In this paper, we discussconsensus measures for typical hesitant fuzzy elements (THFE), which are the finite and nonempty fuzzy membership degrees under the scope of typical hesitant fuzzy sets (THFS). In our approach, we present a model that formally constructs consensus measures by means of aggregations functions, fuzzy implication-like functions and fuzzy negations, using admissible orders to compare the THFE, and also providing an analysis of consistency on them. Our theoretical results are applied into a problem of decision making with multicriteria illustrating our methodology to achieve consensus in a group of experts working with THFS.

Multi Expert-Multi Criteria Decision Making (ME-MCDM) problems have been well explored on hesitant fuzzy environments dealing with membership degrees as subsets which do not necessarily have the same cardinality. Admissible (total) orders collaborate by reducing the collapse in the ranking of alternatives related to preference relations. In such context, three classes of admissible orders are presented in a non-restrictive way, integrating the concepts of linearity and cardinality and providing support to the comparison between two typical hesitant fuzzy elements. In the sense of hesitant fuzzy logic, the study of fuzzy operators and their main properties is extended considering the admissible linear orders. Namely, the typical hesitant fuzzy aggregation functions, negations and implication functions are discussed mainly related to their (iso/anti)tonicity properties w.r.t. these admissible orders. An algorithmic procedure is introduced illustrating our strategy to solve an ME-MCDM problem, by selecting a Computer Integrating Manufacturing software and making use of the achieved theoretical results.