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Circular Intuitionistic Fuzzy ELECTRE III Model for Group Decision Analysis
Volume 34, Issue 4 (2023), pp. 881–908
Pub. online: 17 November 2023      Type: Research Article      Open accessOpen Access
Received
1 February 2023
Accepted
1 November 2023
Published
17 November 2023

Abstract

ELECTRE III is a well-established outranking relation model used to address the ranking of alternatives in multi-criteria and multi-actor decision-making problems. It has been extensively studied across various scientific fields. Due to the complexity of decision-making under uncertainty, some higher-order fuzzy sets have been proposed to effectively model this issue. Circular Intuitionistic Fuzzy Set (CIFS) is one such set recently introduced to handle uncertain IF values. In CIFS, each element of the set is characterized by a circular area with a radius, r and membership/non-membership degrees as the centre. This paper introduces CIF-ELECTRE III, an extension of ELECTRE III within the CIFS framework, for group decision analysis. To achieve this, we define extensions for the group decision matrix and group weighting vector based on CIFS conditions, particularly focusing on optimistic and pessimistic attitudes. These attitudinal characters of the group of actors are constructed using conditional rules to ensure that each element of the set falls within the circular area. Parameterized by $\alpha \in [0,1]$ for the net score degree, we conduct an extensive analysis of group decision-making between optimistic and pessimistic attitudes. To illustrate the applicability of the proposed model, we provide a numerical example of the stock-picking process. Additionally, we conduct a comparative analysis with existing sets and perform sensitivity analyses to validate the results of the proposed model.

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Biographies

Yusoff Binyamin
https://orcid.org/0000-0002-3899-1474
binyamin@umt.edu.my

B. Yusoff received his BSc and MSc degrees in mathematics from Universiti Malaysia Terengganu, Malaysia, in 2007 and 2010, respectively. He obtained his PhD from University of Barcelona, Spain, in 2017. Currently, he is a senior lecturer with the Department of Mathematics, Universiti Malaysia Terengganu. His current research interests are concerned with decision analysis under uncertainty, soft aggregation processes and optimization – broadly falling into the area of computational mathematics and operational research. Specifically, his major foci are: fuzzy set theory and higher order fuzzy sets, decision analysis, and aggregation operators for information fusion. B. Yusoff is a member of PERSAMA, MSORSM, and ASASI.

Pratama Dian
https://orcid.org/0000-0001-8427-3644

D. Pratama is a PhD student at the Faculty of Ocean Engineering Technology and Informatics at the Universiti Malaysia Terengganu (UMT). He received his MSc in mathematics, University of Gadjah Mada (UGM), in 2016. His areas of research are fuzzy sets with their extensions, decision-making theory, and fuzzy algebra.

Kilicman Adem
https://orcid.org/0000-0002-1217-963X

A. Kilicman is a full professor at the Department of Mathematics and Statistics at Universiti Putra Malaysia. He received his bachelor and master degrees from Hacettepe University in 1989 and 1991, respectively, Turkey. He obtained his PhD from University of Leicester in 1995, UK. He started to work in UPM in 1997 and has actively involved several academic activities in the Faculty of Science as well as in the Institute of Mathematical Research (INSPEM). A. Kilicman is also member of some Professional Associations; PERSAMA, SIAM, IAENG, AMS, European Maths. His research areas include differential equations, functional analysis and topology, as well as fuzzy topology, fractional analysis and applications.

Abdullah Lazim
https://orcid.org/0000-0002-6646-4751

L. Abdullah received his PhD in information technology from Universiti Malaysia Terengganu, in 2004. Currently, he is a professor and head of Data and Digital Sciences Research Cluster at the Universiti Malaysia Terengganu. His research and expertise focus on fuzzy set theory of mathematics, decision making, applied statistics, and their applications to social ecology, environment, health sciences and management. He has been ranked among the world’s top 2% scientists since 2019 by Stanford University in the field of artificial intelligence and image processing. L. Abdullah is a member of the IEEE Computational Intelligence Society, and a member of International Society on Multiple Criteria Decision Making.


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© 2023 Vilnius University
Open access article under the CC BY license.

Keywords
ELECTRE III group decision analysis circular intuitionistic fuzzy set optimistic and pessimistic attitudes

Funding
We also acknowledge with gratitude the support from the Ministry of Higher Education Malaysia, which provided funding under the Fundamental Research Grant Scheme (FRGS) (FRGS/1/2023/STG06/UMT/02/4), and from Universiti Malaysia Terengganu.

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