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Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values

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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)

  • Yujuan Zheng

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

  • José Carlos R. Alcantud

    (BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain)

  • Qian Wang

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

Abstract

In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1143-:d:383832
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    References listed on IDEAS

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    1. Xiaoyan Liu & Hee Sik Kim & Feng Feng & José Carlos R. Alcantud, 2018. "Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators," Mathematics, MDPI, vol. 6(11), pages 1-17, October.
    2. José Carlos R. Alcantud & María D. García-Sanz, 2013. "Evaluations of Infinite Utility Streams: Pareto Efficient and Egalitarian Axiomatics," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 432-447, July.
    3. 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.
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