Intuitionistic fuzzy sets and their variants
Nour Abed Alhaleem; Abd Ghafur Ahmad
Abstract
In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' ...
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In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' with a mapping f:NR → NR^', a relation between the intuitionistic fuzzy normed ideal I of NR and the intuitionistic fuzzy normed ideal f(I) (the image of I) of NR^' will been obtained with the support of their (α,β)-level subsets.
Neutrosophic sets and their variants
Jamiatun Nadwa Ismail; Zahari Rodzi; Hazwani Hashim; Nor Hashimah Sulaiman; Faisal Al-Sharqi; Ashraf Al-Quran; Abd Ghafur Ahmad
Abstract
DEMATEL serves as a tool for addressing multi-criteria decision-making problems, primarily by identifying critical factors that exert the most significant influence on a specific system. To enhance its capabilities in handling contextual decision problems, DEMATEL has been further developed through integration ...
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DEMATEL serves as a tool for addressing multi-criteria decision-making problems, primarily by identifying critical factors that exert the most significant influence on a specific system. To enhance its capabilities in handling contextual decision problems, DEMATEL has been further developed through integration with various other MCDM methods. The inherent reliance on direct input from experts for initial decision information in DEMATEL raises concerns about the potential limitations imposed by experts' domain knowledge and bounded rationalities. The effectiveness of decision-making can be compromised if the initial information provided by experts is deemed unreliable, leading to debatable outcomes. To address these challenges, this study proposes the incorporation of a Bonferroni mean aggregation operator within a Pythagorean neutrosophic environment, illustrated through a numerical example applied to DEMATEL. This integration is intended to fortify decision accuracy by introducing a more enhanced decision framework by developing a new normalized weighted Bonferroni mean operator for Pythagorean neutrosophic set aggregation (PN-NWBM). By integrating this operator, this study aims to alleviate the impact of unreliable initial information and enhance the overall reliability of decision outcomes thereby contributing to its improvement in decision making. Through the implementation of the Bonferroni mean aggregation operator, the study anticipates achieving a more comprehensive and accurate representation of decision factors as illustrated in the numerical example. This research includes a comparative and sensitivity analysis to thoroughly examine the implications and effectiveness of the proposed integration.
