Logical Entropy of Partitions for Interval-Valued Intuitionistic Fuzzy Sets

Abstract

In this study, we present the ideas of logical entropy and logical conditional entropy for partitions in interval-valued intuitionistic fuzzy sets, and we establish their fundamental properties. First, we establish the definitions of logical entropy and logical conditional entropy, demonstrating their key characteristics and relationships. We then define logical mutual information and explore its properties, providing a comprehensive understanding of its behavior within the context of interval-valued intuitionistic fuzzy sets. Additionally, we propose the concept of logical divergence of states defined on interval-valued intuitionistic fuzzy sets and examine its properties in detail, including its application and implications for understanding state transitions within these fuzzy sets. Finally, we extend our study to dynamical systems, introducing the logical entropy of such systems when modeled with intervalvalued intuitionistic fuzzy sets. We present several results related to this extension, highlighting the applicability and relevance of logical entropy in analyzing and understanding the behavior of dynamical systems. Overall, this paper offers a thorough exploration of logical entropy, mutual information, and divergence within the framework of interval-valued intuitionistic fuzzy sets, providing new insights and potential applications in various fields.

Keywords

• interval-valued intuitionistic fuzzy sets
• logical entropy.