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Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

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  • Feng Feng

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
    Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

  • Meiqi Liang

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

  • Hamido Fujita

    (Faculty of Software and Information Science, Iwate Prefectural University, 152-52 Sugo, Takizawa, Iwate 020-0693, Japan
    Faculty of Information Technology, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam)

  • Ronald R. Yager

    (Machine Intelligence Institute, Iona College, New Rochelle, NY 10801, USA)

  • Xiaoyan Liu

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

Abstract

Intuitionistic fuzzy multiple attribute decision making deals with the issue of ranking alternatives based on the decision information quantified in terms of intuitionistic fuzzy values. Lexicographic orders can serve as efficient and indispensable tools for comparing intuitionistic fuzzy values. This paper introduces a number of lexicographic orders by means of several measures such as the membership, non-membership, score, accuracy and expectation score functions. Some equivalent characterizations and illustrative examples are provided, from which the relationships among these lexicographic orders are ascertained. We also propose three different compatible properties of preorders with respect to the algebraic sum and scalar product operations of intuitionistic fuzzy values, and apply them to the investigation of compatible properties of various lexicographic orders. In addition, a benchmark problem regarding risk investment is further explored to give a comparative analysis of different lexicographic orders and highlight the practical value of the obtained results for solving real-world decision-making problems.

Suggested Citation

  • Feng Feng & Meiqi Liang & Hamido Fujita & Ronald R. Yager & Xiaoyan Liu, 2019. "Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships," Mathematics, MDPI, vol. 7(2), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:166-:d:205626
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    References listed on IDEAS

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    1. Feng, Feng & Li, Yongming & Çağman, Naim, 2012. "Generalized uni–int decision making schemes based on choice value soft sets," European Journal of Operational Research, Elsevier, vol. 220(1), pages 162-170.
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    Cited by:

    1. Peter Vassilev & Todor Stoyanov & Lyudmila Todorova & Alexander Marazov & Velin Andonov & Nikolay Ikonomov, 2023. "Orderings over Intuitionistic Fuzzy Pairs Generated by the Power Mean and the Weighted Power Mean," Mathematics, MDPI, vol. 11(13), pages 1-15, June.
    2. Feng Feng & Yujuan Zheng & José Carlos R. Alcantud & Qian Wang, 2020. "Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values," Mathematics, MDPI, vol. 8(7), pages 1-30, July.

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