The study of symmetry is one the most important and beautiful themes uniting various areas contemporary arithmetic. Algebraic structures are useful in pure mathematics for learning a geometrical object’s symmetries. In this paper, we introduce new concepts an algebraic structure called BCI-algebra, where present bipolar fuzzy (closed) BCI-positive implicative ideals BCI-commutative BCI-algebras...

We present a new financial decision making model by using the fuzzy generalized probabilistic weighted averaging (FGPWA) operator. The main advantage of this new approach is that it is able to deal with probabilities (objective information) and weighted averages (subjective information) in the same formulation. Moreover, it is also able to deal with an uncertain environment that can be assessed...

This paper presents an efficient fuzzy neural system which consists of modular neural networks combined by the fuzzy integral with ordered weighted averaging (OWA) operators. The ability of the fuzzy integral to combine the results of multiple sources of information has been established in seL'eral preL'ious works. The key point of this paper is to formalize modular neural networks as informati...

Triangular intuitionistic fuzzy number (TIFN) is a more generalized platform for expressing imprecise, incomplete, and inconsistent information when solving multi-criteria decision-making problems, as well as for expressing and reflecting the evaluation information in several dimensions. In this paper, the TIFN has been applied for solving multi-criteria decision-making (MCDM) problems, first, ...

This paper proposes the concepts of a neutrosophic number and a trapezoidal neutrosophic number (TNN), the basic operational relations of TNNs, and the score function of TNN. Then, we develop a trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator and a trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator to aggregate TNN information and investigate their pro...

Bipolar fuzzy soft set theory, which is a very useful hybrid in decision making problems, mathematical model that has been emphasized especially recently. In this paper, the concepts of (α,β)-cuts, first type semi-strong second strong inverse semi-weak (α,β)-cuts and weak bipolar sets were introduced together with some their properties. addition, distinctive properties between established. More...

The concept of an antipodal bipolar fuzzy graph of a given bipolar fuzzy graph is introduced. Characterizations of antipodal bipolar fuzzy graphs are presented when the bipolar fuzzy graph is complete or strong. Some isomorphic properties of antipodal bipolar fuzzy graph are discussed. The notion of self median bipolar fuzzy graphs of a given bipolar fuzzy graph is also introduced.

We introduce the notion of bipolar fuzzy Lie sub-superalgebras (resp. bipolar fuzzy ideals) and present some of their properties. First we investigate the properties of bipolar fuzzy Lie sub-superalgebras and bipolar fuzzy ideals under homomorphisms of Lie superalgebras. Next we study bipolar fuzzy bracket product, solvable bipolar fuzzy ideals and nilpotent bipolar fuzzy ideals of Lie superalg...

We study a stochastic model of influence where agents have yes-no inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators. This allows to study situations where the influence process resembl...

The definition of ordered weighted averaging (OWA) operators and their applications in decision making are reviewed. Also, some generalizations of OWA operators are studied and then, the notion of 2-symmetric OWA operators is introduced. These generalizations are illustrated by some examples.