Enhancing ELECTRE I Method with Complex Spherical Fuzzy Information

Abstract

AbstractThis article is concerned to delineate the strategic approach of ELiminating Et Choice Translating REality (ELECTRE) method for multi-attribute group decision-making (MAGDM) in terms of complex spherical fuzzy sets. The feasible, well-suited, and marvelous structure of complex spherical fuzzy set compliments the decision-making efficiency and ranking calibre of ELECTRE I approach to present a beneficial and supreme aptitude strategy for MAGDM. Beside the proposed methodology, a few non-fundamental properties of complex spherical fuzzy weighted averaging (CSFWA) operator inclusive of shift invariance, homogenous, linearity, and additive property are also explored. The proposed procedure validates the individual opinions into an acceptable form by the dint of CSFWA operator and the aggregated opinions are further analyzed by the proposed complex spherical fuzzy- ELECTRE I (CSF-ELECTRE I) method. Within the consideration of proposed methodology, normalized Euclidean distances of complex spherical fuzzy numbers are also contemplated. In CSF-ELECTRE I method, the score, accuracy, and refusal degrees determine the concordance and discordance sets for each pair of alternatives to calculate the concordance and discordance indices, respectively. Based on aggregated outranking matrix, a decision graph is constructed to attain the ELECTREcally outranked solutions and the best alternative. This article provides supplementary approach at the final step to profess a linear ranking order of the alternatives. The versatility and feasibility of the presented method are embellished with two case studies from the business and IT field. Moreover, to ratify the intensity and aptitude of the presented methodology, we provide a comparative study with complex spherical fuzzy-TOPSIS method.