In this paper the notions of bipolar valued fuzzy subsemigroup, bipolar valued fuzzy bi-ideal, bipolar valued fuzzy (1,2)ideal and bipolar valued fuzzy ideal in a Γ-semigroup have been introduced. Some important characterizations are also obtained. Mathematics Subject Classification: 20M12, 03F55, 03E72

a concept related to the spectrum of a graph is that of energy. the energy e(g) of a graph g is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of g . the laplacian energy of a graph g is equal to the sum of distances of the laplacian eigenvalues of g and the average degree d(g) of g. in this paper we introduce the concept of laplacian energy of fuzzy graphs. ...

As a generalization of a fuzzy finite state machine, the notion of a bipolar fuzzy finite state machine is introduced. Also, the concepts of a bipolar (immediate) successor, a bipolar exchange property and a bipolar subsystem are introduced. Some related properties are discussed. A condition for a bipolar fuzzy finite state machine to satisfy the bipolar exchange property is established. A char...

In our real life, bipolar fuzzy theory is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. In this paper, we provide a general algebraic framework for handling bipolar information by combining the theory of bipolar fuzzy sets with hemirings. First, we present the concepts of b...

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-m...

We introduce the concept of Cayley bipolar fuzzy graphs and investigate some of their properties. We present some interesting properties of bipolar fuzzy graphs in terms of algebraic structures. We also discuss connectedness in Cayley bipolar fuzzy graphs.

A fuzzy bipolar relation is a relation defined by a fuzzy bipolar condition, which could be interpreted as an association of a constraint and a wish. In this context, the extension of the relational division operation to bipolarity is studied in this paper. Firstly, we define a bipolar division when the involved relations are crisp. Then, we define, from the semantic point of view, several form...

Fuzzy Graphs are having numerous applications in problems like Network analysis, Clustering, Pattern Recognition and Neural Networks. The analysis of properties of fuzzy graphs has facilitated the study of many complicated networks like Internet. In this paper we study the structures of complement of many important fuzzy graphs such as Fuzzy cycles, Blocks etc. The complement of fuzzy graphs wi...

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...

In this paper, the notion of the normal level sub HX group is introduced. We discuss the properties of normal level sub HX groups of a bipolar fuzzy normal HX subgroup of a HX group under homomorphism and anti-homomorphism. AMS Subject Classification (2000): 20N25, 03E72, 03F055, 06F35, 03G25. Keywordsfuzzy set, bipolar fuzzy set, bipolar fuzzy HX subgroup, bipolar fuzzy normal HX subgroup, lev...