Robot Selection Problem via Fuzzy TOPSIS Method Using Novel Distance and Similarity Measure for Generalized Fuzzy Numbers with Unequal Heights

Background: Mega multinational companies are highly dependent on robots to handle the maximum of their machinery workload, which significantly reduces human labor and saves valuable time as well. However, as vital as the role of robots is, a much more challenging task is its selection. Moreover, the robots need to be evaluated on the grounds of different specifications and their ease of handling, which results in a smooth and work-efficient environment.Objective: The prime objective of this paper is to devise a fruitful decision-making model for a robot selection problem, which utilizes a multi-criteria decision-making method known as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The TOPSIS method is based on the newly defined distance measure involving generalized fuzzy numbers with unequal heights (GFNUHs).Methodology/Approach: At first, we define a novel distance measure based on the “expected value†and “variance†of GFNUHs, where both the parameters are evaluated with the help of the α-cut method. We then also give the expression for the distance-based similarity measure and investigate some of their properties. Both the distance and the similarity measure(s) are then validated for their effectiveness through a hypothetical case study of pattern recognition. Moreover, we consider 10 different bunches of generalized fuzzy numbers (GFNs) and present a comparative study with the already established measures to establish the efficiency and superiority of our proposed measures. Finally, the distance measure is deployed in the TOPSIS method, which facilitates suitable robot selection by an automobile company.Findings/Results: A comparison of results for the proposed distance measure and the similarity measure with the existing ones is presented which proves that the proposed measure(s) are effective and usable.Novelty/Value: The evaluation of expected value and variance of GFNUHs with the help of α-cut technique is a completely original idea showcased in this paper and its improved version of TOPSIS for GFNUHs as discussed shall add a new direction in the realm of decision-making.