Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations

A novel intuitionistic fuzzy set (IFS) score function and an intuitionistic fuzzy preference relation (IFPR) quantifier guided non-dominance based prioritisation method are introduced. Based on Yager's continuous OWA (COWA) operator, the interval-valued intuitionistic fuzzy COWA (IVIF-COWA) operator is defined, and a new attitudinal expected score function for interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced. The novelty of this attitudinal expected score function is that it allows the comparison of IVIFNs by taking into account of the decision makers' attitudinal character. Moreover, we show that the new attitudinal expected score function extends: (i) the IFS score function introduced in this paper, which is mathematically equivalent to Chen and Tan's score function (Chen and Tan, 1994); and (ii) Xu and Chen's score function for IVIFNs (Xu and Chen, 2007). Using the proposed score functions, a method is developed to construct FPRs from a given IFPR and IVIFPR, respectively. When the hesitancy degree function is null, we prove that the score FPRs coincide with their respective IFPR and IVIFPR. Finally, a ranking sensitivity analysis of the attitudinal expected score function with respect to the attitudinal parameter is provided. (C) 2012 Elsevier Ltd. All rights reserved.