| Zadeh put forward the concept of fuzzy set in 1965,a few years later he put forward another concept which was called fuzzy entropy to describe the fuzziness of fuzzy sets.These theories are widely used in graphic recognition,data mining,information fusion and uncertainty reasoning.Since then,many scholars have studied the fuzzy sets and then put forward more concepts about fuzzy sets,such as intuitionistic fuzzy sets,hesitant fuzzy sets and so on.The corresponding entropy is defined.Because of adding the attribute of hesitation,intuitionistic fuzzy has wider application in the theory of multiple attribute decision making.With the development of fuzzy analysis,the study of fuzzy numbers is becoming more and more mature.As we all know,trapezoidal fuzzy numbers are extension of triangular fuzzy numbers and interval fuzzy numbers.Compared with triangular fuzzy numbers and interval fuzzy numbers,trapezoidal fuzzy numbers have a wider range of applications.Therefore,the study of trapezoidal fuzzy number entropy has an important theoretical significance and practical value.This paper mainly studies the entropy of trapezoidal fuzzy number intuitionistic fuzzy sets.The details are as follows:Firstly,the concepts of fuzzy sets,intuitionistic fuzzy sets,the definitions of their corresponding entropy and their calculation formulas are introduced and there are some related contents of the trapezoid fuzzy numbers.Secondly,the definition of trapezoidal fuzzy number intuitionistic fuzzy set entropy is given,it is pointed out that this definition can be degenerated to the definition of entropy of intuitionistic fuzzy sets.Thirdly,the construction and calculation formula of the entropy of trapezoidal fuzzy number intuitionistic fuzzy sets are given.Finally,some properties of the entropy of the trapezoid fuzzy number intuitionistic fuzzy set are given.And some decision problems in real life are solved by using the intuitionistic fuzzy set entropy of the trapezoid fuzzy number. |
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