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 yet 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.
Highlights
Because of the inherent subjective ambiguity of human thinking and the complexity of practical decision-making (DM) problems, the use of qualitative information is almost an indispensable link in decision makers (DMs)
Compared with the model proposed by wan et al [36], the model proposed in this paper considers the probability distribution of uncertain information, which is more suitable for large-scale group decision-making (GDM) problems in complex environments and can ensure the consistency of collective preference relations
Compared with the goal programming models (GPMs) proposed by liao et al [39], the model proposed in this paper considers both the risk attitude of DMs and the information that they fail to grasp, which improves the rationality and accuracy of decision-making results
Summary
Because of the inherent subjective ambiguity of human thinking and the complexity of practical decision-making (DM) problems, the use of qualitative information is almost an indispensable link in DM. In order to improve the expression of qualitative information and promote the use of LT in DM problems, this paper further proposes a probabilistic uncertain linguistic intuitionistic fuzzy set (PULIFS) based on the above research, which integrates the advantages of LIFS and PULTS. In order to make up for the above defects of the existing methods, this paper further proposes probabilistic uncertain linguistic intuitionistic fuzzy preference relation (PULIFPR). Most of the existing decision-making models fail to consider the risk attitude of DMs and fail to guarantee the consistency of preference information given by DMs. In this paper, two extreme attitudes of DMs under uncertain conditions are considered to establish programming models, which ensures the consistency of preference relations, simplifies GDM process and improves the accuracy of decision-making results.
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