the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

To solve complicated problems in economics, engineering, and environment, we cannot successfully use classical methods because of various uncertainties typical for those problems. There are three theories: theory of probability, theory of fuzzy sets, and the interval mathematics which we can consider as mathematical tools for dealing with uncertainties. Uncertainties cannot be handled using tra...

The starting point of the paper is the (well-known)observation that the “classical” Rough Set Theory as introduced by PAWLAK is equivalent to the S5 Propositional Modal Logic where the reachability relation is an equivalence relation. By replacing this equivalence relation by an arbitrary binary relation (satisfying certain properties, for instance, reflexivity and transitivity) we shall obtain...

This paper concerns the modeling of imprecision, vagueness, and uncertainty in databases through an extension of the relational model of data: the fuzzy rough relational database, an approach which uses both fuzzy set and rough set theories for knowledge representation of imprecise data in a relational database model. The fuzzy rough relational database is formally defined, along with a fuzzy r...

Stochastic groundwater modeling involves the propagation of probabilistic uncertainty from model input parameters to model estimates, usually via a Monte Carlo method. With the increasing reliance upon expert knowledge to define model inputs, and both fuzzy set and possibility theories to characterize this expert knowledge, alternative means of executing model equations are needed. While the fu...

Since its inception in 1965, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found, for example, in artificial intelligence, computer science, medicine, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, and robotics. Mathematical developments have advan...

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...