Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 7, Pages 4948-4971Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.10.006
Keywords
Soft sets; Interval type-2 fuzzy sets; Trapezoidal interval type-2 fuzzy soft sets; Operation; Multi attribute group decision making
Funding
- National Natural Science Foundation of China [61073121]
- Natural Science Foundation of Hebei Province of China [F2010000318, F2012201014, A2012201033]
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Soft set theory, originally proposed by Molodtsov, has become an effective mathematical tool to deal with uncertainty. A type-2 fuzzy set, which is characterized by a fuzzy membership function, can provide us with more degrees of freedom to represent the uncertainty and the vagueness of the real world. Interval type-2 fuzzy sets are the most widely used type-2 fuzzy sets. In this paper, we first introduce the concept of trapezoidal interval type-2 fuzzy numbers and present some arithmetic operations between them. As a special case of interval type-2 fuzzy sets, trapezoidal interval type-2 fuzzy numbers can express linguistic assessments by transforming them into numerical variables objectively. Then, by combining trapezoidal interval type-2 fuzzy sets with soft sets, we propose the notion of trapezoidal interval type-2 fuzzy soft sets. Furthermore, some operations on trapezoidal interval type-2 fuzzy soft sets are defined and their properties are investigated. Finally, by using trapezoidal interval type-2 fuzzy soft sets, we propose a novel approach to multi attribute group decision making under interval type-2 fuzzy environment. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method. (C) 2012 Elsevier Inc. All rights reserved.
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