A framework for choosing an appropriate fuzzy set extension in modeling

Abstract

Real-world problems contain uncertainties. Fuzzy Set Theory (FST) is a popular approach to model these uncertainties. FST extensions (FSTEs) have been offered for better modeling of the uncertainties having different natures. It is essential to use the most suitable FSTE in modeling to achieve reasonable, reliable, and realistic results. However, FSTEs are preferred without stating a clear reason in most of the studies. This makes the quality and the reliability of the results of these studies questionable. Because, to obtain reliable models, the dynamics of the problem and environment should be well understood, the scenario should be well analyzed, and the assumptions and limitations of FSTE theories should be well known. In this study, a guiding framework for choosing the most suitable FSTE in modeling to obtain reliable, applicable, and efficient results is proposed. The framework consists of two parts: (i) conceptual analysis of the uncertainty types and FSTEs, (ii) a guiding procedure fed by the first step for deciding the most suitable FSTE. The procedure is illustrated by multiple numerical examples to make its benefits clear. Conceptual analysis and numerical examples show that some FSTEs have some advantages over the others for specific scenarios and problem types. For example, NS is more suitable than PFS for modeling the problems other than Multi-Criteria Decision-Making (MCDM). Another contribution of this study is showing that it is very important to choose the simplest possible FSTE to obtain reliable and applicable models.