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A Novel Entropy Measure with its Application to the COPRAS Method in Complex Spherical Fuzzy Environment
Volume 34, Issue 4 (2023), pp. 679–711
Pub. online: 20 November 2023      Type: Research Article      Open accessOpen Access
Received
1 October 2022
Accepted
1 November 2023
Published
20 November 2023

Abstract

A complex spherical fuzzy set (CSFS) is a generalization of the spherical fuzzy set (SFS) to express the two-dimensional ambiguous information in which the range of positive, neutral and negative degrees occurs in the complex plane with the unit disk. Considering the vital importance of the concept of CSFSs which is gaining massive attention in the research area of two-dimensional uncertain information, we aim to establish a novel methodology for multi-criteria group decision-making (MCGDM). This methodology allows us to calculate both the weights of the decision-makers (DMs) and the weights of the criteria objectively. For this goal, we first introduce a new entropy measure function that measures the fuzziness degree associated with a CSFS to compute the unknown criteria weights in this methodology. Then, we present an innovative Complex Proportional Assessment (COPRAS) method based on the proposed entropy measure in the complex spherical fuzzy environment. Besides, we solve a strategic supplier selection problem which is very important to maximize the efficiency of the trading companies. Finally, we present some comparative analyses with some existing methods in different set theories, including the entropy measures, to show the feasibility and usefulness of the proposed method in the decision-making process.

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Biographies

Aydoğdu Ebru
https://orcid.org/0000-0002-2777-8651
eaydogdu@dho.edu.tr

E. Aydoğdu is an assistant professor at Turkish National Defense University since 2023. She received her MSc degree in mathematics from the Institute of Natural and Applied Sciences of Atatürk University, in 2012, and PhD degree from Kocaeli University, in 2019. She worked as a research assistant at Kocaeli University between 2012–2023. Her research interests include fuzzy set theory, soft set theory, fixed point theory, metric space and multiple criteria decision analysis.

Aldemir Başak
https://orcid.org/0000-0002-9073-9364
baldemir@aku.edu.tr

B. Aldemir graduated from the Department of Mathematics at Kocaeli University in 2018. She received her master’s degree in mathematics in 2021. She is a PhD student at Kocaeli University. She has been working as a research assistant in the Department of Mathematics at Afyon Kocatepe University since 2021. Her areas of interest are general topology, metric spaces, fuzzy set theory, soft set theory, fixed point theory, decision-making theory, and image processing.

Güner Elif
https://orcid.org/0000-0002-6969-400X
elif.guner@kocaeli.edu.tr

E. Güner graduated from the Department of Mathematics at Kocaeli University in 2015. She received her master’s degree in Mathematics in 2018 and her PhD degree in 2023 from Kocaeli University. She has been working as a research assistant in the Department of Mathematics at Kocaeli University since 2016. Her area of interests are general topology, metric spaces, fuzzy set theory, soft set theory, fixed point theory and decision-making theory.

Aygün Halis
https://orcid.org/0000-0003-3263-3884
halis@kocaeli.edu.tr

H. Aygün graduated from the Department of Mathematics at Karadeniz Technical University in 1989. He received his master’s degree in mathematics from Karadeniz Technical University, in 1992, and his PhD degree from City University in London. He worked as a research assistant at Karadeniz Technical University and Kocaeli University between 1989–1993 and 1993–1998, respectively. He worked as an assistant professor and associate professor at Kocaeli University between 1998–2000 and 2000–2006, respectively. He has been a professor in the Department of Mathematics at Kocaeli University since 2006. His area of interests are general topology, fuzzy topology, metric spaces, fuzzy set theory, (fuzzy) soft set theory, lattice theory, fixed point theory and decision-making theory.


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Keywords
complex spherical fuzzy sets COPRAS entropy multi-criteria group decision-making supplier selection

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