Combination of Fuzzy-Weighted Zero-Inconsistency and Fuzzy Decision by Opinion Score Methods in Pythagorean m-Polar Fuzzy Environment: A Case Study of Sing Language Recognition Systems

Abstract

In the fuzzy multicriteria decision-making approach, a committee of decision-makers is usually involved in the assessment of the suitability of different alternatives based on the evaluation criteria by using linguistic terms and their equivalent fuzzy numbers. In this context, researchers have developed the Pythagorean fuzzy set (PFS) to overcome the limitation of intuitionistic fuzzy set in the description of decision-maker information such as imposing restrictions on the representation of membership and nonmembership grades. On the one hand, PFS still does not have sufficient ability and flexibility to deal with such issues. On the other hand, multipolar technology is used to operate large-scale systems in real-life situations, especially in dealing with dissatisfaction and indeterminacy grades for the alternatives of the reference set. Thus, [Formula: see text]-polar fuzzy set is utilized and applied with other fuzzy sets because of its remarkable ability as a tool for depicting fuzziness and uncertainty under multipolar information in many circumstances. With the practical features of [Formula: see text]-polar fuzzy set in combination with PFS, this paper employs it to extend two considerable MCDM methods, namely, fuzzy decision by opinion score method and fuzzy-weighted zero inconsistency. Such extensions, called Pythagorean [Formula: see text]-polar fuzzy-weighted zero-inconsistency (Pm-PFWZIC) method and Pythagorean [Formula: see text]-polar fuzzy decision by opinion score method (Pm-PFDOSM), are formulated to weight the evaluation criteria followed by alternative ranking progressively. The research methodology is presented as follows. Firstly, the mechanisms of Pm-PFWZIC and Pm-PFDOSM are formulated and integrated into the development phase. Secondly, the description of the real-world case study of the evaluation and benchmarking of the sign language recognition systems is adapted and presented. The result of Pm-PFWZIC shows that the criterion of ‘finger movements’ has the highest weight amongst the rest of the criteria, whereas ‘misclassification error’ has the lowest weight. In the ranking results, a variation of ranking is scored by each expert, and group decision-making is applied to solve the individual ranking variety. The robustness of the formulated methods is evaluated using systematic ranking, sensitivity analysis and comparison analysis.