A Pythagorean Fuzzy-Based MUNRA Method for Handling Uncertainty in Complex Decision Environments

Setiawansyah Setiawansyah

doi:10.58602/jaiti.v4i2.273

Setiawansyah Setiawansyah ^{(Corresponding Author)} Universitas Teknokrat Indonesia

DOI: https://doi.org/10.58602/jaiti.v4i2.273

Keywords: Pythagorean Fuzzy Sets, PF-MUNRA, Multi-Criteria Decision Making, Multi-normalization, Sensitivity Analysis

Abstract

This research develops the Pythagorean Fuzzy Multi-Normalized Rating Analysis (PF-MUNRA) method as a novel approach to address uncertainty and ambiguity in multi-criteria decision making. The main contribution of this study lies in the integration of Pythagorean Fuzzy Sets with a multi-normalization framework consisting of linear, vector, and non-linear normalization within a single decision-making model, enabling more flexible, comprehensive, and unbiased evaluation results compared to conventional single-normalization approaches. This method integrates the concept of Pythagorean Fuzzy Sets, which can represent degrees of membership and non-membership more flexibly, with the multi-normalization approach in MUNRA. Unlike previous studies that generally apply fuzzy environments and normalization techniques separately, the proposed PF-MUNRA simultaneously combines fuzzy uncertainty handling, multi-normalization mechanisms, and objective weighting to improve ranking consistency and decision robustness. In addition, weighted aggregation is used to produce more accurate preference values and reflect the relative importance of each criterion. The experimental results demonstrate that PF-MUNRA produces stable alternative rankings with Spearman correlation values ranging from 0.9464 to 1.0000 under various weight-change scenarios, indicating a very strong level of ranking consistency and robustness. Comparative analysis shows changes in alternative positions that reflect the capability of the proposed method to capture data complexity more effectively than the initial approach, while sensitivity analysis confirms that variations in criterion weights do not significantly affect the final ranking results, thereby proving that PF-MUNRA has high stability and reliability in dynamic and uncertain decision-making environments.

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