A hesitant fuzzy group decision-making framework with data credibility and strategic evaluations

This paper studies a linear programming (LP) and a multiple attribute decision-making (MADM) model with hesitant fuzzy numbers (HFNs) for solving group decision-making problems under uncertainty. We introduce a new type of HFN whose flexibility allows for its direct application to standard LP and MADM methods while facing credibility considerations or strategic reports from the experts evaluating the alternatives. These problems are initially formulated as models with uncertain, crisp data. Decision makers and experts are then invited to evaluate the data and propose HFNs representing its credibility. As a result, the crisp LP and MADM techniques are transformed into hesitant fuzzy LP (HFLP) and MADM (HF-MADM) models. The popular simplex method and the steps defining the corresponding MADM model, namely, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), are extended to implement the new HFNs. The strategic environment introduced allows for the definition of selection strategies and equilibria determined by the credibility profiles of experts providing evaluations. Developing a probabilistic framework applicable to these models would require defining convolution functions that become increasingly complex as further experts are added to the analysis. We present several numerical comparisons between the proposed hesitant fuzzy simplex and MADM results and those derived from the initial crisp models. The strategic importance of data credibility as a fundamental determinant of the optimality of results obtained will also be highlighted.