Logic Operations for Assessment of Experts’ Weight in Fuzzy Rule-Based Systems

Abstract

In Multi-Criteria Group Decision-Making (MCGDM), the assignment of weights to decision-makers is a crucial but methodologically delicate step, especially when the group includes both human experts and artificial experts such as intelligent agents, Artificial Intelligences (AIs) or Large Language Models (LLMs). Existing weighting strategies are often either difficult to interpret or poorly suited to heterogeneous groups of evaluators. In this paper, we investigate a fuzzy rule-based approach to expert weighting, building on a previously introduced methodological framework and focusing here on its application-oriented validation. The proposed method models expert weighting as a Fuzzy Rule-Based System (FRBS) in which the relevant properties of the experts are represented by linguistic variables and combined through interpretable IF–THEN rules. In this way, weighting policies can be expressed transparently and adapted to the requirements of the decision domain. The framework produces normalised weights in the interval [0,1], which can then be incorporated into standard MCGDM aggregation procedures. To assess the operational behaviour of the approach, we consider an application involving the weighting of four open-source LLMs (apertus:8b, gemma4:e4b, mistral-small3.2:24b, and nemotron-cascade-2:30b) over three multilingual criteria (English, Italian, Portuguese) and two resource-side criteria (VRAM, open-sourceness), each modelled by three trapezoidal fuzzy sets and combined into a five-class output partition; the underlying dataset is built from 10 independent repetitions of 100 questions per model. Under a language-focused rule base of five IF–THEN rules, the four experts receive sharply separated normalised weights (0.003,0.149,0.301,0.548)—a top-to-bottom ratio above 180—whereas a combined linguistic/resource-aware rule base of five rules flattens the distribution to (0.227,0.360,0.222,0.191) and selects a different winner, demonstrating that policy changes are encoded explicitly in the output. A 100-run Kendall’s τ perturbation analysis confirms that the induced rankings remain stable under moderate input noise, particularly for the language-focused policy, while substituting the Product t-norm with Gödel or Lukasiewicz leaves the language-focused ranking invariant but induces rank reversals in the more discriminative resource-aware policy. A comparison against three independent baselines (Markov Logic Networks, ProbLog, TOPSIS) shows that ProbLog reproduces the FRBS ordering in both case studies, MLN compresses the normalised scores under its global probabilistic interaction, and TOPSIS diverges whenever conditional IF–THEN preferences must be encoded. A worked end-to-end aggregation example with three alternatives, three criteria, and four experts further shows that the FRBS weights propagate into a clear selection of the best alternative, with aggregated scores (S1,S2,S3)=(8.88,6.78,6.21). These results confirm both the practical usability of the method and its suitability for contexts in which multiple, potentially competing, objectives must be balanced explicitly. Overall, the paper provides an application-oriented study of an FRBS-based weighting scheme for artificial experts, highlighting its interpretability, adaptability, and potential relevance for contemporary MCGDM settings.