A robust aggregation operator for multi-criteria decision-making method with bipolar fuzzy soft environment

Abstract

Molodtsov initiated soft set theory that provided a general mathematical<br />framework 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.<br />The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in considering many problems that contain uncertainties. In present study, aggregation of bipolar fuzzy soft numbers have<br />so far not yet been applied for ranking of alternatives in decision-making problems.<br />To this propose, bipolar fuzzy soft weighted arithmetic averaging (BFSWAA) operator, bipolar fuzzy soft weighted geometric averaging (BFSWGA) operator<br />have been used to compare two bipolar fuzzy soft numbers (BFSNs) for aggregating different bipolar fuzzy soft input arguments in bipolar fuzzy soft environment.<br />Then, their related properties have been investigated.<br />Finally, a practical example for selection of alternatives is given to demonstrate<br />the utility and application of the proposed work.