Uncertain Linguistic Preference Relations Research Articles

Incomplete interval-valued probabilistic uncertain linguistic preference relation in group decision making

In group decision making (GDM), due to complexity of various factors, decision makers (DMs) often provide incomplete preference relations (PRs) in preference matrix. Interval-valued probabilistic uncertain linguistic term set (IVPULTS) is a flexible and accurate tool to depict evaluation information of experts. In this paper, we mainly propose a new concept pertaining to interval-valued probabilistic uncertain linguistic preference relation (IVPULPR) that applies the IVPULTS to preference relations. Firstly, some new basic theoretical concepts of IVPULTS are developed including ordered IVPULTS, normalization method and new expectation function. Secondly, we establish several goal programming models to estimate the unknown elements in incomplete IVPULPR and propose the expected additive consistency of IVPULPR. To improve the consistency level, two optimization models are constructed based on the idea of minimum adjustment. Thirdly, we derive the experts’ weights in terms of information uncertainty, where a new method to measure information uncertainty of IVPULTS is proposed. For the sake of improving group consensus, we construct a group consensus index (GCI) and two optimization models depending on the adjustment mechanism of expert weight. Finally, a complete GDM framework with incomplete IVPULPR is devised based on the analysis of IVPULPR consistency and group consensus. Through an experiment analysis by using an UCI dataset, we find that the proposed GDM model can not only precisely express fuzzy preference information of DMs, but also ensure achievement of acceptable consistency and group consensus under the condition of not changing the initial preference as much as possible.

An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations

The use of probabilistic uncertain linguistic preference relations (PULPRs) enriches the flexibility of decision makers (DMs) in group decision making (GDM). However, the GDM models under PULPRs are mainly focussed on the consensus reaching process rather than the individual consistent improvement. The goal of this paper is to manage the consistency and consensus in GDM based on PULPRs, and provide a feasible method for minimising the preference information loss by optimisation model. First, according to DMs’ psychological preferences (optimistic, pessimistic, and neutral characteristics), we proposed a conversion function to fit uncertain linguistic terms in PULPRs, which may be transformed into probabilistic linguistic preference relations. Second, to preserve as much as possible the original preference information of DMs, a consensus model based on optimisation is established, which not only obtains the acceptable group consensus but also guarantees that the consistency level of individuals is acceptable. Finally, we validated the proposed method through a case study of an investment project selection for central enterprises’ poverty alleviation fund. The proposed method provides a new way to deal with GDM problems under PULPRs, and help DMs to reach a certain level of consensus on basis of acceptable consistent level of individuals.

Missing values estimation for incomplete uncertain linguistic preference relations and its application in group decision making

Missing values estimation for incomplete uncertain linguistic preference relations and its application in group decision making

On Consistency and Priority Weights for Uncertain 2-Tuple Linguistic Preference Relations

Consistency and priority weights of preference relations are two important phases of decision-making process since the decision-making solutions are determined by them. Therefore, it is meaningful to investigate consistency and priority weights for preference relations. In this paper, consistency and uncertain 2-tuple linguistic priority weights of uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First, based on the additive consistency, an additive consistency index is developed to measure the additive consistency level of U2TLPRs. Second, a goal programming model is proposed to adjust the unacceptable additive consistent U2TLPR until it satisfies acceptable additive consistency. Furthermore, an optimization model is developed to derive the uncertain 2-tuple linguistic priority weights from an U2TLPR. Meanwhile, in group decision-making (GDM) problems, similarities and confidence degrees of decision makers (DMs) are defined to determine DMs’ weights. Subsequently the properties of collective U2TLPR are discussed. Finally, the proposed methods are implemented in two examples including a GDM problem to verify the validity of the proposed methods.

The consensus of probabilistic uncertain linguistic preference relations and the application on the virtual reality industry

With the Pandora's Box of the virtual reality (VR) being opened, it is undoubtedly a good choice for those companies that have no VR experience and want a share in the competitive marketplace to cooperate with a leading VR company. How to choose an appropriate leading company becomes a group decision-making (GDM) problem that we want to deal with. Whereas volatile decision-making environment conduces that the decision-making information of the aforementioned GDM problem cannot be expressed by traditional explicit values. Thus, we choose probabilistic uncertain linguistic term set (PULTS) which is one of the most emerging decision-making tools and relatively manifests the unstable decision-making information as an instrument to address the GDM problem. Then this paper studies the consensus among the preference relations (PRs) and selects a suitable alternative for the aforementioned GDM problem. Firstly, we construct the probabilistic uncertain linguistic preference relation (PULPR) and the normalized PULPR. Secondly, the distance measure and similarity degree are defined to measure the consensus degree. Moreover, the two specific consensus processes are described separately. One is based on the distance measure between the individual PULPR and the group PULPR, the other is based on the similarity degree among the individual PULPR. Thirdly, by using the selection process in the light of the proposed possibility degree, two corresponding algorithms are proposed for solving the practical GDM problem. Finally, a practical case of choosing applicable VR company is used to demonstrate the efficiency of the two algorithms.

