Study of Intuitionistic Fuzzy Super Matrices and Its Application in Decision Making

Shah, S; Tewary, R; Sahni, M; Sahni, R; Leon Castro, E; Merigo Lindahl, J

Study of Intuitionistic Fuzzy Super Matrices and Its Application in Decision Making

Shah, S Tewary, R Sahni, M Sahni, R Leon Castro, E Merigo Lindahl, J

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Publisher:: Horizon Research Publishing
Publication Type:: Journal Article
Citation:: Mathematics and Statistics, 2023, 11, (5), pp. 753-766
Issue Date:: 2023-09-01

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Field	Value	Language
dc.contributor.author	Shah, S
dc.contributor.author	Tewary, R
dc.contributor.author	Sahni, M
dc.contributor.author	Sahni, R
dc.contributor.author	Leon Castro, E
dc.contributor.author	Merigo Lindahl, J https://orcid.org/0000-0002-4672-6961
dc.date.accessioned	2024-05-20T03:43:54Z
dc.date.available	2024-05-20T03:43:54Z
dc.date.issued	2023-09-01
dc.identifier.citation	Mathematics and Statistics, 2023, 11, (5), pp. 753-766
dc.identifier.issn	2332-2071
dc.identifier.issn	2332-2144
dc.identifier.uri	http://hdl.handle.net/10453/179057
dc.description.abstract	Recent developments in fuzzy theory have been of great use in providing a framework for the understanding of situations involving decision-making. However, these tools have limitations, such as the fact that multi-attribute decision-making problems cannot be described in a single matrix. Fuzzy and intuitionistic fuzzy matrices are important tools for these types of problems since they can help to solve them. We presented a new super matrix theory in the intuitionistic fuzzy environment in order to overcome these restrictions. This theory is able to readily cope with problems that include numerous attributes while addressing belongingness and non-belonging criteria. Hence, it introduces a fresh perspective into our thinking, which in turn enables us to generalize our findings and arrive at more sound conclusions. For the purpose of theoretical development, we define a variety of different kinds of intuitionistic fuzzy super matrices and present a number of essential algebraic operations in order to make it more applicable to situations that take place in the real world. One multi-criteria decision-making problem based on super matrix theory is discussed here for the sake of validating and illustrating the applicability of the established findings. In addition to this, we suggest a general multi-criteria decision-making algorithm that makes use of intuitionistic fuzzy super matrix theory. This algorithm is more dynamic than both intuitionistic fuzzy matrix and fuzzy super matrix theories, and it can be applied to the resolution of a wide range of issues. The validation of the proposed theory is done by taking a real-world example to show its importance.
dc.language	en
dc.publisher	Horizon Research Publishing
dc.relation.ispartof	Mathematics and Statistics
dc.relation.isbasedon	10.13189/ms.2023.110501
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Study of Intuitionistic Fuzzy Super Matrices and Its Application in Decision Making
dc.type	Journal Article
utslib.citation.volume	11
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	open_access	*
dc.date.updated	2024-05-20T03:43:53Z
pubs.issue	5
pubs.publication-status	Published
pubs.volume	11
utslib.citation.issue	5

Abstract:

Recent developments in fuzzy theory have been of great use in providing a framework for the understanding of situations involving decision-making. However, these tools have limitations, such as the fact that multi-attribute decision-making problems cannot be described in a single matrix. Fuzzy and intuitionistic fuzzy matrices are important tools for these types of problems since they can help to solve them. We presented a new super matrix theory in the intuitionistic fuzzy environment in order to overcome these restrictions. This theory is able to readily cope with problems that include numerous attributes while addressing belongingness and non-belonging criteria. Hence, it introduces a fresh perspective into our thinking, which in turn enables us to generalize our findings and arrive at more sound conclusions. For the purpose of theoretical development, we define a variety of different kinds of intuitionistic fuzzy super matrices and present a number of essential algebraic operations in order to make it more applicable to situations that take place in the real world. One multi-criteria decision-making problem based on super matrix theory is discussed here for the sake of validating and illustrating the applicability of the established findings. In addition to this, we suggest a general multi-criteria decision-making algorithm that makes use of intuitionistic fuzzy super matrix theory. This algorithm is more dynamic than both intuitionistic fuzzy matrix and fuzzy super matrix theories, and it can be applied to the resolution of a wide range of issues. The validation of the proposed theory is done by taking a real-world example to show its importance.

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http://hdl.handle.net/10453/179057