第6期 曾婷，等：相似度三支决策模糊粗糙集模型的决策代价研究 ·1077· 与三支决策的决策代价联系在一起，通过对隶属 2014,279:702-715 频率拟合的过程，得到不同决策动作在不同属性 [12]杨霁琳，张贤勇，唐孝，等.基于最优相似度三支决策的 下的决策代价，再计算其欧氏距离，得到不同决 模糊粗糙集模型).计算机科学，2018,45(10小：27-32. 策动作的决策代价，代入文献[12]得到的阈值对 YANG Jilin,ZHANG Xianyong,TANG Xiao,et al. 表达式来计算（α，）。本文只是在基于相似度的 Fuzzy rough set model based on three-way decisions of 三支决策模糊粗糙集模型中讨论决策代价，还有 optimal similar degrees[J].Computer science,2018, 许多其他的模糊粗糙集模型中的决策代价有待 45(10:27-32. 研究。 [13]衷锦仪，叶东毅.基于模糊数风险最小化的拓展决策粗 糙集模型[U.计算机科学，2014,41(3)：50-54 参考文献： ZHONG Jinyi,YE Dongyi.Extended decision-theoretic [1]DUBOIS D.PRADE H.Rough fuzzy sets and fuzzy rough rough set models based on fuzzy minimum cost[J].Com- sets[J].International journal of general systems,1990. puter science,2014,41(3):50-54 17(2/3):191-209 [14]ZHAO Xuerong,HU Baoqing.Three-way decisions with [2]DUBOIS D.PRADE H.Putting rough sets and fuzzy sets decision-theoretic rough sets in multiset-valued informa- together[M]//SLOWINSKI R.Intelligent Decision Sup- tion tables[J].Information sciences,2020,507:684-699. port:Handbook of Applications and Advances of the [15]LIANG Decui,LIU Dun,PEDRYCZ W,et al.Triangular Rough Sets Theory.Dordrecht:Springer,1992:203-222. fuzzy decision-theoretic rough sets[J].International journ- [3]SUN Bingzhen,MA Weimin,ZHAO Haiyan.Decision- al of approximate reasoning,2013,54(8):1087-1106. theoretic rough fuzzy set model and application[J].Inform- [16]LIU Xinwang.Measuring the satisfaction of constraints in ation sciences,2014,283:180-196. fuzzy linear programming[J].Fuzzy sets and systems, [4]YAO YY,WONG S K M.A decision theoretic frame- 2001,122(2):263-275. work for approximating concepts[].International journal [17]YAO Yiyu,ZHAO Yan.Attribute reduction in decision- of man-machine studies,1992,37(6):793-809. theoretic rough set models[J].Information sciences,2008. [5]ZHAO Xuerong,HU Baoqing.Fuzzy and interval-valued 178(17):3356-3373. fuzzy decision-theoretic rough set approaches based on [18]LI Wentao,XU Weihua.Double-quantitative decision- fuzzy probability measure[J].Information sciences,2015, theoretic rough set[J].Information sciences,2015,316 298:534-554 54-67. [6]YAO Yiyu.An outline of a theory of three-way [19]QIAN Yuhua,ZHANG Hu,SANG Yanli,et al.Multi- decision[C]//Proceedings of the International Conference granulation decision-theoretic rough sets[J].International on Rough Sets and Current Trends in Computing.Berlin, journal of approximate reasoning,2014,55(1):225-237. Heidelberg,Germany,2012:1-17. [20]ZHANG Hongying,YANG Shuyun,MA Jianmin.Rank- [LIANG Decui,LIU Dun.Systematic studies on three-way ing interval sets based on inclusion measures and applica- decisions with interval-valued decision-theoretic rough tions to three-way decisions[J].Knowledge-based sys- sets[J].Information sciences,2014,276:186-203. tems,2016,91:62-70. [8]LIANG Decui,XU Zeshui,LIU Dun.Three-way decisions [21]LI Weiwei,HUANG Zhiqiu,JIA Xiuyi,et al.Neighbor- based on decision-theoretic rough sets with dual hesitant hood based decision-theoretic rough set models[J].Inter- fuzzy information[J].Information sciences,2017,396: national journal of approximate reasoning,2016,69 127-143. 1-17. [9]LIANG Decui,XU Zeshui,LIU Dun.Three-way decisions [22]邢航.基于构造性覆盖算法的三支决策模型D].合肥 with intuitionistic fuzzy decision-theoretic rough sets based 安徽大学，2014 on point operators[J].Information sciences,2017,375: XING Hang.Three-way decisions model based on con- 183-201. structive covering algorithm[D].Hefei:Anhui University. [10]FENG Tao,MI Jusheng.Variable precision multigranula- 2014. tion decision-theoretic fuzzy rough sets[J].Knowledge- [23]徐健锋，何宇凡，刘斓.三支决策代价目标函数的关系 based systems,2016,91:93-101. 及推理研究U.计算机科学，2018.45(6)：176-182 [11]DENG Xiaofei,YAO Yiyu.Decision-theoretic three-way XU Jianfeng,HE Yufan,LIU Lan.Relationship and reas- approximations of fuzzy sets[J].Information sciences oning study for three-way decision cost objective func-(α, β) 与三支决策的决策代价联系在一起，通过对隶属 频率拟合的过程，得到不同决策动作在不同属性 下的决策代价，再计算其欧氏距离，得到不同决 策动作的决策代价，代入文献 [12] 得到的阈值对 表达式来计算 。