Novel group decision-making method based on interval-valued m-polar fuzzy soft expert information

In mathematical modeling and decision analysis, the multipolar uncertainty is prevalent and requires specialized approaches. The theory of m-polar fuzzy (mF, in short) set is a strong extension of the fuzzy set because of its feature for dealing with multi-polar information, and robust hybrid models such as mF soft sets and interval-valued mF soft sets have emerged for significant real-life multi-criteria decision-making applications. However, these models are limited when it comes to accommodating multiple decision-makers individually in some real situations that emphasize making the use of multi-polar, multi-agent, and multi-object approaches of uncertainty. For example, in the selection of a professor, different evaluation reports are considered from more than one expert. In contrast, the soft expert set model can deal with the opinions of multiple experts about available alternatives regarding multiple attributes but fails to accommodate intervalvalued mF knowledge. Motivated by these facts, in this research study, we introduce the notion of an interval-valued mF soft expert set (IVmFSE set) model, a multiple criteria group decision-making (MCGDM) approach, by integrating intervalvalued m-polar fuzziness with soft expert sets. The initiated hybrid model is an expert extension of the IVmF soft sets or an interval-valued extension of the mF soft expert sets. Moreover, we discuss properties of certain unary and binary operations and relations on IVmFSE sets (the 'AND' operation, the 'OR' operation, subset-relation, equality, complement, agree- and disagree-IVmFSE sets, union, and intersection) and illustrate these operations with numerical examples. Further, we implement the proposed theory in a group decision-making problem for the fabrication of upper limb prosthesis samples to visualize its importance and significance. We also design an algorithm to illustrate the procedure of the proposed method. Finally, to validate the aptitude and novelty of the proposed theory, we give its comparative analysis with some preexisting fuzzy theories, including mF soft expert sets and fuzzy soft expert sets, by applying them to a real-world problem in which nine upper limb prosthesis samples are considered, and the computed results depict that the optimal decision alternative is x(2).