This article discusses the fuzzy modeling and situational analysis of technological safety of industrial complexes and decision-making for their management in the face of uncertainty and vagueness of the initial information on the basis of the theory of fuzzy sets and fuzzy logic. A formal model for description of fuzzy situations in the form of fuzzy sets and rational decision-making in a vari...

The notion of extensionality of a fuzzy relation w.r.t. a fuzzy equivalence was first introduced by Höhle and Blanchard. Bělohlávek introduced a similar definition of compatibility of a fuzzy relation w.r.t. a fuzzy equality. In [14] we generalized this notion to left compatibility, right compatibility and compatibility of arbitrary fuzzy relations and we characterized them in terms of left and...

Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this ...

The paper presents a new method to find the optimal solution of a fully intuitionistic fuzzy linear programming (FIFLP) problem. It uses the sign distance between intuitionistic fuzzy numbers for their comparison. The proposed methods have been applied for solving a FIFLP problem with equality constraints. The proposed method is convenient for implementation to solution of FIFLP problems arisin...

Our work is a contribution to the model-theoretic study of equality-free fuzzy predicate logics. We give a characterization of elementary equivalence in fuzzy predicate logics using elementary extensions and introduce an strengthening of this notion, the so-called strong elementary equivalence. Using the method of diagrams developed in [5] and elementary extensions we present a counterexample t...

We consider linear equality systems where all the parameters may be fuzzy variables specified by their possibility distribution, the operations addition and multiplication by a real number of fuzzy parameters are defined via a suptriangular norm composition, and the equations are understood in possibilistic sense. We show that when the triangular norm defining the operations and equations is co...

We use the formal model for similarity-based fuzzy unification in multi-adjoint logic programs to provide new tools for flexible querying. Our approach is based on a general framework for logic programming, which gives a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of first-order logic with equality. As a source of similarities we consider different approach...

This paper focuses on the possible embedding of the uncertainty regarding the colors of an image into histogramtype descriptors. The uncertainty naturally arises from both the quantization of the color components and the human perception of colors. Fuzzy histograms measure the typicality of each color within the image. We define various fuzzy color histograms following a taxonomy that classifie...

In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were generalized by Tripathy, Mitra and Ojha ([13]), who introduced the concepts of approximate (rough) equivalences of sets. Rough equivalences capture equality of se...