Fuzzy Linguistic Preference Relations Research Articles

A NEW MODEL FOR FUZZY PERSONALIZED ROUTE PLANNING USING FUZZY LINGUISTIC PREFERENCE RELATION

Abstract. This paper proposes a new model for personalized route planning under uncertain condition. Personalized routing, involves different sources of uncertainty. These uncertainties can be raised from user’s ambiguity about their preferences, imprecise criteria values and modelling process. The proposed model uses Fuzzy Linguistic Preference Relation Analytical Hierarchical Process (FLPRAHP) to analyse user’s preferences under uncertainty. Routing is a multi-criteria task especially in transportation networks, where the users wish to optimize their routes based on different criteria. However, due to the lake of knowledge about the preferences of different users and uncertainties available in the criteria values, we propose a new personalized fuzzy routing method based on the fuzzy ranking using center of gravity. The model employed FLPRAHP method to aggregate uncertain criteria values regarding uncertain user’s preferences while improve consistency with least possible comparisons. An illustrative example presents the effectiveness and capability of the proposed model to calculate best personalize route under fuzziness and uncertainty.

A NEW MULTI-CRITERIA EVALUATION MODEL BASED ON THE COMBINATION OF NON-ADDITIVE FUZZY AHP, CHOQUET INTEGRAL AND SUGENO λ-MEASURE

Abstract. This paper proposes a new model for multi-criteria evaluation under uncertain condition. In this model we consider the interaction between criteria as one of the most challenging issues especially in the presence of uncertainty. In this case usual pairwise comparisons and weighted sum cannot be used to calculate the importance of criteria and to aggregate them. Our model is based on the combination of non-additive fuzzy linguistic preference relation AHP (FLPRAHP), Choquet integral and Sugeno λ-measure. The proposed model capture fuzzy preferences of users and fuzzy values of criteria and uses Sugeno λ -measure to determine the importance of criteria and their interaction. Then, integrating Choquet integral and FLPRAHP, all the interaction between criteria are taken in to account with least number of comparison and the final score for each alternative is determined. So we would model a comprehensive set of interactions between criteria that can lead us to more reliable result. An illustrative example presents the effectiveness and capability of the proposed model to evaluate different alternatives in a multi-criteria decision problem.

An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations

ABSTRACTAs a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was recently introduced to efficiently deal with situations in which the membership and non-membership are represented as linguistic terms. In this paper, we study the issues of additive consistency and the derivation of the intuitionistic fuzzy weight vector of an IFLPR. First, the new concepts of order consistency, additive consistency and weak transitivity for IFLPRs are introduced, and followed by a discussion of the characterisation about additive consistent IFLPRs. Then, a parameterised transformation approach is investigated to convert the normalised intuitionistic fuzzy weight vector into additive consistent IFLPRs. After that, a linear optimisation model is established to derive the normalised intuitionistic fuzzy weights for IFLPRs, and a consistency index is defined to measure the deviation degree between an IFLPR and its additive consistent IFLPR. Furthermore, we develop an automatic iterative decision-making method to improve the IFLPRs with unacceptable additive consistency until the adjusted IFLPRs are acceptable additive consistent, and it helps the decision-maker to obtain the reasonable and reliable decision-making results. Finally, an illustrative example is provided to demonstrate the validity and applicability of the proposed method.

A Gower Plot-Based Approach to Ascertain and Adjust the Ordinal and Additive Inconsistencies for Fuzzy Linguistic Preference Relations

This paper studies the ordinal and additive consistency issues of fuzzy linguistic preference relations (FLPRs). First, a graphic method of Gower plot is proposed to ascertain ordinal and additive inconsistencies for FLPRs. Then, two optimization models are established to adjust the ordinal and additive inconsistencies at the same time. Furthermore, an approach based on Gower plot is developed to help the decision maker to improve the consistency and rank the alternatives which respects the views of decision makers with greatest degree. Finally, numerical examples and comparisons with the existing methods are furnished to show the effectiveness and advantages of the proposed method.

