Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making

The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their...

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Autores principales: Ajay, D., Selvachandran, Ganeshsree, Aldring, J., Thong, Pham Huy, Son, Le Hoang, Cuong, Bui Cong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10090759/
https://www.ncbi.nlm.nih.gov/pubmed/37362734
http://dx.doi.org/10.1007/s11042-023-14532-9
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author Ajay, D.
Selvachandran, Ganeshsree
Aldring, J.
Thong, Pham Huy
Son, Le Hoang
Cuong, Bui Cong
author_facet Ajay, D.
Selvachandran, Ganeshsree
Aldring, J.
Thong, Pham Huy
Son, Le Hoang
Cuong, Bui Cong
author_sort Ajay, D.
collection PubMed
description The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their corresponding aggregation operators. We introduce the operational laws for exponential and Einstein exponential SFSs in which the base values are crisp numbers and the exponents (weights) are spherical fuzzy numbers. Some of the properties and characteristics of the proposed operations are then discussed. Based on these operational laws, some new aggregation operators for the SFS model, namely Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. Finally, a decision-making algorithm based on these newly introduced aggregation operators is proposed and applied to a multi-criteria decision making (MCDM) problem related to ranking different types of psychotherapy.
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spelling pubmed-100907592023-04-14 Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making Ajay, D. Selvachandran, Ganeshsree Aldring, J. Thong, Pham Huy Son, Le Hoang Cuong, Bui Cong Multimed Tools Appl Article The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their corresponding aggregation operators. We introduce the operational laws for exponential and Einstein exponential SFSs in which the base values are crisp numbers and the exponents (weights) are spherical fuzzy numbers. Some of the properties and characteristics of the proposed operations are then discussed. Based on these operational laws, some new aggregation operators for the SFS model, namely Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. Finally, a decision-making algorithm based on these newly introduced aggregation operators is proposed and applied to a multi-criteria decision making (MCDM) problem related to ranking different types of psychotherapy. Springer US 2023-04-12 /pmc/articles/PMC10090759/ /pubmed/37362734 http://dx.doi.org/10.1007/s11042-023-14532-9 Text en © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Ajay, D.
Selvachandran, Ganeshsree
Aldring, J.
Thong, Pham Huy
Son, Le Hoang
Cuong, Bui Cong
Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making
title Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making
title_full Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making
title_fullStr Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making
title_full_unstemmed Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making
title_short Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making
title_sort einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10090759/
https://www.ncbi.nlm.nih.gov/pubmed/37362734
http://dx.doi.org/10.1007/s11042-023-14532-9
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