Currently, the utilization of semi-overlap functions has become increasingly widespread in constructing fuzzy rough sets. However, intuitionistic set models, grounded functions, and their applications have not been studied. Therefore, this paper introduces a novel β⋆-covering model that builds upon applies it to address multi-criteria decision-making challenges. Initially, we present concepts (semi-grouping) subsequently develop four β⋆-neighborhood operators. Next, propose some new models...

Axiomatic characterization is the foundation of L-fuzzy rough set theory: axiom sets approximation operators guarantee existence relations or coverings that reproduce operators. characterizations based on have not been fully explored, although those studied thoroughly. Focusing three pairs widely used covering-based operators, we establish an for each them, and their independence examined. It should be noted operator different from its crisp counterpart, with either new stronger included in version.

Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to stratified L-convex SL-CS) are defined. The first functor enables us prove that CS can be embedded in SL-CS as reflective subcategory. second coreflective subcategory when satisfying multiplicative condition. By comparing and well known Lowen (between topological L-topological spaces), we exhibit difference between (stratified L-)topological L-)convex spaces.

The theory of abstract convexity exists in many mathematical branches such as algebra, topology and order. fuzzification is one important directions towards the discussion convexity. (L, M)-convex spaces very general fuzzy since it includes oth er convexities its special case. In this paper, we shall introduce a subcategory study property. This called enriched denoted by ELMCS. main results are: (1) ELMCS topological category; (2) coreflective category spaces; (3) M-fuzzifying convex...

The rough sets based on L-fuzzy relations and coverings are the two most well-known sets. Quite recently, we prove that some of these can be unified into one framework—rough L-generalized fuzzy neighborhood systems. So, study system has more general significance. Axiomatic characterization is foundation set theory: axiom approximation operators guarantee existence relations, reproduce operators. In this paper, shall give an axiomatic system-based particular, will seek to characterize...

In this paper, a connectedness in stratified L-generalized convergence spaces, is defined and discussed. This different from Jäger's connectedness, particular, it for L-subsets however crisp subsets. Thus give partly answer to question 2016: define lattice-valued spaces. Then the basic properties of are

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, $L$-fuzzy neighborhoodsystem is introduced then a pair lower upperapproximation operators based on it are defined discussed. It proved that these approximation include system-based operators, $L$-fuzzyrelation-based $L$-fuzzycovering-based as their specialcircumstances. Therefore, research generalizedneighborhood has more generalsignificance. addition, when system...