Mathematics and Statistics Vol. 11(5), pp. 753 - 766
DOI: 10.13189/ms.2023.110501
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Study of Intuitionistic Fuzzy Super Matrices and Its Application in Decision Making

Siddharth Shah ¹, Rudraharsh Tewary ¹, Manoj Sahni ^1,*, Ritu Sahni ¹, Ernesto Leon Castro ², Jose Merigo Lindahl ^3
1 Department of Mathematics, School of Technology, Pandit Deendayal Energy University, India
² Faculty of Economics and Administrative Sciences, Universidad Católica de la Santísima Concepción, Chile
³ University of Technology Sydney, Australia

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.

KEYWORDS
Fuzzy Matrices, Intuitionistic Fuzzy Matrices, Intuitionistic Fuzzy Super Matrices, Multi-criteria Decision Making

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Siddharth Shah , Rudraharsh Tewary , Manoj Sahni , Ritu Sahni , Ernesto Leon Castro , Jose Merigo Lindahl , "Study of Intuitionistic Fuzzy Super Matrices and Its Application in Decision Making," Mathematics and Statistics, Vol. 11, No. 5, pp. 753 - 766, 2023. DOI: 10.13189/ms.2023.110501.

(b). APA Format:
Siddharth Shah , Rudraharsh Tewary , Manoj Sahni , Ritu Sahni , Ernesto Leon Castro , Jose Merigo Lindahl (2023). Study of Intuitionistic Fuzzy Super Matrices and Its Application in Decision Making. Mathematics and Statistics, 11(5), 753 - 766. DOI: 10.13189/ms.2023.110501.