In this paper, based on Hájek, Vychodil, Rachunek and Šalounová’s works, we study the concept of v-filters of residuated lattices with weak vt-operators, axiomatize very true operators, discuss filters and v-filters of residuated lattices with weak vt-operator, give the formulas for calculating the v-filters generated by subsets, and show that lattice of v-filters of a commutative residuated la...

This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χH, χHc) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating cong...

In some knowledge domains, a correct handling of vagueness and imprecision is fundamental for adequate knowledge representation and reasoning. For example, when trying to diagnose a disease, medical experts need to confront symptoms described by the patient, which are by definition subjective, and hence vague. Moreover, a single malady may present a diversity of clinical manifestations in diffe...

Formal concept analysis has become an important and appealing research topic. There exist a number of different fuzzy extensions of formal concept analysis and of its representation theorem, which gives conditions for a complete lattice in order to be isomorphic to a concept lattice. In this paper we concentrate on the study of operational properties of the mappings α and β required in the repr...

Goguen categories were introduced in [13] as a suitable categorical description of L-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In this paper we want to study operations on morphisms of a Goguen category which are derived from suitable binary functions on the underlying lattice of sca...

fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. the main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group g z p1 ...

This paper is a survey of the theory of Goguen categories which establishes a suitable categorical description of L-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In particular, we concentrate on representability, the existence of crisp versions of several categorical constructions, and o...

This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

Autoassociative morphological memories (AMM) are memory models that use operations of mathematical morphology for the storage and recall of pattern associations. These models can be very well de ned in a mathematical structure called complete lattice. In this paper, we introduce the Brouwerian autoassociative morphological memories (BAMMs) that are de ned on a complete Brouwerian lattice. The a...