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Entropy measures of type-2 intuitionistic fuzzy sets and type-2 triangular intuitionistic trapezodial fuzzy sets
Author(s): 
Pages: 774-793
Year: Issue:  4
Journal: Journal of Systems Engineering and Electronics

Keyword:  type-2 intuitionistic fuzzy setintuitionistic fuzzy en-tropytype-2 triangular intuitionistic trapezoidal fuzzy entropy;
Abstract: In order to measure the uncertain information of a type-2 intuitionistic fuzzy set (T2IFS), an entropy measure of T2IFS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy al of the constructive principles. Further, a novel concept of the type-2 triangular in-tuitionistic trapezoidal fuzzy set (T2TITrFS) is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa-tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and il ustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.
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