Decision making under incomplete data: Intuitionistic multi fuzzy ideals of near-ring approach

Nadia  Batool; Sadaqat  Hussain; Nasreen  Kausar; Mohammed  Munir; Rita Yi Man Li; Salma  Khan

doi:10.31181/dmame04012023b

Authors

Nadia Batool Department of Mathematics, University of Baltistan Skardu, Gilgit Baltiistan 16100, Pakistan
Sadaqat Hussain Department of Mathematics, University of Baltistan Skardu, Gilgit Baltiistan 16100, Pakistan
Nasreen Kausar Department of Mathematics, Faculty of Arts ans Sciences, Yildiz Technical University, Istanbul, Turkey https://orcid.org/0000-0002-8659-0747
Mohammed Munir Department of Mathematics, Government Postgraduate College 22010, Khyber Pakhtunkhwa, Pakistan
Rita Yi Man Li Department of Economics and Finance, Hong Kong Shue Yan University, Hong Kong, China https://orcid.org/0000-0002-4582-8659
Salma Khan Department of Mathematics and Statistics Hazara University Mansehra, 21120, Khyber Pakhtunkhwa, Pakistan https://orcid.org/0000-0003-1840-2764

DOI:

https://doi.org/10.31181/dmame04012023b

Keywords:

Intuitionistic Fuzzy Set, Near-ring, Fuzzy Multi Near-ring, Intuitionistic multi fuzzy Near-ring, Ideals, fuzzy multi ring

Abstract

Real-world data is often partial, uncertain, or incomplete. Decision making based on data as such can be addressed by fuzzy sets and related systems. This article studies the intuitionistic multi-fuzzy sub-near rings and Intuitionistic multi-fuzzy ideals of near rings. It presents some of the elementary operations and relations defined on these structures. The concept of level subsets and support of the Intuitionistic multi-fuzzy sub-near ring is also presented. It looks into and demonstrated a few characteristics of intuitionistic multi-fuzzy near-rings and ideals. This research advances fuzzy set theory, which is often applied to problems involving pattern recognition and multiple criterion decision-making. Thus, the results may be beneficial to artificial intelligence related research. Alternatively, the intuitionistic multi-fuzzy approach may be applied to vector spaces and modules or extended to inter-valued fuzzy systems.

Real-world data is often partial, uncertain, or incomplete. Decision making based on data as such can be addressed by fuzzy sets and related systems. This article studies the intuitionistic multi-fuzzy sub-near rings and Intuitionistic multi-fuzzy ideals of near rings. It presents some of the elementary operations and relations defined on these structures. The concept of level subsets and support of the Intuitionistic multi-fuzzy sub-near ring is also presented. It looks into and demonstrates a few characteristics of intuitionistic multi-fuzzy near-rings and ideals. This research advances fuzzy set theory, which is often applied to problems involving pattern recognition and multiple criterion decision-making. Thus, the results may be beneficial to artificial intelligence related research. Alternatively, the intuitionistic multi-fuzzy approach may be applied to vector spaces and modules or extended to inter-valued fuzzy systems.

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