TOPSIS for Multi-expert Decision Making with Incomplete Fuzzy Linguistic Formal Contexts

This paper investigates multi-expert multi-attribute decision making under linguistic uncertainty with incomplete assessments. Building on a linguistic formal context with fuzzy objects, we develop a multi-expert extension to characterize trust-level associations between decision alternatives and linguistic concepts across experts. To address missing evaluations in an incomplete context, a maximum-similarity-based completion strategy is proposed to obtain a complete set of multi-expert fuzzy linguistic information. We then construct a multi-expert fuzzy linguistic-concept decision matrix. When expert weights are completely unknown, an optimization model based on the deviation-maximization principle is established to derive objective expert weights. Furthermore, the classical TOPSIS framework is adapted to the proposed decision matrix by specifying the determination of the positive and negative ideal solutions and introducing a pseudo-distance and a relative closeness measure between alternatives and the ideals, thereby enabling the ranking of alternatives and the selection of the most satisfactory one. A numerical example demonstrates the feasibility and effectiveness of the proposed approach for handling incomplete multi-expert fuzzy linguistic assessments.