Comparison of fuzzy and crisp decision matrices: An evaluation on PROBID and sPROBID multi-criteria decision-making methods

The use of multi-criteria decision-making (MCDM) methods to select the most appropriate one from a range of alternatives considering multiple criteria is a suitable methodology for making informed decisions. When constructing a decision or objective matrix (DOM) for MCDM procedure, either crisp numerical values or fuzzy linguistic terms can be used. A review of relevant literature indicates that decision experts often prefer to give linguistic terms (instead of crisp numerical values) based on their domain knowledge, to establish a fuzzy DOM. However, previous research articles have not adequately studied the selection between fuzzy and crisp DOM in MCDM, especially under the context of assessing the financial performance (FP) of listed firms - a notably complex decision-making problem. As such, the primary motivation of this study is to bridge this research gap through comparative analyses of fuzzy and crisp DOM in MCDM. Along this path, and in order to handle fuzzy DOM, this work also proposes two new fuzzy MCDM methods: fuzzy preference ranking on the basis of ideal-average distance (PROBID) and fuzzy sPROBID (simpler PROBID), extending the applicability of the original crisp PROBID and sPROBID methods. Moreover, for the first time in the literature, this work compares the FP rankings obtained using fuzzy MCDM methods with an objective benchmark we have identified, i.e., the real-life stock return (SR)-based ranking. The case study of ranking the FP of 32 listed firms demonstrates that the fuzzy MCDM methods produce higher correlation results with the SR-based ranking. The results also suggest that the proposed fuzzy sPROBID method with triangular fuzzy DOM performs the best for assessing the FP of firms in terms of Spearman's rank correlation coefficient with the SR-based ranking. Overall, the contributions of this work are three-fold: first, it proposes two new fuzzy MCDM methods (i.e., fuzzy PROBID and fuzzy sPROBID); second, it advances the application of fuzzy MCDM methods in assessing and ranking the FP of listed firms to make rational investment decisions in the financial market; third, it studies the selection between fuzzy and crisp DOM through comparisons with an objective benchmark.