基于区间值毕达哥拉斯Sugeno-Weber Softmax算子的WASPAS多属性决策方法

WASPAS Multi-Attribute Decision-Making Method Based on Interval Valued Pythagorean Sugeno-Weber Softmax Operator

摘要: 针对属性值为区间值毕达哥拉斯模糊数且权重信息完全未知的决策问题，本文提出基于Sugeno-Weber Softmax算子的区间值毕达哥拉斯模糊多属性决策方法。首先，定义了基于Sugeno-Weber三角模的区间值毕达哥拉斯模糊数运算法则。其次，为考虑属性间的优先关系，提出四种区间值毕达哥拉斯模糊Sugeno-Weber Softmax平均和几何集成算子并讨论所提算子的幂等性、有界性和单调性等性质。为确定属性的权重信息，提出基于区间值毕达哥拉斯模糊PSI (Preference Selection Index)方法确定属性的客观权重。进一步提出基于Sugeno-Weber Softmax算子的区间值毕达哥拉斯模糊WASPAS (Weighted Aggregated Sum Product Assessment)方法确定备选方案的排序。通过实际案例验证所提方法的有效性及合理性，并由比较分析和参数分析讨论所提方法的鲁棒性和优越性。

Abstract: This paper addresses decision-making problems characterized by attribute values expressed as interval-valued Pythagorean fuzzy numbers (IVPFNs) and completely unknown weight information. We propose a novel interval-valued Pythagorean fuzzy multi-attribute decision-making (MADM) methodology based on the Sugeno-Weber Softmax operator. Firstly, arithmetic operations for IVPFNs are defined utilizing the Sugeno-Weber t-norm and t-conorm. Secondly, to account for priority relationships among attributes, four Pythagorean fuzzy Sugeno-Weber Softmax averaging and geometric aggregation operators are introduced. Fundamental properties of these operators, including idempotency, boundedness, and monotonicity, are rigorously investigated. To resolve the unknown weight issue, an objective weight determination method for attributes is developed using the Pythagorean fuzzy Preference Selection Index approach. Furthermore, an enhanced Pythagorean fuzzy WASPAS (Weighted Aggregated Sum Product Assessment) method, integrated with the proposed Sugeno-Weber Softmax operators, is presented to determine the ranking of alternatives. The effectiveness and rationality of the proposed methodology are validated through an empirical case study. Comparative analysis and parameter sensitivity analysis further demonstrate its superior robustness and performance over existing methods.