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 research study, we present a novel frame work for handling bipolar fuzzy soft information by combining bipolar fuzzy soft sets with graphs. We introduce several basic notions concerning bipolar fuzzy soft graphs and investigate some related properties. We also consider the application of the bipolar fuzzy soft graphs. In particular, three efficient algorithms are developed to solve mult...

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm...

We have defined fuzzy bipolar soft sets and basic operations of union, intersection and complementation for fuzzy bipolar soft sets. The algebraic properties of fuzzy bipolar soft sets are discussed. The concept of bipolar fuzzy soft set is also given and the equivalence of both structures is established. An application of fuzzy bipolar soft sets in decision making problems is presented with th...

We introduce the notion of bipolar fuzzy soft Lie subalgebras and investigate some of their properties. We also introduce the concept of an (∈,∈ ∨q)-bipolar fuzzy (soft) Lie subalgebra and present some of its properties.

We propose in this paper new tools for dealing with bipolar fuzzy spatial information: particular geometrical objects are defined, as well as measures such as cardinality and perimeter, represented as bipolar fuzzy numbers. A definition of distance from a point to a bipolar fuzzy set is introduced as well. These definitions are based on mathematical morphology operators, recently proposed in th...

The first aim to this paper is introduce the notions of bipolar fuzzy soft metric space and (D-)metric space. In order define these concepts, concept points has been brought literature have examined in detail. Moreover, sequences cauchy were defined some their properties examined. addition all this, many examples are given better understand concepts features studied contribute a understanding p...

In this paper we introduced the space of   bounded and   convergent difference sequence of fuzzy soft real numbers and the space of  lacunary   statistically convergent different sequence of fuzzy soft real numbers relating these concepts some theorem are derive. Keyword Fuzzy soft real number,   bounded,   convergent and  lacunary   statistically convergent.