A consensus-based method for group decision making with incomplete uncertain linguistic preference relations

In practical group decision-making (GDM) problems, it is nature for experts to express their preference relations in uncertain linguistic pattern, due to the ambiguity of the external environments and the internal nature of human judgments. In this paper, a consensus process is introduced to deal with GDM problems with incomplete uncertain linguistic preference relations (ULPRs). Firstly, a consistency level for ULPRs is defined. Secondly, a linear goal programming model is furnished to estimate the missing uncertain linguistic preference values with respect to consistency property. Thirdly, an additively consistent ULPR is constructed. What’s more, one can obtain the collective ULPR by aggregating individual additively consistent ULPRs, where the order-inducing variable is consistency level (CL), based on the thought of more importance will be given to the larger CL. Furthermore, a consensus reaching process is presented to make experts’ opinions achieve to a predefined level. In the end, a new algorithm is proposed to solve the GDM problem with incomplete ULPR, which is further applied to the selection of best cooperator in a water conservancy project.

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

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.

On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and utilize it to determine the optimal weights of experts in the group decision making (GDM). First, the compatibility degree and compatibility index for the two multiplicative linguistic preference relations are proposed. Then, based on the linguistic continuous ordered weighted geometric averaging (LCOWGA) operator, some concepts of the compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are presented. We prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that the uncertain multiplicative linguistic preference relations given by experts are all of acceptable compatibility with the ideal uncertain multiplicative linguistic preference relation, which provides a theoretic basis for the application of the uncertain multiplicative linguistic preference relations in GDM. Next, an optimal model is constructed to determine the weights of experts based on the criterion of minimizing the compatibility index in GDM. Moreover, an approach to GDM with uncertain multiplicative linguistic preference relations is developed, and finally, an application of the approach to supplier selection problem with uncertain multiplicative linguistic preference relations is pointed out.

On compatibility of uncertain additive linguistic preference relations based on the linguistic COWA operator

We develop a new compatibility for the uncertain additive linguistic preference relations and study its properties which are very suitable to deal with group decision making (GDM) problems involving uncertain additive linguistic preference relations. Based on the linguistic continuous ordered weighted averaging (LCOWA) operator, we present some concepts of the compatibility degree and compatibility index for the two uncertain additive linguistic preference relations. Then, we study some desirable properties including the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain additive linguistic preference relations given by experts are all of acceptable compatibility with the ideal uncertain linguistic preference relation, which provides a theoretic basis for the application of the uncertain additive linguistic preference relations in GDM. In order to determine the weights of experts, we construct an optimal model based on the criterion of minimizing the compatibility index in GDM. Finally, we propose a new approach based on the compatibility index and the expected additive linguistic preference relation to GDM and develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the evaluation of schools in a university.

ON COMPATIBILITY OF UNCERTAIN MULTIPLICATIVE LINGUISTIC PREFERENCE RELATIONS AND ITS APPLICATION TO GROUP DECISION MAKING

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and determine the optimal weights of decision makers (DMs), which are very suitable to deal with group decision making (GDM) problems involving uncertain multiplicative linguistic preference relations. First, the concepts of compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are proposed. Then we prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain multiplicative linguistic preference relations given by DMs are all of acceptable compatibility with a specific linguistic preference relation, which is the scientific basis of using the uncertain multiplicative linguistic preference relations in the GDM. Next, in order to determine the weights of decision makers, we construct an optimal model based on the criterion of minimizing the compatibility index. Finally, we develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the selection of investment.

A maximizing consensus approach for alternative selection based on uncertain linguistic preference relations

In alternative selection problems managed by multiple experts in uncertain situations achieving consensus is a desirable objective as incorrect selection may adversely affect stakeholder outcomes. This paper develops an approach to solve consensus problems when expert preference information is in the form of uncertain linguistic preference relations. First, definitions for aggregation operators and group consensus level based on a 2-tuple linguistic representation model are provided. Then, in order to obtain the weights of the experts under the assumption of incomplete weights information, an optimization model is developed which seeks maximum consensus from the current expert preferences in the group. If the consensus level reached does not meet predefined requirements, a consensus reaching algorithm is presented which can automatically achieve the goal. To determine the parameters for the proposed algorithm, a simulation procedure is presented. Finally, an investment company optimal selection example is provided to show the properties of the proposed approach. A comparative study and discussion of the proposed approach are also conducted.

Consolidating SWOT analysis with nonhomogeneous uncertain preference information

SWOT analysis is an important support tool for decision-making, and is commonly used to systematically analyze organizations’ internal and external environments. However, one of its deficiencies is in the measurement and evaluation of prioritization of the factors and strategies. This paper is aimed to present a novel quantified SWOT analytical method based multiple criteria group decision-making (MCGDM) concept, in which the priorities of SWOT factors and groups are derived by multiple decision makers (DMs) with nonhomogeneous uncertain preference information (NUPI), such as interval multiplicative preference relations, interval fuzzy preference relations, and uncertain linguistic preference relations. In this method, the SWOT analysis provides a basic frame within which to perform analyses of decision situations, in turn, MCGDM methods assist in carrying out SWOT more analytically and in elaborating the results of the analyses so that SWOT factors and groups can be prioritized with respect to the entire SWOT. The uniform and aggregation of the NUPI and the derivation of priorities for SWOT groups and factors are investigated in detail. Finally, an example is to validate the procedure of the proposed method.

UNCERTAIN LINGUISTIC HYBRID GEOMETRIC MEAN OPERATOR AND ITS APPLICATION TO GROUP DECISION MAKING UNDER UNCERTAIN LINGUISTIC ENVIRONMENT

In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the special case of the ULHGM operator. The ULHGM operator generalizes both the ULWGM and ULOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWGM and ULHGM operators, we propose a practical method for multiple attribute group decision making with uncertain linguistic preference relations. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method.