Valuations in Nilpotent Minimum Logic

The Euler characteristic can be defined as a special kind of valuation on finite distributive lattices. This work begins with some brief consideration on the role of the Euler characteristic on NM algebras, the algebraic counterpart of Nilpotent Minimum logic. Then, we introduce a new valuation, a modified version of the Euler characteristic we call idempotent Euler characteristic. We show that the new valuation encodes information about the formul{\ae} in NM propositional logic

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

Expanding FLew with a Boolean connective

We expand FLew with a unary connective whose algebraic counterpart is the operation that gives the greatest complemented element below a given argument. We prove that the expanded logic is conservative and has the Finite Model Property. We also prove that the corresponding expansion of the class of residuated lattices is an equational class.Comment: 15 pages, 4 figures in Soft Computing, published online 23 July 201

Interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (\in,\ivq)-fuzzy filters of pseudo $BL$-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo $BL$-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo $BL$-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed