Intuitionistic fuzzy residuated logic and Galois connection

Abstract

This paper aims at developing the logic theories of intuitionistic fuzzy sets. Starting from the intuitionistic fuzzy set and a defined lattice L*, a residuated lattice induced by L* is proposed which shows the structure of truth values of IF logic based on the IF algebra. Some basic properties of logic operation are presented. In the last, we define four pairs of logic operators based on the intuitionistic fuzzy residuated logic and obtain four pairs of Galois connections.