Utilizing 2-tuple linguistic complex picture fuzzy set with TOPSIS method under unknown weight information for multi-criteria decision-making problems

Abstract

Many decision problems depend on linguistic opinions that exhibit uncertain and directional (phase/ angle) information, which standard models capture only partially. Yet efficient decision support requires a combined treatment of these features. Existing complex picture fuzzy sets and 2-tuple linguistic term sets do not jointly encode linguistic evaluations on the complex plane with complete aggregation and ranking procedures. This manuscript introduces an inventive notion, termed 2-tuple linguistic complex picture fuzzy sets, showcasing progress and expansion beyond traditional complex picture fuzzy sets and 2-tuple linguistic term sets. The distinctive feature of 2TLCPFS lies in its remarkable capacity to address both uncertainty and periodicity simultaneously. This is achieved by integrating a phase term that extends the 2TLCPFS range from the real plane to the complex plane, encompassing the unit disk. We explain and authenticate the operational characteristics of 2TLCPFS. Moreover, a novel aggregation operator, such as the 2TLCPF weighted averaging operator, is introduced within the 2TLCPFS framework. The application of this operator, combined with the TOPSIS method, is demonstrated in the context of a multi-criteria decision-making problem. A numerical example reinforces this demonstration, underscoring the validity and efficacy of the proposed method. Additionally, this article explores situations where both decision-makers and criterion weights are undisclosed, underscoring the benefits of the proposed generalized aggregation technique. The work probes the impact of weight perturbations and conducts a comparison analysis, which validates the model's robustness and superiority.