Multiplicative Linguistic Preference Relations Research Articles

Group decision making based on consistency and consensus analysis of dual multiplicative linguistic preference relations

This paper proposes a new group decision making (GDM) method based on the consistency and the consensus analysis of dual multiplicative linguistic preference relations (DMLPRs). A new type of linguistic variables , called dual multiplicative linguistic variables (DMLVs), is presented, which is defined on the multiplicative linguistic scale. DMLVs are used to represent asymmetrical qualitative hesitancy judgments of decision makers (DMs). A maximum-consistency-based interactive algorithm to derive multiplicative linguistic intuitionistic preference relations (MLIPRs) is presented, by which the consistency concept for DMLPRs is obtained. Then, we define the concept of inconsistent DMLPRs and propose an optimal-model-based method for deriving consistent DMLPRs. Furthermore, incomplete DMLPRs also can be dealt with by the proposed maximum-consistency-based interactive algorithm. For GDM, the weights of DMs are determined by the cosine-based correlation coefficient between individual DMLPRs. Moreover, we propose a consensus measure to calculate the agreement degree of DMLPRs and build an optimal model to increase the consensus level of individual DMLPRs. Finally, a new GDM method (call Algorithm III ) is offered and an application example is used to illustrate the proposed GDM method. The proposed GDM method outperforms the former GDM methods for GDM in the environments of DMLPRs.

Addressing site selection for earthquake shelters with hesitant multiplicative linguistic preference relation

To reduce the damage caused by earthquakes, the paper develops a decision-making method under uncertainty, which validly addresses the site selection for earthquake shelters. Since site selection after earthquakes is an emergency decision-making process, during which there always exists inaccuracy and complexity, it is more rational to adopt fuzzy theory to handle this problem. Therefore, we introduce a hesitant multiplicative linguistic preference relation (HMLPR) and propose its consistency measure based on the eigenvector method. An adjustment method is provided to repair the unacceptably consistent HMLPR into acceptably consistent one, and the parameter of the adjustment method is also discussed. To manifest the validity and availability of the proposed method, we choose the Wenchuan Earthquake on May 12th 2008 as the background event. Upon establishing the indicators including scale and location, risk of disaster, rescue facilities, feasibility and resident aspect, three experts from Institute for Disaster Management and Reconstruction of Sichuan University are invited to address the site selection for temporary shelters. The obtained result is approved by the experts as the optimal choice in the case of this paper. Finally, we complete the comparative analysis. The processing efficiency of the proposed method keeps stable and fast when the number of experts and the number of criteria increase from 3 to 10 respectively, which demonstrates that the proposed method is more robust and efficient than the existing method.

Restoring incomplete PUMLPRs for evaluating the management way of online public opinion

In the age of big data explosion, the management of online public opinion has encountered great challenges. Which way can effectively manage online public opinion has become a decision-making question for us to think about. Probabilistic uncertain multiplicative linguistic preference relations (PUMLPRs) are a remarkable instrument to solve uncertain evaluation problems. This paper uses the PUMLPRs to assess the management ways of the online public opinion. Owing to the intricacy of decision-making domain, the PUMLPRs are not always complete. We get the complete PUMLPRs in two steps: the repair for uncertain multiplicative linguistic variables and the repair for probability. Moreover, the consistency of the complete PUMLPRs is researched. Then the final priorities are obtained by the proposed possibility degree formula. After that, the numerical example that helps assess the valid way to manage online public opinion is performed to check the feasibility of the proposed decision-making procedure.

Group Decision Making with Interval-Valued Intuitionistic Multiplicative Linguistic Preference Relations

To express the asymmetrically uncertain preferred and non-preferred qualitative judgments of decision makers, this paper introduces interval-valued intuitionistic multiplicative linguistic variables (IVIMLVs). To show their application in decision making, a ranking method is first offered. Then, we introduce IVIMLVs for preference relations and propose interval-valued intuitionistic multiplicative linguistic preference relations (IVIMLPRs). To obtain the ranking reasonably, a consistency definition for IVIMLPRs is presented. A mathematical optimization model for judging the consistency of IVIMLPRs based on the new concept is constructed. To address two general cases: incompleteness and inconsistency, mathematical optimization models for ascertaining unknown values in incomplete IVIMLPRs and deriving completely consistent IVIMLPRs from inconsistent ones are built, respectively. For group decision making, a consensus index is defined to measure the consensus achieved among the decision makers’ preferences. If the consensus is not enough, a mathematical optimization model for improving the consensus level is established. Furthermore, a linear optimization model for determining the weights of the decision makers based on the consensus analysis is constructed. Finally, a group decision-making method with IVIMLPRs based on consistency and consensus analysis is offered, and its application on selecting supply chain cooperative partners is offered.

