Additive Linguistic Preference Research Articles

Interactive algorithms for normalized probabilistic linguistic preference relations in view of the disjunctive probability based consistency and consensus analysis

This paper investigates decision making with normalized probabilistic linguistic preference relations (NPLPRs). Consistency analysis is indispensable for deriving the reasonable ranking. After recalling previous research, we find that all previous concepts cannot fully define consistent NPLPRs. As a fundamental topic of decision making with preference relations, it is necessary to further study the consistency of NPLPRs. For this purpose, an interactive algorithm for deriving disjunctive probabilistic additive linguistic preference relations (DP-ALPRs) is provided, by which an additive consistency concept for NPLPRs is defined. When NPLPRs are unacceptably consistent, models for obtaining acceptably additively consistent NPLPRs are built. Considering the situation where only incomplete NPLPRs are obtained, a disjunctive probability and additive consistency based interactive algorithm for ascertaining missing judgments is provided. Meanwhile, we discuss group decision making (GDM) with NPLPRs and offer a distance measure based formula to determine the weights of the decision makers. In addition, the method defines a consensus index and builds models for improving the consensus level. Under the additive consistency and consensus discussions, an interactive algorithm for GDM with NPLPRs is proposed. Finally, the new method is applied to select green raw material suppliers to illustrate the application and compared with several previous ones.

Heterogeneous group decision making in the setting of incomplete preference relations

This paper focuses on heterogeneous group decision making (GDM) in the setting of incomplete preference relations, including incomplete fuzzy preference relations, incomplete multiplicative preference relations, incomplete additive linguistic preference relations, and incomplete multiplicative linguistic preference relations. Following the consistency-consensus optimization analysis, a new GDM method is proposed which can address inconsistent and incomplete preference relations. Firstly, we consider how to determine unknown information and how to obtain consistent preference relations. In contrast to the existing methods which rank the alternatives from fuzzy preference relations using the additive or multiplicative consistency analysis, this paper follows the consistency level to decide to use the additive or multiplicative consistency. Following the consensus analysis for each type of consistent preference relations, we calculate their comprehensively consistent preference relations and the priority vectors. After that, we build a consistency-based model for calculating the comprehensive priority vector. Furthermore, we offer an ordered position consensus-based method using the built optimization models. The proposed heterogeneous GDM method with incomplete preference relations provides us with a very useful way for dealing with GDM problems in heterogeneous environments.

Some ILOWA operators and their applications to group decision making with additive linguistic preference relations

The aim of this paper is to present some cases of the induced linguistic ordered weighted averaging (ILOWA) operator which are very suitable to deal with group decision making (GDM) problems with additive linguistic preference relations. We propose the relative consensus degree ILOWA (RCD-ILOWA) operator which uses the relative consensus degree (RCD) variable as the order inducing variable, and the compatibility index ILOWA (CI-ILOWA) operator which uses the compatibility index (CI) variable as the order inducing variable. We also investigate some desired properties of RCD-ILOWA operator and the CI-ILOWA operator which provide theoretic basis for the application of the additive linguistic preference relations in GDM. A general formulation and a nonlinear model to determine experts' weights and two approaches based on the RCD-ILOWA operator and the CI-ILOWA operator for GDM involving additive linguistic preference relations are developed respectively. A numerical example for comprehensive evaluation is given to illustrate the applications of the new operators.

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.

A Direct Approach Based on C2-IULOWA Operator for Group Decision Making with Uncertain Additive Linguistic Preference Relations

With respect to group decision making (GDM) problem with uncertain additive linguistic preference relations (UALPRs), we investigate the efficient aggregation of the uncertain additive linguistic preference information. First, we introduce two measures to assess the consistency level and the consensus level of uncertain additive linguistic preference information, respectively, and study some of their desirable properties. Then, based on both the two measures, we propose a coinduced uncertain linguistic ordered weighted averaging (IULOWA) operator, called the consistency and consensus coinduced uncertain linguistic ordered weighted averaging (C2-IULOWA) operator, to aggregate individual uncertain additive linguistic preference information, in which the consistency level and the consensus level synergistically serve as inducing variables and then guide the determination of the associated weights. We have proved the collective uncertain linguistic preference information aggregated by the C2-IULOWA operator that can maintain the fundamental properties of preference relation, such as indifference, reciprocity, and transitivity. By using the C2-IULOWA operator, we develop a direct GDM approach with UALPRs. Finally, an illustrative example on the selection of chief quality officer is used to demonstrate the effectiveness and rationalitly of the developed approach.

