Zhen Zhang

A method for multi-granularity uncertain linguistic group decision making with incomplete weight information

Due to the uncertainty of decision environment and difference of decision makers cultural and knowledge background, actual group decision making problems are usually with multi-granularity uncertain linguistic information and incomplete weight information. In this paper, we focus on dealing with multi-granularity uncertain linguistic group decision making problems with incomplete weight information. In the proposed method, uncertain linguistic evaluation information of each decision maker is transformed to trapezoidal fuzzy numbers, and then two optimization models are established to minimize the deviation between each decision makers evaluation and the groups collective evaluation on each alternative. By solving the established optimization models, the collective evaluation of the alternatives can be denoted by trapezoidal fuzzy numbers. After that, the closeness coefficient of each alternative can be obtained, which can give the ranking of the alternatives. Finally, a numerical example is given to show the feasibility and applicability of the proposed method.

Managing Multigranular Linguistic Distribution Assessments in Large-Scale Multiattribute Group Decision Making

Linguistic large-scale group decision making (LGDM) problems are more and more common nowadays. In such problems a large group of decision makers are involved in the decision process and elicit linguistic information that are usually assessed in different linguistic scales with diverse granularity because of decision makers’ distinct knowledge and background. To keep maximum information in initial stages of the linguistic LGDM problems, the use of multigranular linguistic distribution assessments seems a suitable choice, however, to manage such multigranular linguistic distribution assessments, it is necessary the development of a new linguistic computational approach. In this paper, it is proposed a novel computational model based on the use of extended linguistic hierarchies, which not only can be used to operate with multigranular linguistic distribution assessments but also can provide interpretable linguistic results to decision makers. Based on this new linguistic computational model, an approach to linguistic large-scale multiattribute group decision making is proposed and applied to a talent selection process in universities.

Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations

Due to the uncertainty of the decision environment and the lack of knowledge, decision-makers may use uncertain linguistic preference relations to express their preferences over alternatives and criteria. For group decision-making problems with preference relations, it is important to consider the individual consistency and the group consensus before aggregating the preference information. In this paper, consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First of all, a formula which can construct a consistent U2TLPR from the original preference relation is presented. Based on the consistent preference relation, the individual consistency index for a U2TLPR is defined. An iterative algorithm is then developed to improve the individual consistency of a U2TLPR. To help decision-makers reach consensus in group decision-making under uncertain linguistic environment, the individual consensus and group consensus indices for group decision-making with U2TLPRs are defined. Based on the two indices, an algorithm for consensus reaching in group decision-making with U2TLPRs is also developed. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithms.

An approach to group decision making with heterogeneous incomplete uncertain preference relations

Abstract For practical group decision making problems, decision makers tend to provide heterogeneous uncertain preference relations due to the uncertainty of the decision environment and the difference of cultures and education backgrounds. Sometimes, decision makers may not have an in-depth knowledge of the problem to be solved and provide incomplete preference relations. In this paper, we focus on group decision making (GDM) problems with heterogeneous incomplete uncertain preference relations, including uncertain multiplicative preference relations, uncertain fuzzy preference relations, uncertain linguistic preference relations and intuitionistic fuzzy preference relations. To deal with such GDM problems, a decision analysis method is proposed. Based on the multiplicative consistency of uncertain preference relations, a bi-objective optimization model which aims to maximize both the group consensus and the individual consistency of each decision maker is established. By solving the optimization model, the priority weights of alternatives can be obtained. Finally, some illustrative examples are used to show the feasibility and effectiveness of the proposed method.

Consistency-based algorithms to estimate missing elements for uncertain 2-tuple linguistic preference relations

AbstractFor actual decision making problems, decision makers sometimes may have difficulty to provide all the preference information over alternatives through pairwise comparisons. In this paper, we focus on estimating missing elements for an incomplete uncertain 2-tuple linguistic preference relation. First, the additive consistency of an uncertain 2-tuple linguistic preference relation is defined. Based on the defined additive consistency, we define acceptable incomplete uncertain 2-tuple linguistic preference relation and propose two new algorithms, including an iterative algorithm and an optimization-based algorithm to estimate the missing elements for an uncertain 2-tuple linguistic preference relation. Finally, some numerical examples are presented to illustrate the applicability of the two algorithms.

Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings

The intuitionistic multiplicative preference relation (IMPR), which takes into account both the ratio degree to which an alternative is preferred to another and the ratio degree to which an alternative is non-preferred to another, is a useful tool for decision makers to elicit their preference information using Saaty’s 1–9 scale. In this paper, we focus on group decision making with IMPRs. First, we analyze the flaws of the consistency definition of an IMPR in previous work and then propose a new definition to overcome the flaws. On this basis, a linear programming-based algorithm is developed to check and improve the consistency of an IMPR. Second, we discuss the relationships between an IMPR and a normalized intuitionistic multiplicative weight vector and develop two approaches to group decision making based on complete and incomplete IMPRs, respectively. Based on the proposed algorithm and approaches, a general framework for group decision making with IMPRs is proposed. Finally, some numerical examples are provided to demonstrate the proposed approaches. The results show that the proposed approaches can deal with group decision-making problems with IMPRs effectively.

Fusion of Heterogeneous Incomplete Hesitant Preference Relations in Group Decision Making

AbstractIn this paper, we focus on the fusion of heterogeneous incomplete hesitant preference relations (including hesitant fuzzy preference relations and hesitant multiplicative preference relations) under group decision making settings. First, some simple formulae are developed to derive a priority weight vector from an incomplete hesitant fuzzy preference relation or an incomplete hesitant multiplicative preference relation based on the logarithmic least squares method. Based on the priority weight vector, an induced fuzzy or multiplicative preference relation can be derived for an incomplete hesitant preference relation. Moreover, the consistency indices of hesitant fuzzy preference relations and hesitant multiplicative preference relations are defined. Afterwards, an approach to group decision making based on incomplete hesitant fuzzy preference relations and incomplete hesitant multiplicative preference relations is developed to deal with group decision making problems with multiple decision organiz...

On priority weights and consistency for incomplete hesitant fuzzy preference relations

Abstract The hesitant fuzzy preference relation (HFPR) is a useful tool for decision makers to elicit their preference information over a set of alternatives. In this paper, it is first proposed an approach to deriving a priority weight vector from an incomplete HFPR using the logarithmic least squares method. Based on the priority weight vector, the consistency index of an incomplete HFPR is defined, which calculates the average deviation between the priority weight vector and all elements of the incomplete HFPR. For an incomplete HFPR which is unacceptably consistent, an automatic algorithm is developed to improve the consistency. These results are then extended to propose a new procedure for group analytic hierarchy process to deal with multi-criteria group decision making problems. The feasibility and effectiveness of the proposed approaches are demonstrated by some numerical examples.

New operations of hesitant fuzzy linguistic term sets with applications in multi-attribute group decision making

The hesitant fuzzy linguistic term set is a useful tool for decision makers to express their linguistic assessments over alternatives. In this paper, some new operations of hesitant fuzzy linguistic term sets are proposed based on 2-tuple linguistic aggregation operators and distribution linguistic aggregation operators, which can avoid the loss of information and make the aggregation results interpretable. Based on the proposed aggregation operators, an approach to multi-attribute group decision making with hesitant fuzzy linguistic term sets is developed. Finally, an example is used to demonstrate the feasibility and effectiveness of the proposed approach.

Additive consistency analysis and improvement for hesitant fuzzy preference relations

Abstract Hesitant fuzzy preference relation (HFPR) is an effective tool to elicit decision makers’ hesitant preference information over alternatives, and consistency analysis is of great importance for an HFPR since inconsistent judgments may result in unreasonable results. In this paper, the best additive consistency index, the worst additive consistency index and the average additive consistency index are defined to measure the consistency level of an HFPR. To improve the additive consistency of an HFPR, some mixed 0–1 linear programming models which aim to minimize the overall adjustment amount and the number of the elements that need to be adjusted are established. Moreover, the proposed models are extended to improve the additive consistency and impute the missing elements for incomplete HFPRs. Some numerical examples are presented to show the characteristics of the proposed models. The results demonstrate that the proposed models can improve the consistency of an HFPR effectively.