Solving the fuzzy 1-center problem with an innovative ranking method for fuzzy numbers

Taghi-Nezhad, Nemat Alalh; Taleshian, F.

doi:10.47974/JIM-2129

Open Access Research Article

Solving the fuzzy 1-center problem with an innovative ranking method for fuzzy numbers

^*Nemat Alalh Taghi-NezhadCorresponding authorntaghinezhad@gonbad.ac.irDepartment of Mathematics Faculty of Basic Sciences Gonbad Kavous UniversityGonbad Kavous, 4971799151, Iran0000-0002-4568-0527View full profile → , F. TaleshianFatemehtaleshian@gmail.comDepartment of Mathematics Faculty of Mathematical Sciences Shahrood University of TechnologyShahrood, IranView full profile →

* Corresponding author · click or hover a name for details

pp. 19–35Vol. 29Issue 1January 2026DOI: 10.47974/JIM-2129XML

Received:: 09 Jul 2024
Published Online:: 24 Nov 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2129
Pages:: 19–35

Abstract

For modeling real-world problems in mathematical form, we encounter uncertain and ambiguous quantities. In such situations, the efficient fuzzy set (FS) theory is employed to model these uncertain and ambiguous quantities in the form of fuzzy numbers (FNs). Since comparing FNs is essential in most optimization problems, we are compelled to utilize a suitable ranking method (RM). In this paper, the limitations of the RMs discussed in the literature are addressed, and a new revised approach for ranking various types of FNs is introduced. Additionally, it has been demonstrated that this innovative RM consistently ensures alignment among the rankings of fuzzy quantities and their associated representations. To illustrate the usages, advantages, and efficiency of the proposed method for ranking fuzzy numbers (RFN), we will present several examples, and several comparative examples are provided. Finally, in order to demonstrate the usage and applicability of our recommended RM, a practical application called the fuzzy 1-center problem is solved.

Keywords

Magnitude of fuzzy number Facility location problem Center problem

Subject Classifications

03B5268U9990C70

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