Consistent Linguistic Preference Relations Research Articles

Measuring Additive Consistency of Linguistic Preference Relations in a Personalized-Individual-Semantics Context: A Systematic Investigation With Axiomatic Design

Measuring Additive Consistency of Linguistic Preference Relations in a Personalized-Individual-Semantics Context: A Systematic Investigation With Axiomatic Design

Consistency Improvement With a Feedback Recommendation in Personalized Linguistic Group Decision Making.

Consistency is an important issue in linguistic decision making with various consistency measures and consistency improving methods available in the literature. However, existing linguistic consistency studies omit the fact that words mean different things for different people, that is, decision makers' personalized individual semantics (PISs) over their expressed linguistic preferences are ignored. Therefore, the aim of this article is to propose a novel consistency improving approach based on PISs in linguistic group decision making. The proposed approach combines the characteristics of personalized representation and integrates the PIS-based model in measuring and improving the consistency of linguistic preference relations. A detailed numerical and comparative analysis to support the feasibility of the proposed approach is provided.

Multiplicative consistency of linguistic preference relations with weakened hedges

Preference relations are often used to derive the priority of attributes and/or alternatives. Linguistic term with weakened hedges (LTWH) as a type of complex linguistic expressions can more straightforwardly describe the linguistic information provided by DMs when evaluating under uncertainties. The preference relations represented by LTWHs are an effective tool to model linguistic information. The concept and properties of additive consistency have been proposed before. This paper aims to study the multiplicative consistency of preference relations expressed by LWTHs. This paper constructs the principle of inspection for multiplicative consistency. Especially, the theories and algorithms for consistency checking and improving are proposed. We develop an automatic approach to improve a LWHPR that is not multiplicatively consistent. Finally, we demonstrate the practicality of the proposed method through a case study of evaluating the attributes in the prevention of haze pollution in China.

Improving Reliability for Linguistic Preference Relations Considering New Ordinal and Cardinal Consistency Measures

Linguistic preference relations (LPRs) and its variations served for different decision-making situations are significantly important instruments of qualitative decision-making. The consistency analysis of LPRs is a necessary prerequisite for further operations of these original preference relations so as to ensure that the final decision results are convincing. However, the existing consistency improvement methods for LPRs are difficult to guarantee the reliability of the revised LPRs. Because the suggested LPRs from these methods either not eliminate the ordinal inconsistency or not satisfy the expectation of minimum modification. In this paper, a new definition of ordinal consistency of LPRs is first proposed and then an optimization approach is constructed to eliminate ordinal inconsistency for LPRs. Secondly, a new cardinal consistency index for LPRs is proposed and a corresponding optimization model to increase the cardinal consistency level is presented. After that, an optimization model is proposed to simultaneously manage ordinal and cardinal inconsistency for LPRs. Last, the proposed models are applied to a real linguistic decision-making problem involving evaluation and selection of investment projects. The comparative analysis and discussion illustrate the applicability and effectiveness of the proposed models.

Algorithm for improving additive consistency of linguistic preference relations with an integer optimization model

Linguistic preference relation (LPR) composed by linguistic terms can well express decision makers’ (DMs’) qualitative preference opinion by comparing alternatives with each other. The investigation of its consistency becomes an important issue to guarantee the rationality of the decision making solutions. Therefore, it is significant to investigate the consistency measure and the consistency improving approach for LPRs. In this paper we present a new method for group decision making (GDM) with LPRs. First, an additive consistency index is introduced on the basis of the information of the original LPR to check whether a LPR is acceptably additive consistency. For unacceptably additively consistent LPR, an integer optimization model is further developed to obtain the acceptably additively consistent LPR. Moreover, the optimization model can guarantee the integrity of the information of the LPR with acceptably additive consistency. Then, with respect to GDM with LPRs, an entropy weight method is proposed to determine the weights of DMs. Finally, the proposed methods are implemented in two numerical examples including a GDM problem. Meanwhile, the comparative analysis with existing methods are discussed in detail to demonstrate the validity of the proposed methods.

