Selection of Power Grids Using the Single-Valued Ambiguous Fuzzy Entropy and Distance Measures

The Single-Valued Ambiguous Fuzzy Set (SVAFS) Theory (SVAFST) was introduced recently to handle uncertain systems with more details and it is one of the generalizations of fuzzy set (FS) theory. This type of theory has the ability to employ four different degrees of membership: true, false, ambiguous-true, and ambiguous-false categories in one compact form and proved as an effective way to model uncertainty. Keeping in view the advantages of FS and thus of SVAFS, we are studying the SVAFS in more details and to see the applicability of it to address different kind of problems. In this paper, we are addressing the entropy measure of SVAFS. Thus, the entropy based on distance measures of SVAFS is proposed. Then, this proposed entropy measure is applied to the Power Grids (PGs) classification. Validation of results are carried out with considering some of the existing studies in the domain of SVAFS. Different structures of entropy and distance of SVAFS will comprise in future study with application in different fields.

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