一种基于对象-语言值决策矩阵的模糊语言TOPSIS决策方法
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摘要
模糊语言决策方法是决策领域的热点研究内容之一.比较现有模糊语言决策方法研究中广泛使用的决策矩阵,提出对象-语言值决策矩阵表示决策专家根据决策属性给出的评价语言信息,分析对象-语言值决策矩阵在区分明晰、部分未知及犹豫的模糊语言决策问题中的优势;借鉴经典TOPSIS决策方法及向量运算,给出基于对象-语言值决策矩阵的正负理想解确定方法以及备选对象与正负理想解的伪距离和贴近度计算方法,分析伪距离和贴近度的相关性质;基于2-元组语言表示模型,提出基于对象-语言值决策矩阵的模糊语言TOPSIS决策方法.通过实例分析,并与已有3种重要的模糊语言决策方法进行比较,比较结果说明所提出的决策方法可以克服已有决策方法的不足,是一种可选的模糊语言决策方法.
Fuzzy linguistic decision making methods are hot in decision making. Compared with the decision matrixes which are widely used in fuzzy linguistic decision making methods, alternatives-linguistic terms decision matrixes are provided to represent decision results of experts with respect to attributes, and the advantage of alternatives-linguistic terms decision matrixes in distinguishing linguistic decision making of distinct, partial unknown or hesitant linguistic environments is analyzed. Inspired by the classical TOPSIS decision method and vector operation, the positive and negative ideal solutions based on alternatives-linguistic terms decision matrixes are presented, pseudo-distances and relative closeness between the positive(negative) ideal solution and alternatives are calculated, and their properties are analyzed. Then based on the 2-tuple linguistic represent model, the fuzzy linguistic TOPSIS decision making method based on alternatives-linguistic terms decision matrixes are proposed. An example is given to illustrate the practicality of the proposed method. Compared with three existed important fuzzy linguistic decision making methods, the proposed method can be used to overcome the drawback of the existed method, which is an alternative fuzzy linguistic decision making method.
Fuzzy linguistic decision making methods are hot in decision making. Compared with the decision matrixes which are widely used in fuzzy linguistic decision making methods, alternatives-linguistic terms decision matrixes are provided to represent decision results of experts with respect to attributes, and the advantage of alternatives-linguistic terms decision matrixes in distinguishing linguistic decision making of distinct, partial unknown or hesitant linguistic environments is analyzed. Inspired by the classical TOPSIS decision method and vector operation, the positive and negative ideal solutions based on alternatives-linguistic terms decision matrixes are presented, pseudo-distances and relative closeness between the positive(negative) ideal solution and alternatives are calculated, and their properties are analyzed. Then based on the 2-tuple linguistic represent model, the fuzzy linguistic TOPSIS decision making method based on alternatives-linguistic terms decision matrixes are proposed. An example is given to illustrate the practicality of the proposed method. Compared with three existed important fuzzy linguistic decision making methods, the proposed method can be used to overcome the drawback of the existed method, which is an alternative fuzzy linguistic decision making method.
引文
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[4] Hwang C L, Yoon K. Multiple attribute decision making:Methods and applications[M]. New York:Springer-Verlag, 1981:22-27.
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[8]徐泽水,潘玲,廖虎昌.基于MACBETH方法的犹豫模糊语言多准则决策方法[J].控制与决策, 2017, 32(7),1266-1272.(Xu Z S, Pan L, Liao H C. Multi-criteria decision making method of hesitant fuzzy linguistic term set based on improved MACBETH method[J]. Control and Decision,2017, 32(7):1266-1272.)
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[12] Guo W T, Huynh V N, Nakamori Y. A proportional3-tuple fuzzy linguistic representation model for screening new product projects[J]. J of Systems Science and Systems Engineering, 2016,25(1):1-22.
[13] Meng D, Pei Z. On weighted unbalanced linguistic aggregation operators in group decision making[J].Information Sciences, 2013,223(3):31-41.
[14] Pei Z, Ruan D, Liu J, et al. A linguistic aggregation operator with three kinds of weights for nuclear safeguards evaluation[J]. Knowledge-Based Systems,2012, 28(3):19-26.
[15] Pei Z, Zou L, Yi L Z. A linguistic aggregation operator including weights for linguistic values and experts in group decision making[J]. Int J of Uncertainty Fuzziness and Knowledge-Based Systems, 2013, 21(6):927-943.
[16] Roszkowska E, Wachowicz T. Application of fuzzy TOPSIS to scoring the negotiation offers in ill-structured negotiation problems[J]. European J of Operational Research, 2015, 242(9):920-932.
[17] Herrera F, Martinez L. A 2-tuple fuzzy linguistic representation model for computing with words[J]. IEEE Trans on Fuzzy Systems, 2000, 8(6):746-752.
[18]谭春桥,贾媛.基于证据理论和前景理论的犹豫-直觉模糊语言多准则决策方法[J].控制与决策, 2017,32(2):333-339.(Tan C Q, Jia Y. Multi-criteria decision-making method based on evidence theory and Prospect theory for hesitant-intuitionistic fuzzy linguistic[J]. Control and Decision, 2017, 32(2):333-339.)
[19] Wei C P, Zhao N, Tang X J. Operators and comparisons of hesitant fuzzy linguistic term sets[J]. IEEE Trans on Fuzzy Systems, 2014, 22(3):575-584.
[20] Beg I, Rashid T. TOPSIS for hesitant fuzzy linguistic term sets[J]. Int J of Intelligent Systems, 2013, 28(5):1162-1171.
[21] Lee L W, Chen S M. Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators[J]. Information Sciences, 2015, 294(1):513-529.
[22] Ren F L, Kong M, Pei Z. A new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making[J]. Symmetry, 2017, 9, DOI:10.3390/sym9120289.
