Incomplete Fuzzy Preference Relations Research Articles

Existence and simulation of multiple solutions to an optimization model for completing incomplete fuzzy preference relations

Existence and simulation of multiple solutions to an optimization model for completing incomplete fuzzy preference relations

Mining Maximum Ordinal–Cardinal Consensus for Large-Scale Group Decision Making With Incomplete Fuzzy Preference Relations

Mining Maximum Ordinal–Cardinal Consensus for Large-Scale Group Decision Making With Incomplete Fuzzy Preference Relations

A multi-criteria group decision-making method with fuzzy preference relations based on filtration-and-weighting-based triangular bounded consistency

In multi-criteria group decision-making (MCGDM) problems with incomplete fuzzy preference relations (FPRs), the consistency based on bounded rationality is preferred to depend on the historical preferences of decision makers to generate complete FPR matrices. There are two factors in influencing the effect of historical preferences on complete FPR matrices and further decision makers’ satisfaction of group solutions. One is the effectiveness of historical preferences and the other is their relative weights. On this basis, this paper proposes a new MCGDM method with FPRs based on the filtration-and-weighting-based triangular bounded consistency (FWBTBC), where historical FPRs between three adjacent pairs of alternatives are characterized by triangles and these two factors are considered comprehensively. A triangle filtration process is designed based on the Grubbs criterion to filter the abnormal triangles in the collected ones. A weight determination process is developed, where a distance measure between remaining triangles is constructed to calculate their weights. Based on the combination of the two processes, the FWBTBC of FPRs is created and then the proposed method is presented. The validity of the proposed method is demonstrated by its application in analyzing a drainage tube supplier selection problem for a tertiary hospital located in Hefei, Anhui, China.

Corrigendum to “Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation” [Applied Mathematical Modelling 37(2013) 5171–5183

Corrigendum to “Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation” [Applied Mathematical Modelling 37(2013) 5171–5183

Deriving priorities based on representable uninorms from fuzzy preference relations

Deriving priorities of objects from preference relations is an important research topic for decision making with preference information. In this paper, this issue is solved for fuzzy preference relations using representable uninorms, with which several alternative definitions of representable uninorm-based consistency (⊗-consistency) are provided for complete and incomplete fuzzy preference relations. In particular, a procedure to evaluate incomplete fuzzy preference relations with arbitrary n−1 independent preference values is provided. Furthermore, a novel acceptable ⊗-consistency is defined by the proposed local priority vectors, and then a method to check and reach the ⊗-consistency of fuzzy preference relations by reducing the distances between the optimal priority vector and local ones is proposed. Specific examples are illustrated to show how the models work, and comparisons with the existing methods are also offered to show the advantages of the proposed method.

Large-scale group decision-making with incomplete fuzzy preference relations: The perspective of ordinal consistency

Incomplete preferences have become increasingly common in light of the redundancy of information and time-related pressures. Incomplete fuzzy preference relations (IFPRs) have thus attracted considerable research interest in recent years. A number of relevant studies have tended to rely on the cardinal consistency of a single IFPR or an aggregated group of preference relations. However, the preference-related information on which the final decision relies may be not reliable because ordinal inconsistency might persist following the application of cardinal consistency or an improvement in consensus. This paper proposes an optimization model that considers both cardinal consistency and ordinal consistency to estimate unknown preferences in IFPRs. The authors develop a model to optimize the consensus in problems involving large-scale group decision-making by using IFPRs. The proposed model can explicitly control ordinal consistency, minimize the extent of requisite modifications to the preferences, and guarantee that the cardinal and ordinal consistencies are well managed when a predefined level of consensus has been achieved to a greater extent than prevalent approaches to estimate unknown preferences. The individual and group FPRs revised by using the proposed model are more reliable as they contain no contradictory elements. Several classical numerical examples are used to verify the superiority of the proposed model to those currently used in the area.

Water–Energy–Food nexus evaluation using an inverse approach of the graph model for conflict resolution based on incomplete fuzzy preferences

With the continuous development of economic globalization and the increasing strengthening of human exchanges, the Water–Energy–Food (WEF) nexus evaluation has become a new research area. The purpose of this paper is to develop an inverse approach of graph model for conflict resolution (GMCR) to the conflict problems of WEF nexus evaluation in real life. Specifically, due to lack of information, some decision makers’ (DMs’) preferences over states may be incomplete fuzzy preference relations. Therefore, an algorithm is devised to amend the incomplete fuzzy preference relation to the complete fuzzy preference relation. Subsequently, a complete ordinal score vector is proposed to describe the preference ranking over different states based on the complete fuzzy preference relation. Moreover, in the framework of the inverse approach of GMCR, some mathematical models with the least constraint conditions are proposed to obtain all the required preference relations for opponent DM, which are required to make a given state be stable under four basic stability definitions. Finally, WEF nexus evaluation in Shandong province is illustrated to demonstrate the usefulness of the inverse approach of GMCR with the incomplete fuzzy preference relations.