Prospect Theory-Based Consistency Recovery Strategies with Multiplicative Probabilistic Linguistic Preference Relations in Managing Group Decision Making

Given the inherent characteristics of a practical case, a group decision making (GDM) support model integrated with prospect theory-based consistency recovery strategies based on multiplicative probabilistic linguistic preference information is proposed. Some basic concepts related to probabilistic linguistic term sets as well as multiplicative linguistic preference relations and prospect theory are reviewed for subsequent analysis. Multiplicative probabilistic linguistic preference relations (MPLPRs) and normalized MPLPRs are also defined to describe practical GDM problems. Subsequently, a consistency measure of MPLPRs is investigated to obtain a consistency level. Moreover, prospect theory-based consistency recovery strategies are explored and used to build a GDM support model that considers different risk attitudes of decision makers. Its applicability and effectiveness are validated by conducting an illustrative example and a comparative analysis with other existing methods in the context of energy site selection. Finally, conclusions are drawn.

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.

Expanding Grey Relational Analysis With the Comparable Degree for Dual Probabilistic Multiplicative Linguistic Term Sets and its Application on the Cloud Enterprise

Under the cloud trend of enterprises, how do traditional businesses get on the cloud becomes a worth pondering question. To help those traditional businesses that have no experience to dispel the clouds and see the sun as soon as possible, we are planning to choose one corporation with rich experience to take them into the cloud market. The quintessence of dual probabilistic linguistic term sets (DPLTSs) is that it uses the combination of several linguistic terms and their proportions to reveal decision information by opposite angles. This paper proposes the dual probabilistic multiplicative linguistic preference relations (DPMLPRs) based upon the dual probabilistic multiplicative linguistic term sets (DPMLTSs). Then, it defines the comparable degree between the DPMLPRs and studies the consensus of the group DPMLPR. Moreover, it probes the expanding grey relational analysis (EGRA) under the proposed comparable degree between the DPMLTSs. After that, one example of choosing the experienced cloud cooperative partner is simulated under the dual probabilistic linguistic circumstance. Besides, the comparative analysis is performed by considering the similarity among the EGRA, TODIM, and VIKOR.

Adaptive consensus model with multiplicative linguistic preferences based on fuzzy information granulation

An adaptive consensus model based on fuzzy information granulation (fuzzy IG) is presented for group consensus decision-making problems with multiplicative linguistic preference relations (MLPRs). Firstly, a granular representation of linguistic terms is concerned with the triangular fuzzy formation of a family of information granules over given Analytical Hierarchy Process (AHP) numerical scales. On this basis, the individual consistency and group consensus measure indices using fuzzy granulation technique are constructed, respectively. Then, the optimal cut-off points of fuzzy information granules are obtained by establishing a multi-objective optimization model together with a multi-objective particle swarm optimization (MOPSO) algorithm. A novel group consensus decision-making approach where consensus reaching process (CRP) is achieved by adaptively adjusting individual preferences through the optimization of the cut-off points is proposed. After conflict elimination, the obtained group preference gives the ranking of the alternatives. Finally, a real emergency decision-making case for liquid ammonia leak is given to illustrate the application steps of the proposed method and comparative analysis with the existing GDM methods. Comparative results demonstrate that the proposed method has some advantages in aspects of avoiding information loss or distortion and improving consensus performance.

The induced linguistic continuous ordered weighted geometric operator and its application to group decision making

In this paper, based on the induced linguistic ordered weighted geometric (ILOWG) operator and the linguistic continuous ordered weighted geometric (LCOWG) operator, we develop the induced linguistic continuous ordered weighted geometric (ILCOWG) operator, which is very suitable for group decision making (GDM) problems taking the form of uncertain multiplicative linguistic preference relations. We also present the consistency of uncertain multiplicative linguistic preference relation and study some properties of the ILCOWG operator. Then we propose the relative consensus degree ILCOWG (RCD-ILCOWG) operator, which can be used as the order-inducing variable to induce the ordering of the arguments before aggregation. In order to determine the weights of experts in group decision making (GDM), we define a new distance measure based on the LCOWG operator and develop a nonlinear model on the basis of the criterion of minimizing the distance of the uncertain multiplicative linguistic preference relations. Finally, we analyze the applicability of the new approach in a financial GDM problem concerning the selection of investments.

