Type-2 intuitionistic fuzzy TODIM for intelligent decision-making under uncertainty and hesitancy

The classical TODIM considers the crisp numbers to handle the information. However, in a real-world applicative context, this information is bounded by noise and vagueness and hence uncertain. There are wide range of works in the literature which utilizes fuzzy sets to handle the uncertainty in the various dimensions. However, there is a constraint of hesitancy in such decision-making problems due to the involvement of various decision-makers. Also, in the TODIM method, decision-maker's bounded rationality and psychological behavior are also taken into consideration which adds up the hesitation and considers the problem with higher dimension of uncertainty. There are various applications of fuzzy TODIM using type-2 fuzzy numbers where uncertainty is being handled in more than one dimensions and also the introduction of intuitionistic fuzzy numbers where hesitancy factor of a decision-maker is taken into account. This paper targets to handle the uncertainty in more than one dimension keeping the hesitancy part into consideration for intelligent decision-making. Therefore, a novel trapezoidal type-2 intuitionistic fuzzy set (TrT2 IFS) is proposed, which is an aggregation of several triangular IFSs having upper and lower membership along with a non-membership value. For this TrT2 IFS, we have defined the generation procedure, operations, comparison and distance between such TrT2 IFSs. In addition, the decision-maker weights and criterion weight computation are also presented with respect to the TODIM approach. Furthermore, we have applied this extended TrT2 IFS-based TODIM method into a renewable energy resource selection problem of multi-criteria decision-making.