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  4. Enhancing decision-making with picture fuzzy Einstein interactive operator: An application in multiple attribute group decision-making

Enhancing decision-making with picture fuzzy Einstein interactive operator: An application in multiple attribute group decision-making

MMC.
2025;
Volume 12, Number 3
: pp. 724–731
Received: January 13, 2025
Revised: June 16, 2025
Accepted: June 18, 2025

Abdullah S. R. G., Ahmad M. Z.  Enhancing decision-making with picture fuzzy Einstein interactive operator: An application in multiple attribute group decision-making.  Mathematical Modeling and Computing. Vol. 12, No. 3, pp. 724–731 (2025)

Authors:
  1. S. R. G. Abdullah
  2. M. Z. Ahmad
1
Institute of Engineering Mathematics, Universiti Malaysia Perlis
2
Institute of Engineering Mathematics, Universiti Malaysia Perlis

Recent advancements in Picture Fuzzy Numbers (PFNs) have significantly contributed to the field of fuzzy systems.  However, the conventional operational rules (ORs) for PFNs have limitations in practical decision-making scenarios.  In particular, traditional picture fuzzy aggregation methods, such as the picture fuzzy Einstein aggregation operators, while useful in uncertain contexts, do not adequately account for interactions among the degrees of positive, neutral, and negative memberships.  This oversight can lead to unsatisfactory outcomes in real-world decision-making.  To address these challenges, this paper introduces novel interactive Einstein ORs for PFNs and proposes a new aggregation operator, the Picture Fuzzy Einstein Interactive Weighted Geometric (PFEIWG) operator.  Moreover, the proposed operator is applied to the multiple attribute group decision making (MAGDM) problem to evaluate its reliability and demonstrate its superiority through a detailed comparative analysis with established methods.

picture fuzzy numbers
operational rules
aggregation operators
Einstein operators
multiple attribute group decision making
comparative analysis
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