Group decision making with linguistic preference relations with application to supplier selection

Linguistic preference relation is a useful tool for expressing preferences of decision makers in group decision making according to linguistic scales. But in the real decision problems, there usually exist interactive phenomena among the preference of decision makers, which makes it difficult to aggregate preference information by conventional additive aggregation operators. Thus, to approximate the human subjective preference evaluation process, it would be more suitable to apply non-additive measures tool without assuming additivity and independence. In this paper, based on λ-fuzzy measure, we consider dependence among subjective preference of decision makers to develop some new linguistic aggregation operators such as linguistic ordered geometric averaging operator and extended linguistic Choquet integral operator to aggregate the multiplicative linguistic preference relations and additive linguistic preference relations, respectively. Further, the procedure and algorithm of group decision making based on these new linguistic aggregation operators and linguistic preference relations are given. Finally, a supplier selection example is provided to illustrate the developed approaches.

On compatibility of uncertain additive linguistic preference relations and its application in the group decision making

We develop a new compatibility for the uncertain additive linguistic preference relations and utilize it to determine the optimal weights of experts in the group decision making (GDM). Based on some operational laws for the uncertain additive linguistic preference labels, we propose some new concepts of the compatibility degree and acceptable compatibility index for the two uncertain additive linguistic preference relations. We also prove the properties that the synthetic preference relation is also of acceptable compatibility under the condition that additive linguistic preference relations provided by experts are all of acceptable compatibility with the specific linguistic preference relation, which provides a theoretic basis for the application of the uncertain additive linguistic preference relations in the GDM. Furthermore, we establish a mathematical model to obtain the weights of experts based on the criterion of minimizing the compatibility in the GDM, and we discuss the solution to the model. Finally, we give a numerical example to make comparative analysis on compatibility index using the optimal experts’ weights approach and the equal experts’ weights approach, which indicates that the model is feasible and effective.

On group decision making with four formats of incomplete preference relations

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in four formats of incomplete preference relations, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations, incomplete additive linguistic preference relations, incomplete multiplicative linguistic preference relations. In order to make the collective opinion close each decision maker’s opinion as near as possible, an optimization model is constructed to integrate the four different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.

Group decision making based on multiple types of linguistic preference relations

In this paper, we investigate group decision making problems with multiple types of linguistic preference relations. The paper has two parts with similar structures. In the first part, we transform the uncertain additive linguistic preference relations into the expected additive linguistic preference relations, and present a procedure for group decision making based on multiple types of additive linguistic preference relations. By using the deviation measures between additive linguistic preference relations, we give some straightforward formulas to determine the weights of decision makers, and propose a method to reach consensus among the individual preferences and the group’s opinion. In the second part, we extend the above results to group decision making based on multiple types of multiplicative linguistic preference relations, and finally, a practical example is given to illustrate the application of the results.

A Direct Approach to Group Decision Making with Uncertain Additive Linguistic Preference Relations

In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of uncertain additive linguistic preference relations. We define the concept of uncertain additive linguistic preference relation, and introduce a formula based on possibility measure for comparing two uncertain linguistic preference values. We introduce some aggregation operators such as the uncertain linguistic averaging (ULA) operator and uncertain linguistic weighted averaging (ULWA) operator, etc. Based on the ULA and ULWA operators, we develop a direct approach to group decision making with uncertain additive linguistic preference relations without loss of information. Finally, an illustrative numerical example is given to verify the developed approach.

EOWA AND EOWG OPERATORS FOR AGGREGATING LINGUISTIC LABELS BASED ON LINGUISTIC PREFERENCE RELATIONS

In this paper, we define two types of linguistic preference relations (multiplicative linguistic preference relation and additive linguistic preference relation), and study some of their desirable properties. We introduce the extended geometric mean (EGM) operator, extended arithmetical averaging (EAA) operator, extended ordered weighted averaging (EOWA) operator and extended ordered weighted geometric (EOWG) operator. An approach based on the EGM and EOWG operators and multiplicative linguistic preference relations and an approach based on the EAA and EOWA operators and additive linguistic preference relations are proposed to ranking the alternatives in the group decision-making problems. Finally, we give a numerical example to illustrate the developed approaches.