=Vue" >Vue</a>
                        <a target="_blank" title="spring" href="/default/index/tags?cid=696&cname=spring" >spring</a>
                        <a target="_blank" title="设计模式" href="/default/index/tags?cid=632&cname=%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F" >设计模式</a>
                        <a target="_blank" title=".net core" href="/default/index/tags?cid=381&cname=.net+core" >.net core</a>
                        <a target="_blank" title=".net" href="/default/index/tags?cid=300&cname=.net" >.net</a>
                        <a target="_blank" title="kubernetes" href="/default/index/tags?cid=2179&cname=kubernetes" >kubernetes</a>
                        <a target="_blank" title="c++" href="/default/index/tags?cid=312&cname=c%2B%2B" >c++</a>
                        <a target="_blank" title="数据库" href="/default/index/tags?cid=284&cname=%E6%95%B0%E6%8D%AE%E5%BA%93" >数据库</a>
                        <a target="_blank" title="数据结构" href="/default/index/tags?cid=247&cname=%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84" >数据结构</a>
                        <a target="_blank" title="大数据" href="/default/index/tags?cid=888&cname=%E5%A4%A7%E6%95%B0%E6%8D%AE" >大数据</a>
                        <a target="_blank" title="js" href="/default/index/tags?cid=159&cname=js" >js</a>
                        <a target="_blank" title="机器学习" href="/default/index/tags?cid=171&cname=%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" >机器学习</a>
                        <a target="_blank" title="微服务" href="/default/index/tags?cid=832&cname=%E5%BE%AE%E6%9C%8D%E5%8A%A1" >微服务</a>
                        <a target="_blank" title="Android" href="/default/index/tags?cid=282&cname=Android" >Android</a>
                        <a target="_blank" title="Go" href="/default/index/tags?cid=839&cname=Go" >Go</a>
                        <a target="_blank" title="程序员" href="/default/index/tags?cid=327&cname=%E7%A8%8B%E5%BA%8F%E5%91%98" >程序员</a>
                        <a target="_blank" title="面试" href="/default/index/tags?cid=637&cname=%E9%9D%A2%E8%AF%95" >面试</a>
                        <a target="_blank" title="JVM" href="/default/index/tags?cid=727&cname=JVM" >JVM</a>
                        <a target="_blank" title="ASP.net core" href="/default/index/tags?cid=179&cname=ASP.net+core" >ASP.net core</a>
                        <a target="_blank" title="云原生" href="/default/index/tags?cid=22056&cname=%E4%BA%91%E5%8E%9F%E7%94%9F" >云原生</a>
                        <a target="_blank" title="人工智能" href="/default/index/tags?cid=270&cname=%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD" >人工智能</a>
                        <a target="_blank" title="后端" href="/default/index/tags?cid=1089&cname=%E5%90%8E%E7%AB%AF" >后端</a>
                        <a target="_blank" title="PHP" href="/default/index/tags?cid=281&cname=PHP" >PHP</a>
                        <a target="_blank" title="git" href="/default/index/tags?cid=226&cname=git" >git</a>
                        <a target="_blank" title="CSS" href="/default/index/tags?cid=817&cname=CSS" >CSS</a>
                        <a target="_blank" title="golang" href="/default/index/tags?cid=409&cname=golang" >golang</a>
                        <a target="_blank" title="k8s" href="/default/index/tags?cid=5067&cname=k8s" >k8s</a>
                        <a target="_blank" title="Nginx" href="/default/index/tags?cid=373&cname=Nginx" >Nginx</a>
                        <a target="_blank" title="Django" href="/default/index/tags?cid=634&cname=Django" >Django</a>
                        <a target="_blank" title="mybatis" href="/default/index/tags?cid=720&cname=mybatis" >mybatis</a>
                        <a target="_blank" title="深度学习" href="/default/index/tags?cid=345&cname=%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0" >深度学习</a>
                        <a target="_blank" title="多线程" href="/default/index/tags?cid=986&cname=%E5%A4%9A%E7%BA%BF%E7%A8%8B" >多线程</a>
                        <a target="_blank" title="React" href="/default/index/tags?cid=560&cname=React" >React</a>
                        <a target="_blank" title="架构" href="/default/index/tags?cid=2070&cname=%E6%9E%B6%E6%9E%84" >架构</a>
                        <a target="_blank" title="devops" href="/default/index/tags?cid=2662&cname=devops" >devops</a>
                        <a target="_blank" title="爬虫" href="/default/index/tags?cid=905&cname=%E7%88%AC%E8%99%AB" >爬虫</a>
                        <a target="_blank" title="云计算" href="/default/index/tags?cid=361&cname=%E4%BA%91%E8%AE%A1%E7%AE%97" >云计算</a>
                        <a target="_blank" title="Spring Boot" href="/default/index/tags?cid=201&cname=Spring+Boot" >Spring Boot</a>
                        <a target="_blank" title="LeetCode" href="/default/index/tags?cid=342&cname=LeetCode" >LeetCode</a>
                </div>
       
   </div>
   
        <div id="rightadbox" style="height: 300px;background-color: #ddd;text-align: center;" class="carditem litem">
            <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-5446233687289962" data-ad-slot="2607637140"  data-ad-format="auto"  data-full-width-responsive="true"></ins><script>(adsbygoogle = window.adsbygoogle || []).push({});</script>
        </div> 
</div>
<div class="clearfix"></div>
</main>
    
<div class="yllinks alink"></div>
 

<footer class="site-footer clearfix">
<section class="copyright">By &copy; 2026 <a href="/" title="www.likecs.com">likecs</a> 版权所有,<br/>本站所有数据收集于网络如有侵犯到您的权益请联系 进行下架处理1。 </section>
<section class="poweredby">  <a target="_blank" href="https://beian.miit.gov.cn/">粤ICP备22038628号</a>Powered By  WordPress </section>
<script charset="UTF-8" id="LA_COLLECT" src="//sdk.51.la/js-sdk-pro.min.js"></script>
<script>LA.init({id: "Je3PjbvUssp6BbvY",ck: "Je3PjbvUssp6BbvY"})</script>
<script>
var _hmt = _hmt || [];
(function() {
  var hm = document.createElement("script");
  hm.src = "https://hm.baidu.com/hm.js?2eb031e42d29b7c1a1f16948d2ae2a9f";
  var s = document.getElementsByTagName("script")[0]; 
  s.parentNode.insertBefore(hm, s);
})();
</script>
</footer>  
</div>
<script>
    $(function(){
                    $(".post-content").append('<p style="padding: 20px;color: #cacaca;">原文链接：https://www.cnblogs.com/dmego/p/9990414.html</p>')  
            }) 
</script> 
</body>
</html>