A New Notion of Fuzzy Function Ideal Convergence

Dimitrios Georgiou () and Georgios Prinos
Additional contact information
Dimitrios Georgiou: Department of Mathematics, University of Patras, 265 00 Patras, Greece
Georgios Prinos: Department of Mathematics, University of Patras, 265 00 Patras, Greece

Mathematics, 2024, vol. 12, issue 2, 1-13

Abstract: P.M. Pu and Y.M. Liu extended Moore-Smith’s convergence of nets to fuzzy topology and Y.M. Liu provided analogous results to J. Kelley’s classical characterization theorem of net convergence by introducing the notion of fuzzy convergence classes. In a previous paper, the authors of this study provided modified versions of this characterization by using an alternative notion of convergence of fuzzy nets, introduced by B.M.U. Afsan, named fuzzy net ideal convergence. Our main scope here is to generalize and simplify the preceding results. Specifically, we insert the concept of a fuzzy function ideal convergence class, L , on a non-empty set, X , consisting of triads ( f , e , I ) , where f is a function from a non-empty set, D , to the set FP ( X ) of fuzzy points in X , which we call fuzzy function, e ∈ FP ( X ) , and I is a proper ideal on D , and we provide necessary and sufficient conditions to establish the existence of a unique fuzzy topology, δ , on X , such that ( f , e , I ) ∈ L iff f I -converges to e , relative to the fuzzy topology δ .

Keywords: fuzzy set; fuzzy topology; fuzzy function ideal convergence; fuzzy function ideal convergence class (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/2/260/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/2/260/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:2:p:260-:d:1318363

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().