Fuzzy Modeling of non-MCDM Problems Under Indeterminacy

Abstract

Fuzzy set theory (FST) is a useful approach for modeling the uncertainties of real-life problems. In some cases, uncertainty level of the events may not be determined surely because of some environmental factors. This is named “incomplete information” case and the hesitation level about the uncertainty is represented with the indeterminacy concept. There are various FST extensions in the literature that consider indeterminacy in modeling. These FST extensions consider similar scenarios, and some parts of the theories overlap with some others so the theories and the nature of considered scenarios must be understood well to obtain reliable results. Nevertheless, most of the studies in the literature do not conceptually analyze the nature of the uncertainty and decides an FST extension as a pre-step of the study without expressing an apparent reason. Therefore, the quality of the obtained results becomes questionable. Moreover, these FST extensions have been developed in line with the requirements of Multi-Criteria Decision-Making (MCDM) problem so, assumptions and the limitations of these theories can cause reliability issues for the fuzzy models of non-MCDM problems and continuous systems. In the scope of this study, capabilities, advantages, and disadvantages of well-known FST extensions that consider indeterminacy are conceptually analyzed and compared in line with the needs of modeling of non-MCDM problems and continuous systems. The analysis has also been illustrated on numerical examples to make findings clear. The analysis showed that, some extensions have clear advantages over others in terms of applicability, ease of calculation and scenario comprehensiveness. This study builds a preliminary step for a guiding approach for the selection of the most reliable FST extension in fuzzy modeling. Besides, it is an invitation to fulfill the gap in the field of fuzzy modeling of non-MCDM problems.