New degrees for functions in (L, M)-fuzzy topological spaces based on (L, M)-fuzzy semiopen and (L, M)-fuzzy preopen operators

Article type: Research Article

Authors: Ghareeb, A.^{a; b; *} | Al-Omeri, Wadei F.^c

Affiliations: [a] Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt | [b] Department of Mathematics, College of Science, Al-Baha University, Al-Baha, Saudi Arabia | [c] Department of Mathematics, Al-Balqa Applied University, Salt, Jordan

Correspondence: [*] Corresponding author. A. Ghareeb. E-mail: [email protected].

Abstract: In this paper, we will introduce the notions of semiopenness, semicontinuity, preopenness, precontinuity, irresolutness and preirresolutness degree of functions in (L, M)-fuzzy topological spaces based on the implication operation. Their elementary properties in topology will be extended to the setting of (L, M)-fuzzy topology through graded concepts. Further we characterize and discuss their relationships with the degree of semi(pre)-compactness, semi(pre)-connectedness, Semi - T1, Pre - T1, Semi - T2, and Pre - T2.

Keywords: (L, M)-fuzzy topological space, semiopen function, semicontinuous function, irresolute function, semi-homomorphism, preopen function, precontinuous function, preirresolute function, pre-homomorphism

DOI: 10.3233/JIFS-18251

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 787-803, 2019