Linguistic Single and Interval-valued Hybrid Intuitionistic Fuzzy Multi-sets and Applications to Multi-criteria Group Decision Making

In this paper, we propose the concepts of linguistic single and interval-valued hybrid intuitionistic fuzzy multi-set (LSIVHIFMS) and linguistic single and interval-valued hybrid intuitionistic fuzzy multi-value (LSIVHIFMV) by merging linguistic intuitionistic fuzzy sets (values) and linguistic interval-valued intuitionistic fuzzy sets (values). The main contribution of a LSIVHIFMS or a LSIVHIFMV, which contains hybrid information, is the presentation of a qualitative and sensitive assessment tool for multi-criteria group decision making (MCGDM). We also define some algebraic operations between LSIVHIFMVs and provide a weighted arithmetic aggregation operator with the help of these operations by considering t-norms and t-conorms. Then, we give a score and an accuracy function to rank LSIVHIFMVs. Moreover, we give a MCGDM method based on the proposed aggregation operator and score function. This method is applied to a real life MCGDM problem (selection of the company problem to establish a computer laboratory) and the comparison analysis is given with the existing methods to show the efficiency of the proposed method.