This work presents an alternative non-fuzzy perspective on the method proposed in ‘The Properties of Fuzzy Tensor and Its Application’ paper for solving multiple attribute group decision-making problems (MAGDM). We analyze the general form of the fuzzy synthetic evaluation model introduced in the paper and demonstrate that it can be interpreted as an extension of the weighted average (WA) method within probability theory rather than a truly fuzzy approach. Through numerical examples, we illustrate that the so-called fuzzy formulation can be understood as probability-weighted results, thereby showcasing the feasibility and efficiency of explaining their method through probability theory. Furthermore, we highlight the impact of specific numerical data characteristics in the conducted examples, where a highly recognized item can significantly influence the final ranking, thereby diminishing the fundamental role of fuzzy reasoning in their numerical applications. We introduced a bias-eliminating tensor ranking formula to improve fairness and robustness in MAGDM. Tests on two numerical examples showed results aligning with established methods, confirming the reliability and accuracy of our model. These findings highlight its potential as a scalable and effective tool for complex decision-making.

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Scalable Tensor Ranking in Simplifying Multi-criteria Group Decision Making

  • Lingping Kong,
  • Jan Zdražil,
  • Abhishek Kumar,
  • Zhonghai Bai,
  • Shu-Chuan Chu

摘要

This work presents an alternative non-fuzzy perspective on the method proposed in ‘The Properties of Fuzzy Tensor and Its Application’ paper for solving multiple attribute group decision-making problems (MAGDM). We analyze the general form of the fuzzy synthetic evaluation model introduced in the paper and demonstrate that it can be interpreted as an extension of the weighted average (WA) method within probability theory rather than a truly fuzzy approach. Through numerical examples, we illustrate that the so-called fuzzy formulation can be understood as probability-weighted results, thereby showcasing the feasibility and efficiency of explaining their method through probability theory. Furthermore, we highlight the impact of specific numerical data characteristics in the conducted examples, where a highly recognized item can significantly influence the final ranking, thereby diminishing the fundamental role of fuzzy reasoning in their numerical applications. We introduced a bias-eliminating tensor ranking formula to improve fairness and robustness in MAGDM. Tests on two numerical examples showed results aligning with established methods, confirming the reliability and accuracy of our model. These findings highlight its potential as a scalable and effective tool for complex decision-making.