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.

Measuring consistency of linguistic preference relations: a 2-tuple linguistic approach

By using the 2-tuple fuzzy linguistic representation model and by proposing the concept of the individual consistency evaluations, this paper develops a 2-tuple linguistic index to measure the consistency degree of linguistic preference relations. Comparing with the existing numerical consistency indexes, the proposed linguistic index not only measures the consistency degree of linguistic preference relations via a linguistic way, but also can reflect the individual difference on consistency degree of linguistic preference relations. Further, this paper proposes an algorithm to improving consistency degree in linguistic preference relations, and the proof of the convergence of this algorithm is also given. The results in this paper provide a theoretic basis for the application of consistent linguistic preference relations in decision making problems.

Measuring the success possibility of implementing ERP by utilizing the Incomplete Linguistic Preference Relations

This paper applies an analytic hierarchical prediction model based on the Multi-Criteria Decision Making with Incomplete Linguistic Preference Relations (InLinPreRa) to help the organizations become aware of the essential factors affecting the Enterprise Resource Planning (ERP), as well as identify the actions necessary before implementing ERP. The subjectivity and vagueness in the prediction procedures are dealt with linguistic variables quantified in an interval [−t, t]. Then predicted success/failure values are obtained to enable organizations to decide whether to initiate ERP, inhibit adoption or take remedial actions to increase the success possibility of ERP. Pairwise comparisons are used to determine the priority weights of influential factors, and the possible occurrence ratings of success or failure outcome amongst decision makers. There are not any inconsistency occurred in this procedures because this proposed approach allows every decision expert to choose an explicit criterion or alternative for the without restriction. When there are n criteria in a decision matrix, only n−1 times of pairwise comparisons are taken. This approach not only improves the efficiency of pairwise comparison compared with the traditional AHP, but also avoids the checking the consistency of linguistic preference relation when the decision makers undertake the pairwise comparison processes.

Some properties of linguistic preference relation and its ranking in group decision making

The group decision making problem with linguistic preference relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent linguistic preference relation are studied. In order to rank the alternatives in the group decision making with the linguistic preference relations, the weighted average is first utilized to combine the group linguistic preference relations to one linguistic preference relation, and then the transformation function is proposed to transform the linguistic preference relation to the multiplicative preference relation, and thus the Saaty's eigenvector method (EM) of multiplicative preference relation is utilized to rank the alternatives in group decision making with the linguistic preference relations. Finally, an illustrative numerical example is given to verify the proposed method. A comparative study to the linguistic ordered weighted averaging (LOWA) operator method is also demonstrated.

On consistency measures of linguistic preference relations

Inspired by the concept of deviation measure between two linguistic preference relations, this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. This method is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons using the linguistic label set. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. These results are of vital importance for group decision making with linguistic preference relations.

Incomplete linguistic preference relations and their fusion

Various linguistic preference relations, including incomplete linguistic preference relation, consistent incomplete linguistic preference relation and acceptable incomplete linguistic preference relation, are introduced. Some desirable properties of the incomplete linguistic preference relation are studied. Based on the operational laws of the linguistic evaluation scale, and the acceptable incomplete linguistic preference relation with the least judgments, we develop a simple and practical method for constructing a consistent complete linguistic preference relation by using the additive transitivity property. The method not only relieves the decision maker of time pressure and makes sufficiently using of the provided preference information, but also maintains the decision maker's consistency level and avoids checking the consistency of linguistic preference relation. Furthermore, an approach to multi-person decision making based on incomplete linguistic preference relations is developed. The approach fuses all the consistent complete linguistic preference relations, constructed by using the individual acceptable incomplete linguistic preference relations with the least judgments, into a collective complete linguistic preference relation, and then the overall information corresponding to each decision alternative is aggregated. Finally, an illustrative example is given.