Toward Effective Uncertainty Management in Decision-Making Models Based on Type-2 Fuzzy TOPSIS

Abstract

Over the past century, there has been a dramatic increasing interest in the multi-criteria group decision-making (MCGDM) technique, with a considerable amount of studies published regarding it. One of the well-known approaches in the MCGDM paradigm is Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The integration of the TOPSIS method with fuzzy set theory has proven to be successful in various applications. Recently, a wide array of publications has proposed implementing a type-2 fuzzy set with TOPSIS. However, the additional degree of uncertainty represented by type 2 has largely been ignored, especially in a few specific mathematical operations in the model. We propose constructing interval type-2 fuzzy membership functions (IT2 MFs) using interval-based data gathered from a survey, where this is used to generate a new scale to represent ratings for each alternative. This procedure utilized all information gathered from decision makers. In addition, we present a complete algorithm for TOPSIS based on IT2 fuzzy sets (IT2 FSs) which preserve the interval-based form output. The output in the form of intervals offers decision makers (DMs) with more detailed information, enabling them to make more nuanced decisions. This can include cautious decisions when intervals are wider and overlapping. Although understanding the exact meaning of these intervals and their widths in a decision-making context is challenging, this paper introduces a systematic method for connecting input uncertainty to output uncertainty in the TOPSIS technique. This approach establishes a solid foundation for future research. Thus far, no other researchers have suggested a data-driven method that combines TOPSIS with fuzzification and provides intervals as the final output.