Molodtsov initiated soft set theory that provided a general mathematicalframework for handling with uncertainties in which we encounter the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as bipolar fuzzy set theory.The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in ...

In this article, we develop a new method and an algorithm to solve a system of fuzzy relation equations. We first introduce a solution-base-matrix and then give a tractable mathematical logic representation of all minimal solutions. Next, we design a new universal algorithm to get them. Two simplification rules are found to simplify the solution-base-matrix. We show that a polynomial time algor...

Systems which use a fuzzy rule base and an inference mechanisms are quite frequently used in many applications. Fuzzy rules and inference mechanisms can be described by a system of fuzzy relation equations. A solution to a given system of fuzzy relation equations can serve us a proper model of fuzzy rules (fuzzy model for short). But only two particular solutions, let us call them disjunctive a...

In this paper, we eneralize our previous results regarding approximate solutions of fuzzy relation e uations [lo] to systems offuzzy relation equations. By employing the e uality index proposed by Gottwald 731, we introduce a goodness measure of the performance of approximate sAutions and derive a lower bound and an upper bound of solvability of s stems of fuzzy relation equations. We also show...

Bipolar max-? equations, with ? a triangular norm, have recently become popular research topic embedded in the broad field of fuzzy relational equations. In this paper, we lift work from restrictive setting real unit interval — obfuscating underlying lattice-theoretical essence to general complete distributive symmetric residuated lattices, allowing build upon vast body knowledge on unipolar su...

In this paper, we define the concept of a bipolar fuzzy cosets of a bipolar fuzzy HX subgroup, bipolar anti fuzzy HX subgroup, bipolar fuzzy middle coset of a bipolar fuzzy HX subgroup and bipolar anti fuzzy HX subgroup, conjugate bipolar fuzzy HX subgroup, conjugate bipolar anti fuzzy HX subgroup and discussed some of its properties with the examples. Further we define the level subsets and lo...

In this paper, the notion ofgraph operationsdisjunction and symmetric difference on bipolar fuzzy graphs are defined and it is proved that the new graph is a bipolar graph. Furthermore,the new concepts of bipolar fuzzy graphs calledupperstrong and lower strongbipolar fuzzy graphare introduced and some related </...

In this paper we investigate the System of fuzzy relation equations with inf → composition. We base on the knowledge of he system of fuzzy relation equations with sup−∗-composition. First, the general notions are explained and then are shown the smallest and maximal solutions. Finally is investigated a simple criterion of solvability for a special case of fuzzy sets.