Residual implications on lattice L of intuitionistic truth values based on powers of continuous t-norms

Abstract Residual implications are a special class of implications on the lattice L of intuitionistic truth values which possess interesting theoretical and practical properties. Many studies have investigated the properties of the types of implications on L and established the relationships among them. In this paper, the powers of the continuous t-norms T on L are introduced, and their properties studied. A new type of implication on L , termed the T -power based implication, is derived from the powers of the continuous t-norms T , as denoted by I I T and satisfies certain properties of the residual implications defined on the interval [0, 1] under certain conditions. Some important properties are analyzed. These results collectively reveal that they do not intersect the most well-known classes of fuzzy implications. Finally, we investigate the solutions of some Boolean-like laws for I I T .

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