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Abstract

In recent years, interval type-2 fuzzy set has played an increasingly important role in decision-making. The purpose of this paper is firstly to propose fuzzy factor and interval factor of interval type-2 fuzzy sets (IT2FSs) based on α-cuts. Then, entropy and cross-entropy formulas of IT2FSs are put forward to measure the fuzzy information and mutual information between IT2FSs based on the two factors. Furthermore, IT2FS comprehensive cross-entropy formula is brought forward to measure the relative uncertain relationships among IT2FSs based on IT2FS cross-entropy formula and total probability formula. In the next moment, a utility function of IT2FS is proposed to compare the ordering relationship among IT2FSs. On the other hands, an optimal linear programming model is constructed based on IT2FS entropy, comprehensive cross-entropy and utility function to solve the optimal alternative. Finally, a simple example is utilized to testify the practicability and effectiveness of the proposed approach.

Keywords

IT2FS fuzzy factor IT2FS interval factor cross-entropy comprehensive relative cross-entropy utility function

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Comprehensive cross-entropy and entropy measures and their applications under interval type-2 fuzzy environment

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