Analysis of Fuzzy Implication

Abstract

Fuzzy logic (fuzzy sets) possesses some widespread application in decision-making due to its ability to handle uncertainties in the implemented data and information. The application of fuzzy logic in decision-making usually involves the design of fuzzy rule-based systems. The functioning of the designed fuzzy systems can be compactly defined as the fuzzy inference process. One of the main steps of fuzzy inference is fuzzy implication, and, therefore, the selection of proper implication function possesses the great impact on the corresponding decision-making process. The currently reported research provides a comparative analysis on two fuzzy implications: Ali-2 and Zadeh. The reported research involves the application of an efficiency index and is performed on a real-world example.

Keywords: Fuzzy implication, If-Then rules, membership function, fuzzy set, efficiency index