A critical review on theoretical drawbacks and mathematical incorrect assumptions in fuzzy OR methods: Review from 2010 to 2020

Abstract

As a practical approach for handling uncertainty, various fuzzy sets combined with traditional OR (operations research) methods have found huge applications. However, the fuzzy arithmetic is still a key challenge in this field. Moreover, some researchers have ignored the critical fact that traditional arithmetic operations will produce meaningless or questionable results when applied to fuzzy numbers in general. Thus, many papers in the field of OR have applied fuzzy numbers in a wrong way. Despite the very extensive use of combination of fuzzy sets with OR methods, literature shows that it has been less concentrated on the study of fallacy that may be generated using these methods. Motivated by some theoretical drawbacks and incorrect assumptions in fuzzy sets in conjunction with traditional methods in OR literature, the papers about these pitfalls are reviewed. The papers are included in this review, if they disclose directly a certain pitfall or incorrect assumption in the integration of fuzzy sets with OR methods. Because many other researchers may employ the same assumptions to solve real-life problems, the aim of this study is to make general users aware that many of these fuzzy arithmetic operations are incorrectly used and can lead to untrue and misleading consequences. In this paper, we review 102 papers published in 29 influential journals from 2010 to 25th, January, 2020. ISI Web of Science is adopted as the database of our review and the majority of selected journals (around 70%) are ranked as Q1 determined by SJR.11SCImago Journal & Country Rank (https://www.scimagojr.com/). To help scholars obtain quick information, the collected articles are summarized in a tabular layout. We hope that researchers who apply fuzzy-based methods in the field of OR would understand the serious problems and deep pitfalls associated with these models.