A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making

Jeevaraj Selvaraj and Abhijit Majumdar
Additional contact information
Jeevaraj Selvaraj: Department of Mathematics, Atal Bihari Vajpayee Indian Institute of Information Technology and Management, Gwalior 474015, India
Abhijit Majumdar: Department of Textile and Fibre Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India

Mathematics, 2021, vol. 9, issue 21, 1-11

Abstract: Ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs) is an important task for solving real-life Decision-Making problems. It is a potential area of research that has attracted the researchers working in fuzzy mathematics. Researchers worldwide are looking for a unique ranking principle that can be used to discriminate any two arbitrary IVIFNs. Various ranking functions on the set of IVIFNs have been proposed. However, every method has some drawbacks in ranking arbitrary IVIFNs due to the partial ordering. This paper introduces a new ranking principle for comparing two arbitrary IVIFNs by defining a new score function based on the non-membership value of IVIFNs. In this paper, firstly, the limitations of a few well-known and existing ranking methods for IVIFNs have been discussed. Secondly, a new non-membership score on the class of IVIFNs has been introduced. Thirdly, the superiority of the proposed score function in ranking arbitrary IVIFNs over the existing methods has been demonstrated. Finally, the proposed non-membership score function has been utilized in interval-valued intuitionistic fuzzy TOPSIS (IVIF-TOPSIS) using numerical examples.

Keywords: interval-valued intuitionistic fuzzy number; non-membership score function; MCDM; IVIF-TOPSIS; IVIF-MCDM; defuzzification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/21/2647/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/21/2647/ (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:9:y:2021:i:21:p:2647-:d:660452

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 ().