Interval-valued algebras and fuzzy logics

In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter

MORE ON INTUITIONISTIC FUZZY SUBLATTICES AND THEIR IDEALS

In this paper, we study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals with respect to an intuitionistic fuzzy t-norm on an adequate lattice. Some characterizations and properties of these intuitionistic fuzzy sublattices and ideals with respect to intuitionistic fuzzy t-norm are established