摘要
In order to measure the uncertain information of a type-2 intuitionistic fuzzy set(T2IFS), an entropy measure of T2 IFS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular intuitionistic trapezoidal fuzzy set(T2TITr FS) is developed, and a geometric interpretation of the T2 TITr FS 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 T2 TITr FS 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 satisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2 TITr FS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.
In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all 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 illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.
基金
supported by the National Natural Science Foundation of China(71371156
70971017)
the Research Grants Council of the Hong Kong Special Administrative Region,China(City U112111)
关键词
直觉模糊集
模糊熵
三角
2型
不确定性信息
公理化定义
几何解释
复杂系统
type-2 intuitionistic fuzzy set, intuitionistic fuzzy en-tropy, type-2 triangular intuitionistic trapezoidal fuzzy entropy.
