One of the most important features of fuzzy set theory and fuzzy logic is their power to model semantics of a certain part of natural language. The results are further elaborated in topics such as computing with words which encompasses computing with fuzzy numbers, the theory of evaluating linguistic expressions as well as that of fuzzy IF-THEN rules and approximate reasoning. In the talk, we w...

Of special interest in abstract algebraic logic currently is the problem of extending the general theory of algebraization to logical systems that fail to be structural. The annotated logics PL were introduced in the late eighties as a logical framework to deal with deductive databases that contain inconsistent, conflicting or contradictory information. Like many paraconsistent logics they are ...

In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

Closure (interior) operators and closure systems are important tools in many mathematical environments. Considering the logical sense of a complete residuated lattice L, this paper aims to present concepts L-closure (L-interior) by means infimums (supremums) L-families L-subsets show their equivalence categorical sense. Also, two types fuzzy relations between corresponding L-interior proposed, ...

Fuzzy semantics comprehension and fuzzy inference are two of the central abilities of human brains that play a crucial role in thinking, perception, and problem solving. A formal methodology for rigorously describing and manipulating fuzzy semantics and fuzzy concepts is sought for bridging the gap between humans and cognitive fuzzy systems. A mathematical model of fuzzy concepts is created bas...

This paper deals with propositional fuzzy modal logic with evaluated syntax based on MV-algebras. We focus on its semantical theory from the viewpoint of Pavelka’s graded semantics of propositional fuzzy logic, investigate the L-tautologies based on different Kripke frames. We also define the notion of Lsemantical consequence operation, its some basic properties are obtained. Finally, this pape...

The given article provides some views on the development of problems formalization and representation a notion «sense», which is being conceptualized by an outstanding German philosopher Gottlob Frege, what’s mainly analyzed elaborated in his work “On Sense Reference”. key critical theories understanding «sense» according to Frege are characterized conceptual aspect, that is, paradigmatic conce...

The fuzzy rough sets and generalized fuzzy rough sets have been extended by three pairs of fuzzy logical operators to deal with real-valued data for a variety of models. Three pairs of fuzzy logical operators are triangular norm or t-norm and its dual (t-conorm), residual implicator or R-implicator and its dual, fuzzy implicator and t-norm, which are frequently discussed in generalization model...