On ideal convergence in measure for sequences of fuzzy valued functions

Article type: Research Article

Authors: Hazarika, Bipan^{; *}

Affiliations: Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, India

Correspondence: [*] Corresponding author. Bipan Hazarika, Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, India. E-mail: bipan.hazarika@rgu.ac.in.

Abstract: We introduce the notions of pointwise and uniform ideal convergence and kind of convergence lying between aforementioned convergence methods, namely, equi-ideal convergence of sequences of fuzzy valued functions and obtain various results related to these kinds of convergence and their representations of sequences of α-level cuts. We prove the ideal version of the Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space (X,M,μ). We also define the notion of ideal convergence in measure for sequences of fuzzy valued functions and prove some interesting results.

Keywords: Fuzzy valued function, ideal convergence, Egorov’s theorem, convergence in measure

DOI: 10.3233/JIFS-17237

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 5, pp. 5729-5740, 2018