A BCF–CRITIC–WASPAS method for green supplier selection with cross-entropy and Archimedean aggregation operators.

Bipolar complex fuzzy set (BCFS) is an enlargement of the bipolar fuzzy set and complex fuzzy set. A bipolar complex fuzzy number (BCFN) is used to represent both the bipolarity of ambiguity and bipolarity of periodicity semantics. This paper develops an integrated BCF–CRITIC–WASPAS methodology to elucidate the multi-criteria decision-making (MCDM) problems with bipolar complex fuzzy (BCF) data. Firstly, we propose the idea of cross-entropy of BCFSs followed by the introduction of some Archimedean operations between the BCFNs. Secondly, we discuss some BCF-Archimedean weighted aggregation operators with the proposed Archimedean aggregation operators that are generalizations of many renowned operators' namely algebraic operator, Einstein operator, Hamachar operator and Frank operator to combine the BCF information. Thirdly, a procedure is given to estimate the decision expert's weights using proposed cross-entropy measure of BCFSs. Since cross-entropy measure quantifies the degree of uncertain information and hence it reflects the influence of each expert. Fourthly, criteria weights are estimated through CRITIC (criteria importance through inter-criteria correlation) method which is a well-known objective method based on aggregated score values of options, intensity contrast of every criteria and conflict among attributes. Further, a green supplier selection (GSS) problem is taken to show the applicability of the developed methodology in real decision problems. We also exhibit a sensitivity investigation with diverse parameter values and criteria weights sets to examine the stability of proposed approach. Finally, we draw attention towards a comparison between the proposed approach and the extant methods to show its superiority. [ABSTRACT FROM AUTHOR]