Affiliations: Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
Correspondence:
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Corresponding author. Shumaiza, Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan. E-mail: shumaiza00@gmail.com.
Abstract: The q-rung picture fuzzy sets serve the fuzzy set theory as a competent, broader and accomplished extension of q-rung orthopair fuzzy sets and picture fuzzy sets which exhibit excellent performance in modeling the obscure data beyond the limits of existing approaches owing to the parameter q and three real valued membership functions. The accomplished strategy of VIKOR method is established on the major concepts of regret measure and group utility measure to specify the compromise solution. Further, TOPSIS method is another well established multi-criteria decision-making strategy that finds out the best solution with reference to the distances from ideal solutions. In this research study, we propose the innovative and modified versions of VIKOR and TOPSIS techniques using the numerous advantages of q-rung picture fuzzy information for obtaining the compromise results and rankings of alternatives in decision-making problems with the help of two different point-scales of linguistic variables. The procedure for the entropy weighting information is adopted to compute the normal weights of attributes. The q-rung picture fuzzy VIKOR (q-RPF VIKOR) method utilizes ascending order to rank the alternatives on the basis of maximum group utility and minimum individual regret of opponent. Moreover, a compromise solution is established by scrutinizing the acceptable advantage and the stability of decision. In the case of TOPSIS technique, the distances of alternatives to ideal solutions are determined by employing the Euclidean distance between q-rung picture fuzzy numbers. The TOPSIS method provides the ranking of alternatives by considering the descending order of closeness coefficients. For explanation, the presented methodologies are practiced to select the right housing society and the suitable industrial robot. The comparative results of the proposed techniques with four existing approaches are also presented to validate their accuracy and effectiveness.