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 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.

POWER GEOMETRIC OPERATORS FOR GROUP DECISION MAKING UNDER MULTIPLICATIVE LINGUISTIC PREFERENCE RELATIONS

The aim of this paper is to develop some new linguistic aggregation operators, such as linguistic power geometric (LPG) operator, linguistic weighted PG operator, LPOWG operator which are based on PG operator. We have studied some desired properties of the developed operators, such as commutativity, idempotency, boundary, etc. Moreover, we have developed two approaches to deal with group decision making problems under multiplicative linguistic preference relations. If the weighting vector of the decision makers is known, we develop an approach which is based on the linguistic weighted PG operator. On the other hand, if the weighting vector of the decision makers is unknown, we develop another approach which is based on the LPOWG. Finally, a practical example is given to illustrate the multiple attribute group decision making process; a comparative study to the linguistic weighted geometric average (LWGA) operator method is also demonstrated.

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 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.

An ILOWG operator based group decision making method and its application to evaluate the supplier criteria

The aim of this work is to present some cases of the induced linguistic ordered weighted geometry (ILOWG) operators and study their desired properties, which are very suitable to deal with group decision making (GDM) problems involving multiplicative linguistic preference relations. First, the concepts of compatibility index (CI) for two multiplicative linguistic preference relations are defined. Then, we provide some ILOWG operators to aggregate multiplicative linguistic preference relations in GDM problems. In particular, we present the compatibility index ILOWG (CI-ILOWG) operator, which induces the order of argument values by utilizing the compatibility index of experts; and the importance ILOWG (I-ILOWG) operator, which induces the order of argument values based on the importance index of the experts. Next, the reciprocity, consistency and compatibility properties of the collective multiplicative linguistic preference relations obtained by these cases of ILOWG operators are verified. Finally, the aggregation of individual judgements (AIJ) and the aggregation of individual priorities (AIP) provide the same priorities of alternatives by utilizing the row geometric mean method (RGMM) as a prioritization procedure and the ILOWG operators as an aggregation procedure. Our results show that if all the individual decision makers have an acceptable consensus degree, then the collective preference relation is also of an acceptable consensus degree. Moreover, the compatibility index induced linguistic ordered weighted geometric mean complex judgement matrix (CI-ILOWGCJM) guarantees that the group compatibility degree is at least as good as the arithmetic mean of all the individual compatibility degrees. Accordingly, a theoretic basis has been developed for the application of these cases of ILOWG operators in linguistic group decision making. Finally, a numerical example for evaluating criteria of supply selection is given to illustrate the application of the results.

Interactive group decision making procedure based on uncertain multiplicative linguistic preference relations

Group decision making problems are investigated with uncertain multiplicative linguistic preference relations. An unbal- anced multiplicative linguistic label set is introduced, which can be used by the experts to express their linguistic preference informa- tion over alternatives. The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncer- tain multiplicative linguistic preference relations into a collective one, and then a simple approach is developed to determining the experts' weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference re- lations. Furthermore, a practical interactive procedure for group decision making is proposed based on uncertain multiplicative lin- guistic preference relations, in which a possibility degree formula and a complementary matrix are used to rank the given alterna- tives. Finally, the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.

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.

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 Practical Procedure for Group Decision Making under Incomplete Multiplicative Linguistic Preference Relations

The aim of this paper is to investigate a group decision making problem with incomplete multiplicative linguistic preference relations. We first define the concept of an incomplete multiplicative linguistic preference relation, and then develop a simple algorithm to extend each incomplete multiplicative linguistic preference relation to a complete multiplicative linguistic preference relation. Finally, we develop a practical procedure for group decision making under incomplete multiplicative linguistic preference relations, and give a numerical example to illustrate the developed procedure.

Extended IOWG Operator and its Use in Group Decision Making Based on Multiplicative Linguistic Preference Relations

In [1], Xu and Da introduced the Induced Ordered Weighted Geometric (IOWG) operator, which takes as its argument pairs, called OWG pairs, in which one component is used to induce an ordering over the second components which are exact numerical values and then aggregated. In this study, we develop an extended IOWG (EIOWG) operator, in which the second components are linguistic variables. We study some desirable properties of the EIOWG operator, and then apply the EIOWG operator to group decision making based on multiplicative linguistic preference relations.