A New Interval-Valued Fuzzy Set Knowledge and Accuracy Measure with Applications in Multi-Criteria Decision-Making and Recognizing Patterns

Fuzzy sets with interval values are a generalization of conventional fuzzy sets. The theoretical understanding of interval-valued fuzzy sets rests under the presumption that each element possesses a single real-valued truth membership degree that falls within a specified interval. Information and knowledge measures are crucial in the theory of interval-valued fuzzy sets. The primary aim of this manuscript is to explore these measures within the context of interval-valued fuzzy sets. This manuscript introduces an axiomatically-defined knowledge measure for interval-valued fuzzy sets. Numerous numerical instances including organized syntax contrast, inconsistency, and the calculation of criterion values within an interval-valued fuzzy framework are used to demonstrate the effectiveness and dependability of the recommended knowledge measure. Using the suggested knowledge measure, an accuracy measure is constructed in the interval-valued fuzzy domain. The recommended accuracy measure is applied to pattern detection challenges. A revised version of the Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) method, utilizing the proposed accuracy measure, is introduced to address Multi-Criteria Decision-Making (MCDM) challenges within a interval fuzzy context. Lastly, a case study is provided to demonstrate the process of selecting the optimal wastewater treatment technology for handling wastewater.