Stronger Forms of Sensitivity for Induced Fuzzified Map. Issue 3 (2nd July 2020)

• Record Type: Journal Article
• Authors: Kumar, Praveen; Khan, Ayub
• Is Part Of: Fuzzy information and engineering. Volume 12:Issue 3(2020)
• Page Start: 381
• Page End: 391
• Publication Date: 2020-07-02
• Subjects: Zadeh's extension -- sensitivity -- strong sensitivity -- asymptotically sensitive -- cofinite sensitivity; Fuzzy systems -- Periodicals; Intelligent control systems -- Periodicals; 629.89
• DOI: 10.1080/16168658.2021.1915450
• Languages: English
• ISSNs: 1616-8658

Abstract

Abstract : Every dynamical system ( X, f ) on a compact metric space X induces a fuzzy dynamical system ( F ( X ), f ^ ), on the space of fuzzy sets F ( X ), by Zadeh's extension principle. In this paper we consider stronger forms of sensitivity, viz. strong sensitivity, asymptotic sensitivity, syndetic sensitivity, multi-sensitivity and cofinite sensitivity. Some examples are given to expound the interrelation between them. Our main concern here is to find the relationship between f and f ^ in terms of these forms of sensitivity. We Prove that these forms of sensitivity for f partially imply the same for f ^ and in other way we also get partial induction.