Two-stage aggregation paradigm for HFLTS possibility distributions: A hierarchical clustering perspective

Abstract The integration of possibility distribution into hesitant fuzzy linguistic term set (HFLTS) adds an extra dimension to individual opinion approximation process and significantly leads to enhanced data quality and reliability. However, aggregation of HFLTS possibility distributions involves merely associated possibilities of linguistic terms without taking into account all possible combinations of individual linguistic opinions. Therefore, computing with HFLTS possibility distributions in such a way has a high possibility of distorting final decisions due to loss of information. The introduction of hesitant 2-tuple linguistic term set (H2TLTS), which technically includes the HFLTS as a special case, offers us a different point of view in consolidating the aggregation process of HFLTSs. Due to the resemblance with H2TLTS, the alternative explantation of HFLTS, i.e., possibility distribution, can be analogously adapted to the theory of H2TLTS. By means of a conceptually simple recasting of HFLTS possibility distribution into a unified framework for H2TLTS possibility distribution with the development of possibilistic 2-tuple linguistic pair (P2TLP) concept, we develop a novel two-stage aggregation paradigm for HFLTS possibility distributions. At the first stage, the initial aggregation takes all possible combinations of P2TLPs in separate HFLTS possibility distributions together to generate an aggregated set of P2TLPs. Building on that, the subsequent stage proposes a similarity measure-based agglomerative hierarchical clustering (SM-AggHC) algorithm to reduce the cardinality of the aggregate set under consideration. The centroid approach combined with the normalization process finally guarantees the aggregation outcomes to be operated as H2TLTS possibility distributions.