Decision-making analysis based on bipolar fuzzy N-soft information

Abstract

In this research article, we present a new framework for handling imprecisely acquired bipolar information along with parameterized graded descriptions. The formal model that implements all these desirable features is called bipolar fuzzy N-soft set (also BFNS$_\text {f}$S for brevity). We discuss basic operations of our proposed hybrid model, including weak complement, bipolar fuzzy complement, weak bipolar fuzzy complement, extended union, restricted union, extended intersection, restricted intersection, and BFNS$_\text {f}$S associated with a threshold. Furthermore, we illustrate some standard algebraic operations on BFNS$_\text {f}$ numbers and produce related results. Moreover, we develop BFNS$_\text {f}$-TOPSIS methods for the solution of multi-attribute decision-making (MADM) and multi-attribute group decision-making (MAGDM) problems defined by bipolar fuzzy N-soft information. In the MAGDM version of the solution, we use the bipolar fuzzy N-soft weighted average operator to aggregate the decisions of all experts according to the performance of alternatives and traits of the attributes. We evaluate the normalized Euclidean distance of alternatives and BFNS$_\text {f}$ positive and negative ideal solutions, respectively, and relative closeness index to find the most optimal solution. Moreover, three algorithms are proposed to handle MADM problems in the environment of BFNS$_\text {f}$S. To demonstrate the effectiveness of the algorithms and the BFNS$_\text {f}$-TOPSIS approach for MADM problems, a numerical application regarding the selection of best psychiatrist in Karachi is presented. The validity of the proposed BFNS$_\text {f}$-TOPSIS technique for MAGDM is illustrated through an example which examines the best construction company in West Midlands. Finally, we conduct a comparative study with the bipolar fuzzy TOPSIS method to endorse the qualities of the proposed model.