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A Novel Method for Solving Multi-Attribute Decision Making by Using Expected Value Under Interval Type-2 Fuzzy Environment

Interval type-2 fuzzy set (IT2FS) is a very helpful tool to deal with Multi-Attribute Decision-Making (MADM) problem in real world. In this paper, a novel method is developed to solve MADM problem under IT2FS environment. Firstly, three kinds of interval type-2 fuzzy set (IT2FS) average expectation operator formulas are put forward, and a new expected value formula of interval type-2 fuzzy sets (IT2FSs) is proposed by combining the three average expectation operators in interval type-2 fuzzy environment. Then, fuzzy factor, hesitant factor and interval factor of IT2FS are put forward to measure uncertain information of IT2FS. Next, a new cross-entropy formula is proposed to measure uncertain relationship between IT2FSs, and a new comprehensive cross-entropy formula of IT2FS is put forward based on cross-entropy formula and total probability formula to reflect influence relationship among alternatives in decision-making. Meanwhile, we put forward a novel entropy formula to measure the uncertainty of IT2FSs themselves. On the other hand, an optimal linear programming model is constructed with the expected value, comprehensive cross-entropy and entropy. Finally, an example analysis is utilized to show the feasibility and effectiveness of the proposed method.