一种新犹豫模糊符号距离及其应用
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摘要
研究了属性权重部分已知的犹豫模糊多属性决策问题.针对犹豫模糊元中为便于计算添加的多余数值影响方案排序等问题,提出一种新的犹豫模糊决策方法.首先,提出一种新的犹豫模糊元得分函数与犹豫度.基于此,构造一种新的犹豫模糊符号距离,对犹豫模糊元中添加的多余数值具有很好的鲁棒性.其次,基于max-min算子思想,建立属性权重优化模型.最后,将新的犹豫模糊符号距离应用于求解多属性决策问题中,并通过算例说明所提方法的可行性与有效性.
The hesitant fuzzy multiple attribute decision making problems with partly known weight information are investigated. With respect to the problem that the ranking of alternatives is affected by additional values added in a hesitant fuzzy element(HFE), a novel hesitant fuzzy decision method is proposed. Firstly, a novel score function and hesitancy index of a HFE are presented, based on which a novel hesitant fuzzy signed distance which is robust to the additional values added in a HFE is developed.Secondly, motivated by the idea of max-min operator, a programming model for determining the attribute weights is constructed. Lastly, the hesitant fuzzy signed distance is applied to solve multiple attribute decision making problems and the feasibility and validity of the proposed approach is illustrated by an example.
The hesitant fuzzy multiple attribute decision making problems with partly known weight information are investigated. With respect to the problem that the ranking of alternatives is affected by additional values added in a hesitant fuzzy element(HFE), a novel hesitant fuzzy decision method is proposed. Firstly, a novel score function and hesitancy index of a HFE are presented, based on which a novel hesitant fuzzy signed distance which is robust to the additional values added in a HFE is developed.Secondly, motivated by the idea of max-min operator, a programming model for determining the attribute weights is constructed. Lastly, the hesitant fuzzy signed distance is applied to solve multiple attribute decision making problems and the feasibility and validity of the proposed approach is illustrated by an example.
引文
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[16]刘小弟,朱建军,刘思峰·犹豫模糊a信息-下的双~向投影决策方法[J].系统工程理论与实践j,2014, 34(10):2637-2644.Liu X D, Zhu J J, Liu S F. The bidirectional projection method under hesitant fuzzy information[J]. Systems Engineering—Theory Sc Practice, 2014, 34(10):2637-2644.
[17] Xu Z S, Zhang X L. Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J]. Knowledge-Based Systems, 2013, 52(6):53-64.
[18] Zhang X L,Xu Z S. The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment[J]. Knowledge-Based Systems, 2014, 61(2):48-58.
[19] Zhang N, Wei G W. Extension of VIKOR method for decision making problem based on hesitant fuzzy set[J].Applied Mathematical Modelling, 2013, 37(7):4938-4947.
[20] Zhang X L, Xu Z S. Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives[J]. Computers&Industrial Engineering, 2014, 75(1):217-229.
[21] Chen N, Xu Z S, Xia M M. The ELECTRE I multi-criteria decision-making method based on hesitant fuzzy sets[J]. International Journal of Information Technology Sz Decision Making, 2015, 14(3):621-657.
[22] Farhadinia B. Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making[J].Information Sciences,2016, 327(1):233-245.
[23]朱斌.基于偏好关系的决策方法研f究及应用[D].南京:东南大学,2014.Zhu B. Decision method for research and application based on preference relation[D]. Nanjing:Southeast Uni?versity, 2014.
[24] Zhang S, Xu Z S, He Y. Operations and integrations of probabilistic hesitant fuzzy information in decision making[J]. Information Fusion, 2017, 38:1-11.
[25] Ding J, Xu Z S, Zhao N. An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information[J]. Journal of Intelligent&Fuzzy Systems, 2017, 32:2523-2536.
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[27] Chen T Y. A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set[J]. Knowledge and Information Systems, 2013, 35(1):193-231.
[28] Zhang X L, Xu Z S. Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis[J]. Expert Systems with Applications, 2015, 42(2):873—884.
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[30] Liao H C,Xu Z S. Satisfaction degree based interactive decision making under hesitant fuzzy environment with incomplete weights[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2014,22(4):553-572.
[31] Xia M M, Xu Z S. Hesitant fuzzy information aggregation in decision making[J]. International Journal of Approximate Reasoning, 2011, 52(3):395-407.
[32] Park S K,Kim S H. Tools for interactive multi-attribute decision making with incompletely identified informar tion[J]. European Journal of Operational Research, 1997, 98(1):111-123.
[2] Dubois D, Prade H. Fuzzy sets and systems:Theory and Applications[M]. New York:Academic Press, 1980:30-32.
[3] Yager R R. On the theory of bags[J]. International Journal of Geineral Systems, 1986, 1:3(1):23-37.
