Novel knowledge and accuracy measures for interval-valued fuzzy sets with applications in cluster analysis and pattern detection

Interval-valued fuzzy sets are the generalization of classical fuzzy sets. The assumption behind the theoretical interpretation of interval-valued fuzzy sets is that each element has exactly one real-valued truth membership degree from an interval. Information and knowledge measures play a major part in the interval-valued fuzzy set theory. This manuscript’s main objective is to investigate the information and knowledge measures in an interval-valued fuzzy context. A knowledge measure for interval-valued fuzzy sets is proposed axiomatically in this manuscript. The effectiveness and consistency of the proposed knowledge measure are demonstrated by numerical examples for structured linguistic comparison, ambiguity, and criteria weights computation in the interval-valued fuzzy context. An accuracy measure in interval-valued fuzzy-context is developed using the proposed knowledge measure. Apart from that, a similarity and a dissimilarity measure in an interval-valued fuzzy context are proposed. The suggested accuracy, similarity, and dissimilarity measures are used to solve cluster analysis and pattern detection issues. Additionally, a case study on the damage caused by floods and heavy rainfall in India between 2012 and 2021 is discussed, and the data obtained from this study are used to create clusters using the suggested accuracy measure. Furthermore, the accuracy, similarity, and dissimilarity measures that have been proposed, are used to address the pattern detection problems.