the concept of an $l$-bornology is introduced and the theory of $l$-bornological spacesis being developed. in particular the lattice of all $l$-bornologies on a given set is studied and basic properties ofthe category of $l$-bornological spaces and bounded mappings are investigated.

The aim of this paper is to construct some new fuzzy categories related to many-valued sets and many valued topologies and to consider their properties. Keywords— Fuzzy categories, GL-monoids, L-valued equalities, L-topologies and L-fuzzy topologies.

The concept of an M-approximative system is introduced. Basic properties of the category of M-approximative systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximative systems. Keywords— Approximative operator...

Fuzzy covering-based rough set models are hybrid models using both rough set and fuzzy set theory. The former is often used to deal with uncertain and incomplete information, while the latter is used to describe vague concepts. The study of fuzzy rough set models has provided very good tools for machine learning algorithms such as feature and instance selection. In this article, we discuss diff...

The lower and upper approximations are basic concepts in rough set theory, and the approximations will change dynamically over time. Incremental methods for updating approximations in rough set theory and its extension has been received much attention recently. This paper presents an approach for incrementally updating approximations of fuzzy rough sets in dynamic fuzzy decision systems when a ...

The notion of three-way decisions was originally introduced by the needs to explain the three regions of probabilistic rough sets. Recent studies show that rough set theory is only one of possible ways to construct three regions. A more general theory of three-way decisions has been proposed, embracing ideas from rough sets, interval sets, shadowed sets, three-way approximations of fuzzy sets, ...

Rough set concept is a methodology of information processing for relational databases. It unique uncertainty mathematics topic closely connected to fuzzy theory. When the rough combined with neutrosophic theory, an effective tool working indeterminacy arises. In this study, we defined multi-valued and matrix. Using separation measures, introduced new approach structure. We consider problem dete...

A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in va...