A decision support model for group decision making with intuitionistic fuzzy linguistic preferences relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was introduced to efficiently cope with situations in which the membership degree and non-membership degree are represented as linguistic terms. For group decision making (GDM) problems with IFLPRs, two significant and challenging issues are individual consistency and group consensus before deriving the reliable priority weights of alternatives. In this paper, a novel decision support model is investigated to simultaneously deal with the individual consistency and group consensus for GDM with IFLPRs. First, the concepts of multiplicative consistency and weak transitivity for IFLPRs are introduced and followed by a discussion of their desirable properties. Then, a transformation approach is developed to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFLPR. Based on the distance of IFLPRs, the consistency index, individual consensus degree and group consensus degree for IFLPRs are further defined. In addition, two convergent automatic iterative algorithms are proposed in the investigated decision support model. The first algorithm is utilized to convert an unacceptable multiplicative consistent IFLPR to an acceptable one. The second algorithm can assist the group decision makers to achieve a predefined consensus level. The main characteristic of the investigated decision support model is that it guarantees each IFLPR is still acceptable multiplicative consistent when the predefined consensus level is achieved. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate the effectiveness and practicality of the investigated model.

A group consensus decision support model for hesitant 2-tuple fuzzy linguistic preference relations with additive consistency

Hesitant fuzzy linguistic term sets suit the modelling of qualitative setting so that experts provide several possible linguistic values than a single term for an indicator, alternative, variable, etc. This paper proposes a consistency and consensus based decision support model for group decision m aking with hesitant 2-tuple fuzzy linguistic preference relations (H2TFLPRs). A revised definition of hesitant fuzzy linguistic preference relation (HFLPR) is presented. In order to measure the consensus degrees, two indexes, an individual to group consensus index (ICI) and a group consensus index (GCI) are introduced, respectively. A consistency control process is developed to transform an unacceptable consistency H2TFLPR to an acceptable one. Then, an iterative group consensus reaching process is designed to conduct the decision makers (DMs) to achieve the predefined consensus level. In the consistency and consensus improving process, both the feedback mechanism and no-feedback mechanism are devised to conduct the DMs how to modify their original judgments, and both mechanisms can retain the DMs’ original information as much as possible. Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed method.

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness.

Fuzzy multicriteria decision‐making tools for selecting a professional property management company

AbstractThis study develops a model to assist a condominium committee in selecting an appropriate property management company. This model adopts the literature reviews and expert interviews to construct the suitable evaluation criteria of property management companies, then applies the fuzzy linguistic preference relations to determine the relative weights of evaluation criteria, and adopts the fuzzy technique for order preference by similarity to ideal solution (TOPSIS) and fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) approaches to rank the alternatives for the condominium committee. Additionally, a condominium in Da'an District of Taipei is used as an example of how an appropriate property management firm can be selected using these two models. The results of fuzzy TOPSIS and fuzzy VIKOR are compared and discussed to understand the properties of selecting alternatives. The model proposed here allows the condominium committee to select professional property management firms systematically, making it highly applicable for academia and practices.

Comments on “A note on “Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP” ”

A very recent note by Pandey and Kumar [3] pointed out some mathematical incorrect assumptions with respect to the statement and proof of the results given by Wang and Chen [8]. Furthermore, the note had modified the statement and proof of the results. This paper shows that the modified results are technically and logically incorrect. New properties of fuzzy linguistic preference relations are developed to correct flaws in the existing results, and a triangular fuzzy addition based transitivity equation is introduced to define additively consistent fuzzy linguistic preference relations.

A model based on subjective linguistic preference relations for group decision making problems

In a group decision making problem, experts often express their opinions through the so-called preference relations. In recent years, several different definitions of preference relations depending on the framework and the nature of the problem have been introduced. These approaches vary from interval-valued fuzzy preference relations to incomplete fuzzy linguistic preference relations. In this paper, a novel definition of preference relation, the so-called subjective linguistic preference relation, is proposed. These preference relations are based on the concept of subjective evaluations, introduced in the linguistic computational model based on discrete fuzzy numbers. In this framework, the experts have more flexibility to express their opinions and the solid mathematical background of this model is a guarantee of no loss of information. Finally, an example of a multi-expert decision making problem with a hierarchical multi-granular linguistic context is analyzed to illustrate the potential of the proposed method and its advantages with respect to other methods.

A note on ‘‘Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP”

Wang and Chen (2008) stated and proved some results (Proposition 5.1, Proposition 5.2, Information Sciences, 178 (2008), 3759) and used these results to propose a method to construct fuzzy linguistic preference relation matrices. In this paper, it is pointed out that Wang and Chen have used some mathematical incorrect assumptions for proving these results. Hence, the statement and proof of these results as well as the method, proposed by Wang and Chen, are not valid. Further, the exact results are stated and proved.

