(2, M)- Double fuzzifying topological spaces and (2, M)-double fuzzifying preproximity spaces

Article type: Research Article

Authors: Abd El-latif, A.A.^{a; b; *} | Khalaf, Mohammed M.^c

Affiliations: [a] Department of Mathematics, Faculty of Science and Arts at Belqarn, Sabt Al-Alaya, University of Bisha, Kingdom of Saudi Arabia | [b] High Institute of Computer King Marriott, Alexandria, Egypt | [c] High Institute of Engineering and Technology King Marriott, Alexandria, Egypt

Correspondence: [*] Corresponding author. A.A. Abd El-latif. E-mails: ahmeda73@yahoo.com and abdultif@ub.edu.sa.

Abstract: In this paper, (2, M)-double fuzzifying topology as a generalized (2, M)-fuzzifying topology introduced by Höhle [7] is introduced. The relations between (2, M)-double fuzzy topology and (2, M)-double fuzzifying topology are studied. Also, we provided the definition of (2, M)-double fuzzifying preproximity structure. Not only that we studied the properties of these new notions, but we have also generated (2, M)-double fuzzifying topology from (2, M)-double fuzzifying preproximity. Finally, we introduced (2, M)-double fuzzifying preproximially continuous mapping which it used in more properties.

Keywords: (2, M)-double fuzzifying topology, (2, M)-double fuzzifying preproximity, double fuzzifying preproximally continuous mapping

DOI: 10.3233/JIFS-17691

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 4643-4655, 2018