Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relat...

Symmetric Division Deg index is one of the 148 discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. Symmetric Division Deg index is defined by $$ SDD(G) = sumE left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right), $$ where $d_i$ is the degree of vertex $i$ in graph $G$. In th...

Using the method of generic continuity of set-valued mappings, this paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibria for multiobjective population games, when payoff functions are perturbed. More precisely, the paper investigates the continuity properties of the set of weakly Pareto-Nash equilibria and that of the set of Pareto-Nash equilibria under sufficiently smal...

In practice, some of information systems are based on dominance relations, and values of decision attribute are fuzzy. So, it is meaningful to study attribute reductions in ordered decision tables with fuzzy decision. In this paper, upper and lower approximation reductions are proposed in this kind of complicated decision table, respectively. Some important properties are discussed. The judgeme...

In this paper, we introduce the notion of double-framed fuzzy quotient lattice in a fuzzy lattice and then some basic properties are investigated. Characterizations of double-framed fuzzy quotient lattices are given. Using a collection of lattices, a double framed fuzzy quotient lattice is established. The notion of fuzzy quotient lattice relation on the family of all I double-framed fuzzy sub ...

In this paper, we introduce the notion of intuitionistic fuzzy equipotent lattice in a fuzzy lattice and then some basic properties are investigated. Characterization of intuitionistic fuzzy equipotent lattices are given. Using a collection of lattices, an intuitionistic fuzzy equipotent lattice is established. The notion of fuzzy equipotent lattice relation on the family of all intuitionistic ...

The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces a...

–Rough set theory is a powerful tool to extract classification rules from a database that usually is given in the form of information system in which information is expressed by attributes and their values. In this paper, we first evaluate every example data (tuple) using, not a singleton but, a fuzzy number (or, suppose the original information system is along with such fuzzy numbers), due to ...