A new group decision making approach based on incomplete probabilistic dual hesitant fuzzy preference relations

As an enhanced version of probabilistic hesitant fuzzy sets and dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets (PDHFSs) combine probabilistic information with the membership degree and non-membership degree, which can describe decision making information more reasonably and comprehensively. Based on PDHFSs, this paper investigates the approach to group decision making (GDM) based on incomplete probabilistic dual hesitant fuzzy preference relations (PDHFPRs). First, the definitions of order consistency and multiplicative consistency of PDHFPRs are given. Then, for the problem that decision makers (DMs) cannot provide the reasonable associated probabilities of probabilistic dual hesitant fuzzy elements (PDHFEs), the calculation method of the associated probability is given by using an optimal programming model. Furthermore, the consistency level for PDHFPRs is tested according to the weighted consistency index defined by the risk attitude of DMs. In addition, a convergent iterative algorithm is proposed to enhance the unacceptable consistent PDHFPRs’ consistency level. Finally, a GDM approach with incomplete PDHFPRs is established to obtain the ranking of the alternatives. The availability and rationality of the proposed decision making approach are demonstrated by analyzing the impact factors of haze weather.

On the Analytic Hierarchy Process Structure in Group Decision-Making Using Incomplete Fuzzy Information with Applications

The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts’ inclinations. Under essential conditions, the fuzzy MCDM method can provide more acceptable and efficient outcomes to select the best alternatives. This work consists of a consensus-based technique for selecting and evaluating suppliers in an incomplete fuzzy preference relations (IFPRs) environment utilizing TL-transitivity (Lukasiewicz transitivity). The suggested method is developed based on the criteria of the Analytical Hierarchy Process (AHP) Fframework, and the decision matrix is construtced using consistent fuzzy preference relations (FPRs). We use the symmetrical decisional matrix approach. A variety of numerical explanations and an analysis of quantitative results illustrate the suggested methodology’s logic and effectiveness.

Social network community analysis based large-scale group decision making approach with incomplete fuzzy preference relations

Large-scale group decision making (LSGDM) is characterized by a large number of participators, multiple groups and a mass of decision data provided by the participators. With the development of social media and e-democracy technologies, the social relationships among group decision makers should be taken into consideration when we address LSGDM problems with incomplete fuzzy preference relations. In this paper, a social network community detection approach of social networks based on the fuzzy clustering method is proposed. Then, a method of repairing incomplete fuzzy preference relations based on the divided communities is proposed. Moreover, we have proposed a two-stage consensus reaching method to balance the number of iterations and modification range of original decision information, in which the group closeness centrality of community is applied to measure its importance. Also, the procedure for LSGDM with fuzzy preference relations based on social network community analysis is established. The feasibility and advantages of the proposed method for LSGDM based on social network community analysis are illustrated by an illustrative example of a flexible manufacturing system.

Two new methods for decision-making with incomplete reciprocal fuzzy preference relations based on additive consistency

ABSTRACT In this paper, we propose two new methods to solve the problem of incomplete reciprocal fuzzy preference relations. Sometimes decision-maker(s) might not be able to provide complete information about their preferences on the alternatives. In general, an incomplete preference relation can be completed if at least a set of nonleading diagonal preference values are known and each one of the alternatives is compared directly or indirectly at least once. However, this is not always the case. Sometimes, the decision-maker(s) might not be able to provide any information with regards to at least one of the alternatives, which is called the ignorance situation. We propose two new methods based on additive consistency for solving these two problems in a multi-attributes/group decision-making environment. The first method is based on a system of equations, which is suitable for estimating missing information in the general case. The second method, which is an extension of the system of equations, utilizes a goal programming model to address the ignorance situations. Our validation of these two methods shows that the proposed methods generate a high consistency level irrespective of the nature of the problem under study. The proposed methods outperform other comparable methods without a need to modify or change the original decision-maker(s) preferences.