[23] Pang Q, Wang H, Xu Z H. Probabilistic linguistic term sets in multi-attribute group decision making[J]. Information Sciences, 2016, 369(1):128-143.
[24] Ou Y, Yi L Z, Zou B, et al. The linguistic intuitionistic fuzzy set TOPSIS method for linguistic multi-criteria decision makings[J]. Int J of Computational Intelligence Systems, 2017, 11(2):120-132.
[25] Massanet S, Riera J V, Torrens J, et al. A new linguistic computational model based on discrete fuzzy numbers for computing with words[J]. Information Sciences, 2014,258(1):277–290.
[26] Pei Z, Liu J, Hao F, et al. FLM-TOPSIS:The fuzzy linguistic multiset TOPSIS method and its application in linguistic decision making[J]. Information Fusion, 2019,45:266-281.
[2] Xu Z S. Hesitant fuzzy sets theory, studies in fuzziness and soft computing[M].Heildelberg:Springer, 2014:65-68.
[3] Martinez L, Rodriguez R M, Herrera F. The 2-tuple linguistic model-computing with words in decision making[M]. Switzerland:Springer Int Publishing, 2015:142-145.
[4] Hwang C L, Yoon K. Multiple attribute decision making:Methods and applications[M]. New York:Springer-Verlag, 1981:22-27.
[5] Rodriguez R M, Martinez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making[J]. IEEE Trans on Fuzzy Systems, 2012, 20(1):109-119.
[6] Rodriguez R M, Bedregal B. A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making[J]. Towards High Quality Progress,Information Fusion, 2016, 29(3):89-97.
[7] Silva V B S, Morais D C. A group decision-making approach using a method for constructing a linguistic scale[J]. Information Sciences, 2014, 288(5):423-436.
[8]徐泽水,潘玲,廖虎昌.基于MACBETH方法的犹豫模糊语言多准则决策方法[J].控制与决策, 2017, 32(7),1266-1272.(Xu Z S, Pan L, Liao H C. Multi-criteria decision making method of hesitant fuzzy linguistic term set based on improved MACBETH method[J]. Control and Decision,2017, 32(7):1266-1272.)
[9] Zadeh L A. Fuzzy logic=computing with words[J]. IEEE Trans on Fuzzy Systems, 1996, 4(10):103-111.
[10] Herrera F, Martinez L. A 2-tuple fuzzy linguistic representation model for computing with words[J]. IEEE Trans on Fuzzy Systems, 2000, 8(6):746-752.
[11] Martinez L, Herrera F. An overview on the 2-tuple linguistic model for computing with words in decision making:Extensions, applications and challenges[J].Information Sciences, 2012, 207(1):1-18.
[12] Guo W T, Huynh V N, Nakamori Y. A proportional3-tuple fuzzy linguistic representation model for screening new product projects[J]. J of Systems Science and Systems Engineering, 2016,25(1):1-22.
[13] Meng D, Pei Z. On weighted unbalanced linguistic aggregation operators in group decision making[J].Information Sciences, 2013,223(3):31-41.
[14] Pei Z, Ruan D, Liu J, et al. A linguistic aggregation operator with three kinds of weights for nuclear safeguards evaluation[J]. Knowledge-Based Systems,2012, 28(3):19-26.
[15] Pei Z, Zou L, Yi L Z. A linguistic aggregation operator including weights for linguistic values and experts in group decision making[J]. Int J of Uncertainty Fuzziness and Knowledge-Based Systems, 2013, 21(6):927-943.
[16] Roszkowska E, Wachowicz T. Application of fuzzy TOPSIS to scoring the negotiation offers in ill-structured negotiation problems[J]. European J of Operational Research, 2015, 242(9):920-932.
[17] Herrera F, Martinez L. A 2-tuple fuzzy linguistic representation model for computing with words[J]. IEEE Trans on Fuzzy Systems, 2000, 8(6):746-752.
[18]谭春桥,贾媛.基于证据理论和前景理论的犹豫-直觉模糊语言多准则决策方法[J].控制与决策, 2017,32(2):333-339.(Tan C Q, Jia Y. Multi-criteria decision-making method based on evidence theory and Prospect theory for hesitant-intuitionistic fuzzy linguistic[J]. Control and Decision, 2017, 32(2):333-339.)
[19] Wei C P, Zhao N, Tang X J. Operators and comparisons of hesitant fuzzy linguistic term sets[J]. IEEE Trans on Fuzzy Systems, 2014, 22(3):575-584.
[20] Beg I, Rashid T. TOPSIS for hesitant fuzzy linguistic term sets[J]. Int J of Intelligent Systems, 2013, 28(5):1162-1171.
[21] Lee L W, Chen S M. Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators[J]. Information Sciences, 2015, 294(1):513-529.
[22] Ren F L, Kong M, Pei Z. A new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making[J]. Symmetry, 2017, 9, DOI:10.3390/sym9120289.
[23] Pang Q, Wang H, Xu Z H. Probabilistic linguistic term sets in multi-attribute group decision making[J]. Information Sciences, 2016, 369(1):128-143.
[24] Ou Y, Yi L Z, Zou B, et al. The linguistic intuitionistic fuzzy set TOPSIS method for linguistic multi-criteria decision makings[J]. Int J of Computational Intelligence Systems, 2017, 11(2):120-132.
[25] Massanet S, Riera J V, Torrens J, et al. A new linguistic computational model based on discrete fuzzy numbers for computing with words[J]. Information Sciences, 2014,258(1):277–290.
[26] Pei Z, Liu J, Hao F, et al. FLM-TOPSIS:The fuzzy linguistic multiset TOPSIS method and its application in linguistic decision making[J]. Information Fusion, 2019,45:266-281.