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Mathematics 2019, 7(2), 166; https://doi.org/10.3390/math7020166

Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

1
Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2
Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
3
Faculty of Software and Information Science, Iwate Prefectural University, 152-52 Sugo, Takizawa, Iwate 020-0693, Japan
4
Faculty of Information Technology, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam
5
Machine Intelligence Institute, Iona College, New Rochelle, NY 10801, USA
*
Author to whom correspondence should be addressed.
Received: 16 January 2019 / Revised: 1 February 2019 / Accepted: 6 February 2019 / Published: 13 February 2019
(This article belongs to the Section Engineering Mathematics)
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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. View Full-Text
Keywords: fuzzy set; intuitionistic fuzzy set; intuitionistic fuzzy value; lexicographic order; decision making fuzzy set; intuitionistic fuzzy set; intuitionistic fuzzy value; lexicographic order; decision making
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Feng, F.; Liang, M.; Fujita, H.; Yager, R.R.; Liu, X. Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships. Mathematics 2019, 7, 166.

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