A New Parametrically Extended Exponential Information Measure on Fuzzy Set Framework

Objective: To generalize an existing fuzzy information measure and verify its fundamental characteristics. Methods: Both objective and descriptive methodologies, as well as problem-posing and problem-solving techniques, have been employed. New fuzzy information measures are established using a set of attributes proposed by De Luca and Termini as a standard. Findings: The fuzzy information measure is widely used for characterizing and quantifying fuzzy unpredictability and vagueness. A novel parametrically extended exponential information measure on a fuzzy set framework has been presented to address this. Once the validity of the proposed information measure is established, several features are also provided. Novelty: A new parametrically extended exponential information measure on fuzzy set framework has been introduced. The unique quality of the suggested fuzzy information measure is found in its parameters. The proposed measure of information is substantial and justifiable; it reduces to the present information measure if the parameters are substituted with a suitable value. Furthermore, certain notable and interesting properties of this information measure have been studied. Consequently, from an application standpoint, the stated information measure is more adaptable. Mathematics Subject Classification 2020: 94 D05 Keywords: Fuzzy set, Information measure, Fuzzy entropy, Parametric exponential measure, Uncertainty