*Article* **A Programming-Based Algorithm for Probabilistic Uncertain Linguistic Intuitionistic Fuzzy Group Decision-Making**

#### **Kaixin Gongand Chunfang Chen \***

Department of Mathematics, Nanchang University, Nanchang 330031, China; gkxflw@163.com **\*** Correspondence:ccfygd@sina.com

Received: 7 January 2019; Accepted: 11 February 2019; Published: 15 February 2019

**Abstract:** As an effective tool to express the subjective preferences of decision makers, the linguistic term sets (LTS) have been widely used in group decision-making (GDM) problems, such as hesitant fuzzy LTS, linguistic hesitant fuzzy sets, probabilistic LTS, etc. However, due to the increasing complexity of practical decision-making (DM) problems, LTS still has a lot of room to expand in fuzzy theory. Qualitative uncertainty information in the application of GDM is ye<sup>t</sup> to be improved. Therefore, in order to improve the applicability of linguistic terms in DM problems, a probabilistic uncertain linguistic intuitionistic fuzzy set (PULIFS) that can fully express the decision-maker's (DM's) evaluation information is first proposed. To improve the rationality of DM results, we give a method for determining individual weights in the probabilistic uncertain linguistic intuitionistic fuzzy preference relation (PULIFPR) environment. In addition, we present two consistency definitions of PULIFPR to reflect both the assessment information and risk attitudes of decision makers. Subsequently, a series of goal programming models (GPMs) are established, which effectively avoid the consistency check and correction process of existing methods. Finally, the developed method is applied to an empirical example concerning the selection of a virtual reality (VR) project. The advantages of the proposed method are demonstrated by comparative analysis.

**Keywords:** group decision-making (GDM); probabilistic uncertain linguistic intuitionistic fuzzy preference relation (PULIFPR); consistency; goal programming model (GPM); risk preference

**MSC:** 34A08; 34B10