[4] Atanassov K. Intuitionistic fuzzy sets[.J]. Fuzzy Sets and Syst.cems, 1986, 2(0(1):87 96.
[5] Torra V. Hesitant fuzzy sets[J]. Internat.ional Journal of Intelligent, Systems, 2010, 25(6):529-539.
[6] Rodriguez R. M, Bedregal B, Bustince H, et al. A position and perspcect.ive analysis of hesitant fuzzy sets orn information fusion in decision making:Towards high qualit.y progress[,J]. Iinforiimation Fusion, 2016, 29(:3):89-97.
[7] Xu Z S,Xia M M. Distance and similarity measures for hesitant fuzzy sets[J]. Information Sciences, 2011,181(11):2128-2138.
[8] Xu Z S, Xia M M. On distance and correlation measures of hesitant fuzzy information[J]. International Journal of Intelligent Systems, 2011, 26(5):410-425.
[9] Li D Q, Zeng W Y, Zhao Y B. Note on distance measure of hesitant fuzzy sets[J]. Information Sciences, 2015,321(11):103-115.
[10] Farhadinia B. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets[J]. Information Sciences, 2013, 240(10):129-144.
[11] Zhang X L, Xu Z S. Novel distance and similarity measures on hesitant fuzzy sets with applications to clustering analysis[J]. Journal of Intelligent&Fuzzy Systems, 2015, 28(5):2279-2296.
[12] Xu Z S, Xia M M. Hesitant fuzzy entropy and cross-entropy and their use in multi-attribute decision-making[J].International Journal of Intelligent Systems, 2012, 27(9):799-822.
[13] Chen N, Xu Z S, Xia M M. Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis[J]. Applied Mathematical Modelling, 2013, 37(4):2197-2211.
[14] Zhang X L, Xu Z S. Hesitant fuzzy agglomerative hierarchical clustering algorithms[J]. International Journal of Systems Science, 2013, 46(3):562-576.
[15] Zhang X L, Xu Z S. A MST clustering analysis method under hesitant fuzzy environment[J]. Control and Cybernetics, 2012, 41(3):645-666.
[16]刘小弟,朱建军,刘思峰·犹豫模糊a信息-下的双~向投影决策方法[J].系统工程理论与实践j,2014, 34(10):2637-2644.Liu X D, Zhu J J, Liu S F. The bidirectional projection method under hesitant fuzzy information[J]. Systems Engineering—Theory Sc Practice, 2014, 34(10):2637-2644.
[17] Xu Z S, Zhang X L. Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J]. Knowledge-Based Systems, 2013, 52(6):53-64.
[18] Zhang X L,Xu Z S. The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment[J]. Knowledge-Based Systems, 2014, 61(2):48-58.
[19] Zhang N, Wei G W. Extension of VIKOR method for decision making problem based on hesitant fuzzy set[J].Applied Mathematical Modelling, 2013, 37(7):4938-4947.
[20] Zhang X L, Xu Z S. Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives[J]. Computers&Industrial Engineering, 2014, 75(1):217-229.
[21] Chen N, Xu Z S, Xia M M. The ELECTRE I multi-criteria decision-making method based on hesitant fuzzy sets[J]. International Journal of Information Technology Sz Decision Making, 2015, 14(3):621-657.
[22] Farhadinia B. Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making[J].Information Sciences,2016, 327(1):233-245.
[23]朱斌.基于偏好关系的决策方法研f究及应用[D].南京:东南大学,2014.Zhu B. Decision method for research and application based on preference relation[D]. Nanjing:Southeast Uni?versity, 2014.
[24] Zhang S, Xu Z S, He Y. Operations and integrations of probabilistic hesitant fuzzy information in decision making[J]. Information Fusion, 2017, 38:1-11.
[25] Ding J, Xu Z S, Zhao N. An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information[J]. Journal of Intelligent&Fuzzy Systems, 2017, 32:2523-2536.
[26] Rezaei J. Best-worst multi-criteria decision-making method[J]. Omega, 2015, 53:49-57.
[27] Chen T Y. A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set[J]. Knowledge and Information Systems, 2013, 35(1):193-231.
[28] Zhang X L, Xu Z S. Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis[J]. Expert Systems with Applications, 2015, 42(2):873—884.
[29] Zimmermann H J, Zysno P. Latent connectives in human decision making[J]. Fuzz Sets and Systems, 1980, 4(1):37-51.
[30] Liao H C,Xu Z S. Satisfaction degree based interactive decision making under hesitant fuzzy environment with incomplete weights[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2014,22(4):553-572.
[31] Xia M M, Xu Z S. Hesitant fuzzy information aggregation in decision making[J]. International Journal of Approximate Reasoning, 2011, 52(3):395-407.
[32] Park S K,Kim S H. Tools for interactive multi-attribute decision making with incompletely identified informar tion[J]. European Journal of Operational Research, 1997, 98(1):111-123.