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Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5604-5617. doi: 10.3934/mbe.2020301
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TOPSIS-based entropy measure for intuitionistic trapezoidal fuzzy sets and application to multi-attribute decision making

  • 1.
    School of Economics and Management, East China JiaoTong University, Nanchang 330013, China
  • 2.
    College of Modern Economics & Management, Jiangxi University of Finance and Economics, Nanchang 330013, China
  • 3.
    Collaborative Innovation center, Jiangxi University of Finance and Economics, Nanchang 330013, China
  • Received: 08 May 2020 Accepted: 31 July 2020 Published: 18 August 2020

  • As an extension of intuitionistic fuzzy numbers, intuitionistic trapezoidal fuzzy numbers (ITrFNs) are useful in expressing complex fuzzy information with an 'interval value'. This study focuses on multi-attribute decision-making (MADM) problems with unknown attribute weights under an ITrFN environment. We initially present an entropy measure for ITrFNs by using the relative closeness of technique for order preference by similarity to an ideal solution. From the view of the reliability and certainty of decision data, we present an approach to determine the attribute weights. Subsequently, a new method to solve intuitionistic trapezoidal fuzzy MADM problems with unknown attribute weight information is proposed. A numerical example is provided to verify the practicality and effectiveness of the proposed method.

    Citation: Yefu Zheng, Jun Xu, Hongzhang Chen. TOPSIS-based entropy measure for intuitionistic trapezoidal fuzzy sets and application to multi-attribute decision making[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5604-5617. doi: 10.3934/mbe.2020301

    Related Papers:

  • As an extension of intuitionistic fuzzy numbers, intuitionistic trapezoidal fuzzy numbers (ITrFNs) are useful in expressing complex fuzzy information with an 'interval value'. This study focuses on multi-attribute decision-making (MADM) problems with unknown attribute weights under an ITrFN environment. We initially present an entropy measure for ITrFNs by using the relative closeness of technique for order preference by similarity to an ideal solution. From the view of the reliability and certainty of decision data, we present an approach to determine the attribute weights. Subsequently, a new method to solve intuitionistic trapezoidal fuzzy MADM problems with unknown attribute weight information is proposed. A numerical example is provided to verify the practicality and effectiveness of the proposed method.


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    [1] A. Si, S. Das, S. Kar, An approach to rank picture fuzzy numbers for decision making problems, Decis. Making Appl. Manage. Eng., 2 (2019), 54-64.
    [2] I. Petrovic, M. Kankaras, A hybridized IT2FS-DEMATEL-AHP-TOPSIS multi-criteria decision making approach: Case study of selection and evaluation of criteria for determination of air traffic control radar position, Decis. Making Appl. Manage. Eng., 3 (2020), 146-164.
    [3] S. Biswas, G. Bandyopadhyay, B. Guha, & M. Bhattacharjee, An ensemble approach for portfolio selection in a multi-criteria decision making framework, Decis. Making Appl. Manage. Eng., 2 (2019), 138-158.
    [4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87-96.
    [5] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 31 (1989), 343-349.
    [6] H. Garg, K. Kumar, A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory, Artif. Intell. Rev., 1 (2020), 595-624.
    [7] K. Kumar, H. Garg, Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making, Appl. Intell., 48 (2018), 2112-2119.
    [8] K. Kumar, H. Garg, TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment, Comput. Appl. Math., 37 (2018), 1319-1329.
    [9] H. Garg, K. Kumar, An extended technique for order preference by similarity to ideal solution group decision-making method with linguistic interval-valued intuitionistic fuzzy information, J. Multi. Crite. Decis. Anal., 26 (2019), 16-26.
    [10] P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets Syst., 118 (1996), 305-316.
    [11] E. Szmidt, J. Kacprzyk, Entropy for intuitionistic fuzzy sets, Fuzzy Sets Syst., 118 (2001), 467-477.
    [12] T. Y. Chen, C. H. Li, Determing objective weights with intuitionistic fuzzy entropy measures: A comparative analysis, Inf. Sci., 180 (2010), 4207-4222.
    [13] Q. S. Zhang, H. Y. Xing, F. C. Liu, J. Ye, P. Tang, Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures, Inf. Sci., 283 (2014), 55-69.
    [14] A. De Luca, S. Termini, A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory, Inf. Control, 20 (1972), 301-312.
    [15] R. Joshi, S. Kumar, Parametric (R, S)-norm entropy on intuitionistic fuzzy sets with a new approach in multiple attribute decision making, Fuzzy Inf. Eng., 9 (2019), 181-203.
    [16] F. Liu, X. H. Yuan, Fuzzy number intuitionistic fuzzy set, Fuzzy Syst. Math., 21 (2007), 88-91.
    [17] M. H. Shu, C. H. Cheng, J. R. Dong, Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly, Microelectron. Reliab., 46 (2006), 2139-2148.
    [18] X. F. Wang, Fuzzy number intuitionistic fuzzy geometric aggregation operators and their application to decision making, Control Decis., 10 (2008), 104-111.
    [19] G. W. Wei, Induced fuzzy number intuitionistic fuzzy ordered weighted averaging (I-FIFOWA) operator and its application to group decision making, Chin. Jou. Manage., 7 (2010), 903-908.
    [20] Y. Gao, D. Q. Zhou, C. C. Liu, L. Zhang, Triangular fuzzy number intuitionistic fuzzy aggregation operators and their application based on interaction, Syst. Eng. Theory Prac., 32 (2012), 1964-1972.
    [21] Shan, Yu, Z. S. Xu, Aggregation and decision making using intuitionistic multiplicative triangular fuzzy information, J. Syst. Sci. Syst. Eng., 23 (2014), 20-38.
    [22] C. L. Hwang, K. Yoon, Multiple attributes decision making methods and applications, Berlin Heidelberg: Springer, (1981).
    [23] X. C. Liu, Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets Syst., 52 (1992), 305-318.
    [24] H. Y. Zhang, W. X. Zhang, C. L. Mei, Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure, Knowledge-Based Syst., 22 (2009), 449-454.
    [25] H. Garg, Intuitionistic fuzzy Hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems, Iran. J. Sci. Technol.-Trans. Electr. Eng., 43 (2019), 597-613.
    [26] H. Garg, Generalized intuitionistic fuzzy entropy-based approach for solving multi-attribute decision-making problems with unknown attribute weights, Proc. Natl. Acad. Sci. ndia Sect. A, 89 (2019), 129-139.
    [27] X. W. Qi, C. Y. Liang, J. L. Zhang, Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment, Comput. Ind. Eng., 79 (2015), 52-64.
    [28] H. Garg, K. Kumar, Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems, IEEE Trans. Fuzzy Syst., 27 (2019), 2302-2311.
    [29] H. Zhang, G. Kou, Y. Peng, Soft consensus cost models for group decision making and economic interpretations, Eur. J. Oper. Res., 277 (2019), 964-980.
    [30] G. Kou, P. Yang, Y. Peng, F. Xiao, Y. Chen, F. E. Alsaadi, Evaluation of feature selection methods for text classification with small datasets using multiple criteria decision-making methods, Appl. Soft Comput., 86 (2020), 105836.
    [31] G. Kou, Y. Peng, G. Wang, Evaluation of clustering algorithms for financial risk analysis using MCDM methods, Inf. Sci., 275 (2014), 1-12.
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