Affiliations: Department of Mathematics, University of the Punjab, Lahore, Pakistan
Correspondence:
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Corresponding author. Muhammad Riaz, Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan. E-mail: mriaz.math@pu.edu.pk
Abstract: In multi-attribute group decision-making (MAGDM) problems, there exist some multi-polarity for the attributes and criteria. Sometimes in real life situations, we deal with the both membership and non-membership grades for the attributes in the presence of multi-polarity. For this purpose, we change verbally stated information into mathematical language with the help of uncertain linguistic variables to deal with the ambiguities and uncertainties. In that case, we construct some extensions from the existing hybrid structures of fuzzy set to handle these types of problems. That’s why from the prevailing concepts of cubic set and m-polar fuzzy set, we innovate the concept of cubic m-polar fuzzy set (CMPFS). We investigate its numerous operations with the help of examples. With the enthusiasm of CMPFS, we establish certain aggregation operators based on cubic m-polar fuzzy numbers (CMPFNs) namely Cubic m-polar fuzzy weighted averaging (CMPFWA), Cubic m-polar fuzzy ordered weighted averaging (CMPFOWA) and Cubic m-polar fuzzy hybrid averaging (CMPFHA) operators corresponding to R-order and P-order, simultaneously. Using the score function and accuracy function a relation is proposed, through which we can compare the CMPFNs. This manuscript presents a novel approach for treating ambiguities based on the application of land selection using linguistic variables in CMPF decision theory. An algorithm based on MAGDM is intended for a given agricultural project, which will produce results according to the proposed operators one by one. Furthermore, a comparative analysis is listed to demonstrate the difference, advantages, validity, simplicity, flexibility and superiority to the proposed operators.