本文只是在基于相似度的 三支决策模糊粗糙集模型中讨论决策代价，还有 许多其他的模糊粗糙集模型中的决策代价有待 研究。 参考文献： DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough sets[J]. International journal of general systems, 1990, 17(2/3): 191–209. [1] DUBOIS D, PRADE H. Putting rough sets and fuzzy sets together[M]//SŁOWIŃSKI R. Intelligent Decision Sup￾port: Handbook of Applications and Advances of the Rough Sets Theory. Dordrecht: Springer, 1992: 203−222. [2] SUN Bingzhen, MA Weimin, ZHAO Haiyan. Decision￾theoretic rough fuzzy set model and application[J]. Inform￾ation sciences, 2014, 283: 180–196. [3] YAO Y Y, WONG S K M. A decision theoretic frame￾work for approximating concepts[J]. International journal of man-machine studies, 1992, 37(6): 793–809. [4] ZHAO Xuerong, HU Baoqing. Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure[J]. Information sciences, 2015, 298: 534–554. [5] YAO Yiyu. An outline of a theory of three-way decision[C]//Proceedings of the International Conference on Rough Sets and Current Trends in Computing. Berlin, Heidelberg, Germany, 2012: 1−17. [6] LIANG Decui, LIU Dun. Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets[J]. Information sciences, 2014, 276: 186–203. [7] LIANG Decui, XU Zeshui, LIU Dun. Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information[J]. Information sciences, 2017, 396: 127–143. [8] LIANG Decui, XU Zeshui, LIU Dun. Three-way decisions with intuitionistic fuzzy decision-theoretic rough sets based on point operators[J]. Information sciences, 2017, 375: 183–201. [9] FENG Tao, MI Jusheng. Variable precision multigranula￾tion decision-theoretic fuzzy rough sets[J]. Knowledge￾based systems, 2016, 91: 93–101. [10] DENG Xiaofei, YAO Yiyu. Decision-theoretic three-way approximations of fuzzy sets[J]. Information sciences, [11] 2014, 279: 702–715. 杨霁琳, 张贤勇, 唐孝, 等. 基于最优相似度三支决策的 模糊粗糙集模型 [J]. 计算机科学, 2018, 45(10): 27–32. YANG Jilin, ZHANG Xianyong, TANG Xiao, et al. Fuzzy rough set model based on three-way decisions of optimal similar degrees[J]. Computer science, 2018, 45(10): 27–32. [12] 衷锦仪, 叶东毅. 基于模糊数风险最小化的拓展决策粗 糙集模型 [J]. 计算机科学, 2014, 41(3): 50–54. ZHONG Jinyi, YE Dongyi. Extended decision-theoretic rough set models based on fuzzy minimum cost[J]. Com￾puter science, 2014, 41(3): 50–54. [13] ZHAO Xuerong, HU Baoqing. Three-way decisions with decision-theoretic rough sets in multiset-valued informa￾tion tables[J]. Information sciences, 2020, 507: 684–699. [14] LIANG Decui, LIU Dun, PEDRYCZ W, et al. Triangular fuzzy decision-theoretic rough sets[J]. International journ￾al of approximate reasoning, 2013, 54(8): 1087–1106. [15] LIU Xinwang. Measuring the satisfaction of constraints in fuzzy linear programming[J]. Fuzzy sets and systems, 2001, 122(2): 263–275. [16] YAO Yiyu, ZHAO Yan. Attribute reduction in decision￾theoretic rough set models[J]. Information sciences, 2008, 178(17): 3356–3373. [17] LI Wentao, XU Weihua. Double-quantitative decision￾theoretic rough set[J]. Information sciences, 2015, 316: 54–67. [18] QIAN Yuhua, ZHANG Hu, SANG Yanli, et al. Multi￾granulation decision-theoretic rough sets[J]. International journal of approximate reasoning, 2014, 55(1): 225–237. [19] ZHANG Hongying, YANG Shuyun, MA Jianmin. Rank￾ing interval sets based on inclusion measures and applica￾tions to three-way decisions[J]. Knowledge-based sys￾tems, 2016, 91: 62–70. [20] LI Weiwei, HUANG Zhiqiu, JIA Xiuyi, et al. Neighbor￾hood based decision-theoretic rough set models[J]. Inter￾national journal of approximate reasoning, 2016, 69: 1–17. [21] 邢航. 基于构造性覆盖算法的三支决策模型 [D]. 合肥: 安徽大学, 2014. XING Hang. Three-way decisions model based on con￾structive covering algorithm[D]. Hefei: Anhui University, 2014. [22] 徐健锋, 何宇凡, 刘斓. 三支决策代价目标函数的关系 及推理研究 [J]. 计算机科学, 2018, 45(6): 176–182. XU Jianfeng, HE Yufan, LIU Lan. Relationship and reas￾oning study for three-way decision cost objective func- [23] 第 6 期 曾婷，等：相似度三支决策模糊粗糙集模型的决策代价研究 ·1077·