Intuitionistic fuzzy possibility measure-based three-way decisions for incomplete data

Intuitionistic Fuzzy Three-Way Decision Model Based on the Three-Way Granular Computing Method

“…This section briefly reviews some basic concepts [1,13,17,18,41,54,55]. Throughout this paper, we assume that the domain of discourse U and attribute set A are both non-empty finite sets.…”

“…Reference [41] considers the composition of intuitionistic fuzzy probability measured from a macro perspective, but from a micro perspective, if the overlap of the membership degree of elements is not large or the conflict of non-membership degree is not strong, then the useful information of used elements cannot be integrated and utilized. If attribute B ∈ A has multiple states under object x i ∈ U, the possibility in a certain state is simply referred to as the state possibility.…”

“…Qi et al [31] and Yu et al [32] explored the relationship between three-way concept lattices and three-way decisions from the perspective of formal concept analysis. The research on the application of three-way decision theory mainly focuses on three-way clustering [33,34], three-way classification [35,36], three-way attribute reduction [37][38][39], three-way uncertainty decision [25,40,41], and three-way conflict analysis [42,43]. For instance, Xu et al [35] focused on the semantics of three-way decisions from the perspective of a confusion matrix and investigated related clustering methods.…”

Object-First Incremental Algorithms for Updating Approximations in Multi-Granulation Fuzzy Probabilistic Rough Sets Over Two Universes

“…In this regard, Qian et al [19], [20] proposed multi-granulation rough set (MRS) model by using multiple equivalence relations to define the approximation of a group of objects. MRS model extended applications of RS theory in the multi-granulation structure, such as decision making [21], [22] and feature selection [23], [24]. Therefore, so as to extend the model of the fuzzy probabilistic rough set over two universes from single granulation into multiple granulations, Mandal et al [25] proposed a model of multi-granulation bipolar-valued fuzzy probabilistic rough set over two universes.…”