Stable two-sided matching decision making with incomplete fuzzy preference relations: A disappointment theory based approach

Practical two-sided matching decision making problems, such as marriage matching and person-job matching, are often characterized by a lack of knowledge and time constraints. Therefore, matching objects tend to provide comparative preferential information over other matching objects represented by incomplete fuzzy preference relations. In this paper, it is proposed a new approach to stable two-sided matching decision making with incomplete fuzzy preference relations based on disappointment theory. In the proposed approach, the subjective satisfaction degrees of each matching object on one side over matching objects on the other side are first calculated based on priority weight vectors derived from incomplete fuzzy preference relations. Based on disappointment theory, both the disappointment and elation degrees associated with each matching object over matching objects on the other side are calculated. This process is undertaken by considering the probability of each possible matching pair, which are further used to derive the adjusted satisfaction degrees of matching objects. Afterwards, a stable matching optimization model that aims to maximize the total adjusted satisfaction degrees of both sides is constructed by considering stable matching conditions under incomplete information. The optimal stable matching result can be further determined by solving the optimization model. Finally, a numerical example and some comparative studies are presented to demonstrate the characteristics, innovations and added value of the proposed approach.

Water allocation analysis of the Zhanghe River basin using the Graph Model for Conflict Resolution with incomplete fuzzy preferences

An incomplete fuzzy preference framework for the Graph Model for Conflict Resolution (GMCR) is proposed to handle both complete and incomplete fuzzy preference information. Usually, decision makers’ (DMs’) fuzzy preferences are assumed to be complete fuzzy preference relations (FPRs). However, in real-life situations, due to lack of information or limited expertise in the problem domain, any DM’s preference may be an incomplete fuzzy preference relation (IFPR). An inherent advantage of the proposed framework for GMCR is that it can complete the IFPRs based on additive consistency, which is a special form of transitivity, a common property of preferences. After introducing the concepts of FPR, IFPR, and transitivity, we propose an algorithm to supplement IFPR, that is, to find an FPR that is a good approximation. To illustrate the usefulness of the incomplete fuzzy preference framework for GMCR, we demonstrate it using to a real-world conflict over water allocation that took place in the Zhanghe River basin of China.

Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity

In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process.

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.

Managing incomplete preferences and consistency improvement in hesitant fuzzy linguistic preference relations with applications in group decision making

Incomplete hesitant fuzzy linguistic preference relations (IHFLPRs) are useful in decision making which combine advantages of hesitant fuzzy linguistic term sets and incomplete fuzzy preference relations. The existing researches on IHFLPRs pay little attention to missing elements, and the consistency improvement processes change original information greatly. Inspired by the worst and the best consistency indexes of hesitant fuzzy linguistic preference relations, this paper constructs several optimization models to calculate the missing elements of IHFLPRs. As a result, a complete hesitant fuzzy linguistic preference relation is obtained. Furthermore, an algorithm is introduced to improve the additive consistency of the hesitant fuzzy linguistic preference relation to an acceptable level. Finally a group decision making model based on IHFLPRs is introduced and an example is presented.

An Interactive Consensus Model for Group Decision-Making with Incomplete Multi-Granular 2-Tuple Fuzzy Linguistic Preference Relations

As a result of the heterogeneity of decision-makers, it is more suitable to use multi-granular linguistic information to express assessing information over alternatives for decision-makers. Decision-makers may only provide partial preference information as the limitation of knowledge over the alternatives. Thus, the incomplete multi-granular 2-tuple fuzzy linguistic preference relations (IMGFLPRs) can be applied to manage the GDM problems in complex environments. In this paper, we propose a novel group decision-making (GDM) model based on mathematical programming with IMGFLPRs. It is more important that the proposed mathematical programming can directly deal with IMGFLPRs and does not need to be converted into a uniform form. By this means, we construct a consensus reaching process based on IMGFLPRs, considering simultaneously dynamic adjustment of experts’ weight. Finally, an emergency plan selection problem is solved by the proposed model, which shows the result of GDM is effectiveness.

Addressing consistency and consensus with group decision support model based on incomplete hesitant fuzzy linguistic preference relations

Addressing consistency and consensus with group decision support model based on incomplete hesitant fuzzy linguistic preference relations

Group decision making based on incomplete multiplicative and fuzzy preference relations

The main aim of this paper is to investigate the group decision making on incomplete multiplicative and fuzzy preference relations without the requirement of satisfying reciprocity property. This paper introduces a new characterization of the multiplicative consistency condition, based on which a method to estimate unknown preference values in an incomplete multiplicative preference relation is proposed. Apart from the multiplicative consistency property among three known preference values, the method proposed also takes the multiplicative consistency property among more than three values into account. In addition, two models for group decision making with incomplete multiplicative preference relations and incomplete fuzzy preference relations are presented, respectively. Some properties of the collective preference relation are further discussed. Numerical examples are provided to make a discussion and comparison with other similar methods.

Notes on “Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations”

In this note, we provide some numerical examples and theoretical analysis to demonstrate that a theorem and two corollaries in a recent paper (Xu et al., 2013) are incorrect.