On algebras for interval-valued fuzzy logic

Abstract

This work aims to introduce other approaches to the interval-valued fuzzy logic. These new approaches were inspired by Lodwick and Chalco’s works on constraint intervals. These constraint intervals were used in this thesis to extend the fuzzy operators into two modes, named Single-Level Constrained Interval Operators and Constrained Interval Operators and studied their properties. A new algebra, called SBCI algebra, which arises from the intervalization of BCI-algebras, is also introduced. These algebras aims to be the algebraic model for intervalvalued fuzzy logics, which take into account the notion of correctness. A new class of fuzzy implications, called (T, N)-implications has also been studied. The author investigated the behavior of the BCI/SBCI algebras and (T, N)-implications.