A decision framework under probabilistic hesitant fuzzy environment with probability estimation for multi-criteria decision making

With growing hesitation in human perception, hesitant fuzzy set, an important extension of fuzzy set, has gained much attention from the research community. The concept of HFS gives decision makers the ability to provide multiple preferences for the same instance. However, the chance of these preferences occurring is assumed to be equal, which is unreasonable in practice. To circumvent this issue, probabilistic hesitant fuzzy set (PHFS) is adopted in this work, which is an extension of hesitant fuzzy set with associated probability values. Based on the literature review on PHFS, it is evident that (i) occurrence probability of each element was not methodically calculated; (ii) hesitation was not properly captured during criteria weight calculation; (iii) interrelationship among criteria was not captured during aggregation; and (iv) broad/rational ranking of alternatives with compromise solution was lacking. Motivated by these challenges and to alleviate the same, a systematic procedure is proposed in this paper to estimate these probabilities. Additionally, in this procedure, decision makers’ preferences are aggregated using the newly proposed probabilistic hesitant fuzzy generalized Maclaurin symmetric mean operator and criteria weights are calculated using the proposed statistical variance method in the context of PHFS. A new ranking method is also proposed that extends a well-known VIKOR method to the PHFS context. Further, the practical use of the proposed decision framework is demonstrated by two examples viz., selecting a suitable coordinator for a research and development project and selection of a doctoral candidate for the supervisor position. Finally, the strength and weakness of the proposed decision framework are realized by comparing it with state-of-the-art methods