Selecting appropriate ERP software using integrated fuzzy linguistic preference relations – fuzzy TOPSIS method

AbstractDue to the high uncertainty of business environment, the complexity and diversity of enterprise resource planning (ERP) projects and conflicting assessment criteria, appropriate ERP software selection can be viewed as a multi-criteria decisionmaking (MCDM) problem. Among the MCDM methods, extent analysis method (EAM) has been employed in many applications due to its computational simplicity. However, in EAM, inconsistency rises as the numbers of criteria or alternatives increase. In order to address this inconsistency problem, fuzzy linguistic preference relations (FLPR) has been proposed to obtain consistent solutions in the decision-making processes. This study proposes a robust ERP selection framework where the weights of the evaluation criteria are computed through FLPR and the ranking of the alternative ERP systems is obtained via Fuzzy TOPSIS. A real life application has been executed in a Turkish wholesale food company.

An Evaluation of Abidjan Container Terminal Competitive Position in West Africa Using a Fuzzy Quantified SWOT Framework

This article proposes a quantified SWOT framework which integrates fuzzy linguistic preference relation to evaluate the competitive position of Abidjan container terminal in West Africa. The integration of fuzzy linguistic preference relation in the quantified SWOT framework circumvents the difficulties in terms of data collection and consistency of judgment matrices prevailing in the conventional AHP and Fuzzy AHP. Moreover, the study provides relevant evidences about the key internal and external attributes shipping lines considered as important and hence the attributes that ports/ terminals most need to enhance in order to improve their attractiveness and be well positioned in the market. On the other hand, the change in terminals competitive position between 2010 and 2013 highlights that the difficulties of West African ports in attracting customers in the sub-region are not only related to internal problems such as inadequate infrastructures, facilities or inefficiency, but significant political and economic constraint outside the ports constraints their competitiveness.

Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations

The use of hesitant information in pairwise comparisons enriches the flexibility of qualitative decision making and allows for hesitant fuzzy linguistic preference relation (HFLPR). This paper develops separate consistency and consensus processes to deal with HFLPR individual rationality and group rationality. First, a possibility distribution approach and a 2-tuple linguistic model are introduced as support tools. Then, a new consistency measure is defined and a convergent algorithm described to aid the consistency improvement process in a given HFLPR. The algorithm adopts a local revision strategy and can be easily interpreted. Further, a direct consensus reaching process is presented to solve the HFLPR consensus problems. A prominent characteristic of this consensus reaching process is that the feedback system is based directly on the consensus degrees, thereby reducing the proximity measure calculations. Finally, the proposed consistency and consensus processes are applied to an investment project selection problem. The results and an in-depth comparative analysis verify the potential use and effectiveness of the proposed methods.

A new consensus model for group decision making using fuzzy linguistic preference relations with heterogeneous experts

Group decision making (GDM) problems consist of finding the most acceptable solution based on a group of experts’ preferences. Sometimes, the experts experience difficulty expressing their preferences using crisp values or making comparisons between each pair of alternatives. Meanwhile, because of their different backgrounds or knowledge concerning a specific problem, the opinions of different experts may carry different weights along the decision process. Thus, a new consensus model is proposed to solve these problems. First, experts are required to express their opinions using fuzzy linguistic preference relations, and then, a new method is proposed for classifying the experts into three different importance levels according to these opinions. Then, consistency measures and proximity measures are used to guide the decision-making process. A new feedback mechanism that generates advice for experts according to their different levels is proposed. The importance degrees of experts are taken into consideration throughout the process, which is one of the main novelties of this model. Finally, a numerical example is conducted to illustrate the utilization and compared results are also presented to check the feasibility of the proposed model.

Group decision making with fuzzy linguistic preference relations via cooperative games method

When we consider the weighting approach for group decision making with fuzzy linguistic preference relations, the groupment of experts has merely been studied. In this paper, a novel weighting approach on the basis of cooperative games method is developed. The group decision error matrix is built to reflect the deviations of all experts with given initial weighting vector. An iterative algorithm is designed to lower the sum of the decision error so that a final convergence result can be obtained. The advantage of the weighting algorithm is that it can consider the contribution of each expert and reduce the sum of decision error with increasing iteration numbers. Then an optimization model using triangular fuzzy numbers as alternatives’ weights is constructed, whose results are used to rank the alternatives. Finally, a numerical example of subjective evaluation of vehicle sound quality is considered to illustrate the feasibility and validity of the proposed weighting approach in the group decision making problem.

