On Algebras for Interval-Valued Fuzzy Logic
Interval-valued fuzzy logic, Interval Mathematics, Fuzzy Logic, BCI algebras, SBCI algebras, Fuzzy Implications.
This work aims at introducing a new approach to interval-valued fuzzy logic. This new approach was inspired by Lodwick and Chalco's works on constraint interval. These constraint intervals were used to extend the fuzzy operators, in which they were called Single-Level Constrained Interval Operators (C-operators) and studied their properties. A new algebra, called SBCI algebra, which it arises from the intervalization of BCI-algebras, is also introduced. These algebras aims to be the algebraic model for interval-valued fuzzy logics which take into account the notion of correctness (Moore Approach).
A new class of fuzzy implications, called (T,N)-implications has also been studied. The author is willing to investigate the behavior of BCI/SBCI algebras and (T,N)-implications in the new logic.