*Article* **Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making**

#### **Jingqian Wang 1 and Xiaohong Zhang 2,\***


Received: 7 September 2018; Accepted: 29 September 2018; Published: 4 October 2018

**Abstract:** Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) *β*-covering and an IF covering rough set model. In this paper, some properties of IF *β*-covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF *β*-covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.'s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

**Keywords:** intuitionistic fuzzy; covering; neighborhood system; decision making