Group Decision Making Using Fuzzy Linguistic Preference Relations under Uncertain Environment

When facing problems, evaluators use fuzzy preference relations to express their opinions toward attributes or alternatives. Studies on fuzzy preference relations have been gained much attention recently, but the values of constructing fuzzy preference relations are crisp. This paper thus proposes the evaluators the consistent fuzzy linguistic preference relations (Fuzzy LinPreRa) parameterized with fuzzy linguistic variables rather than crisp values to compare the alternatives/attributes. Furthermore, an approach for group decision making based on the Fuzzy LinPreRa method is presented. The proposed method enables evaluators to deal with some uncertainty or vagueness and ensures a more convincing and effective decision making. A practical example is demonstrated to illustrate this method.

Some consistency measures of extended hesitant fuzzy linguistic preference relations

Linguistic preference relations (LPRs) enable decision makers to express preferences by pair-wise comparisons in qualitative setting. The fundamental aspect of LPRs is to measure the degrees of consistency when applying them in decision making. Extended hesitant fuzzy linguistic term sets (EHFLTSs) are a powerful tool for modeling uncertain linguistic information in group decision making. Based on which we first present the concept of extended hesitant fuzzy linguistic preference relations (EHFLPRs), and then develop the additive consistency measure and the weak consistency measure respectively. Furthermore, in order to solve the consistency problem by the perspective of graphs, two algorithms are proposed based on two kinds of predefined graphs, i.e., the hesitant preference graphs and the symmetric hesitant preference graph. The selective algorithm selects the arcs with the highest additive consistency level from the symmetric hesitant preference graph and constructs a LPR. While the broken circle algorithm removes the arcs from circular triads of the hesitant preference graph, it makes the EHFLPR with weak consistency and divides the EHFLPR into several possible LPRs satisfying weak consistency. This paper therefore explores a visible interpretation of consistency measures. The rationality of the proposed algorithms is verified by several examples, and some related issues are also discussed.

On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations

As a new preference structure, the hesitant fuzzy linguistic preference relation (HFLPR) was recently introduced by Rodríguez, Martínez, and Herrera to efficiently address situations in which the decision makers (DMs) are hesitant about several possible linguistic terms for the preference degrees over paired comparisons of alternatives. In this paper, we define the multiplicative consistency of HFLPRs to ensure that the DMs are being neither random nor illogical, and propose a characterization about the multiplicative consistency of HFLPRs. A consistency index is defined to measure the deviation degree between a HFLPR and its multiplicative consistent HFLPR. For a HFLPR with unacceptably multiplicative consistency, we develop a consistency-improving process to adjust it into an acceptably multiplicative one. Moreover, we use the hesitant fuzzy linguistic aggregation operators to aggregate preferences in the acceptably multiplicative HFLPR to obtain the ranking results. Several illustrative examples are further provided to verify the developed methods. Finally, a comparison with other methods in the existing literature is performed to illustrate the advantages of the new methods.

Iterative algorithms for improving consistency of intuitionistic preference relations

Consistency of preference relations is an important research topic in decision making with preference information. The existing research about consistency mainly focuses on multiplicative preference relations, fuzzy preference relations and linguistic preference relations. Intuitionistic preference relations, each of their elements is composed of a membership degree, a non-membership degree and a hesitation degree, can better reflect the very imprecision of preferences of decision makers. There has been little research on consistency of intuitionistic preference relations up to now, and thus, it is necessary to pay attention to this issue. In this paper, we first propose an approach to constructing the consistent (or approximate consistent) intuitionistic preference relation from any intuitionistic preference relation. Then we develop a convergent iterative algorithm to improve the consistency of an intuitionistic preference relation. Moreover, we investigate the consistency of intuitionistic preference relations in group decision making situations, and show that if all individual intuitionistic preference relations are consistent, then the collective intuitionistic preference relation is also consistent. Moreover, we develop a convergent iterative algorithm to improve the consistency of all individual intuitionistic preference relations. The practicability and effectiveness of the developed algorithms is verified through two examples.