| Summary: | Fuzzy set theory (FST) is a popular 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. There are various FST extensions in the literature that consider such indeterminacy cases in modeling. Since some parts of the theories of FST extensions overlap with some others, 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. Most of the FST extensions have been developed in line with the requirements of Multi-Criteria Decision-Making (MCDM) problem thus assumptions and limitations of these theories can cause reliability issues for the fuzzy models of the problems different from MCDM. 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 the continuous systems, MCDM problems, and different problems from MCDM. The analysis has also been illustrated on numerical examples to make findings clear. The analysis showed that some extensions have clear advantages over others for specific scenarios. This study is an invitation to fulfill the gap in the field of fuzzy modeling of the different problems from MCDM.
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