A method for solving bipolar fuzzy complex linear systems with real and complex coefficients

Abstract

An extensive variety of human decision making is based on two-sided or bipolar cognitive assessment of a positive side and a negative side. Zhang’s bipolar fuzzy set is represented as

$$\begin{aligned} \{\forall ~ (x, y) ~|~ (x, y) \in [-1,0] \times [0,1]\}. \end{aligned}$$

The multiagent decision analysis is based on bipolar judgment of a positive side and a negative side. In this paper, we consider the issues posed by bipolar fuzzy linear systems (BFLSs) and bipolar fuzzy complex linear (BFCL) systems of equations with real and complex coefficients. Primarily, we find the solution of the BFLS of equations by the resort into two parts: one is negative$(\bullet )$ and other is positive$(\star )$ $n \times n$ linear fuzzy systems; to this aim, we use $n \times n$ bipolar fuzzy center system and $2n \times 2n$ bipolar fuzzy width system. We describe the fundamentals of proposed method with the aid of $n= 2,5$-dimensional numerical examples, and we get the weak and strong solutions of the system. Subsequently, we describe a technique to solve BFCL systems of equations whose coefficients are real and complex by a pair of positive$(\star )$ and negative$(\bullet )$ $n \times n$ real and complex crisp linear systems; to this aim, we use bipolar fuzzy complex center and width. Ultimately, we use our proposed technique to solve a current flow circuit which is defined in terms of a BFCL system with complex coefficients, and we get the unknown current in the form of bipolar fuzzy complex number.