Two-dimensional discrete fuzzy numbers and applications

In this paper, the concept of two-dimensional discrete fuzzy numbers is presented based on the idea of representation theorem of one-dimensional discrete fuzzy numbers. Then a sufficient condition is proposed, which makes a fuzzy set on R2 become a two-dimensional discrete fuzzy number, and the repr...

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Bibliographic Details
Published in:Information Sciences Vol. 326; pp. 258 - 269
Main Authors: Wang, Guixiang, Shi, Peng, Xie, Yunyan, Shi, Yan
Format: Journal Article
Language:English
Japanese
Published: Elsevier Inc 01.01.2016
Elsevier BV
Subjects:
0802 Computation Theory and Mathematics
Ambiguity
College of Science and Engineering
Discrete fuzzy numbers
Fuzzy
Fuzzy logic
Fuzzy numbers
Fuzzy set theory
Fuzzy systems
probability functions
Ranking
Representations
Theorems
Two dimensional
Weak orders
Weak orders
Ranking
Fuzzy numbers
Discrete fuzzy numbers
ISSN:0020-0255, 1872-6291
Online Access:Get full text
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Summary:In this paper, the concept of two-dimensional discrete fuzzy numbers is presented based on the idea of representation theorem of one-dimensional discrete fuzzy numbers. Then a sufficient condition is proposed, which makes a fuzzy set on R2 become a two-dimensional discrete fuzzy number, and the representations of joint membership function and the two edge membership functions of two-dimensional discrete fuzzy number are given. Some special two-dimensional discrete fuzzy numbers are also defined. And then some weak orders in the two-dimensional discrete fuzzy number space are set up based on the mass centers and the degree of ambiguities of two-dimensional discrete fuzzy numbers, and their properties are also investigated. At last, some practical examples are included to demonstrate the effectiveness and potential of the theoretic results obtained.
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ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2015.07.045