Fuzzy Preference Information Research Articles

Incomplete interval-valued probabilistic uncertain linguistic preference relation in group decision making

In group decision making (GDM), due to complexity of various factors, decision makers (DMs) often provide incomplete preference relations (PRs) in preference matrix. Interval-valued probabilistic uncertain linguistic term set (IVPULTS) is a flexible and accurate tool to depict evaluation information of experts. In this paper, we mainly propose a new concept pertaining to interval-valued probabilistic uncertain linguistic preference relation (IVPULPR) that applies the IVPULTS to preference relations. Firstly, some new basic theoretical concepts of IVPULTS are developed including ordered IVPULTS, normalization method and new expectation function. Secondly, we establish several goal programming models to estimate the unknown elements in incomplete IVPULPR and propose the expected additive consistency of IVPULPR. To improve the consistency level, two optimization models are constructed based on the idea of minimum adjustment. Thirdly, we derive the experts’ weights in terms of information uncertainty, where a new method to measure information uncertainty of IVPULTS is proposed. For the sake of improving group consensus, we construct a group consensus index (GCI) and two optimization models depending on the adjustment mechanism of expert weight. Finally, a complete GDM framework with incomplete IVPULPR is devised based on the analysis of IVPULPR consistency and group consensus. Through an experiment analysis by using an UCI dataset, we find that the proposed GDM model can not only precisely express fuzzy preference information of DMs, but also ensure achievement of acceptable consistency and group consensus under the condition of not changing the initial preference as much as possible.

Dual consistency-driven group decision making method based on fuzzy preference relation

Consistency testing and adjustment of preference relations are prerequisites for group decision making; the forced integration of preference relations without consensus may lead to misleading decisions. To address this issue, following the principle of minimal information loss in consensus reaching, we propose a dual consistency-driven group decision making method based on the fuzzy preference relation between individuals and groups. First, a bidirectional adjustment amount is introduced in the individual consistency process to avoid unidirectional expansion or reduction of the degree of fuzzy preference. Second, considering that the adjustment of fuzzy preference information in the process of group negotiation will change the weight of expert, a goal programming based on the dual adjustment of dynamic weights and preference information is constructed, which can solve the problem of contradictory order values before and after the expert weights adjustment and improve the level of group consensus and the efficiency of group consensus reaching. Finally, the effectiveness of the proposed methodology through an analysis of case studies is verified.

A new multi-objective decision-making method with diversified weights and Pythagorean fuzzy rough sets

In reality, there are many multi-objective decision-making problems with fuzziness and uncertainty, such as the choice of clinical treatment schemes. To effectively cope with such problems, it is urgent to scientifically handle fuzzy and uncertain information. Given the fact that the Pythagorean fuzzy set is a useful tool to tackle fuzzy information, and the rough set theory is superior in dealing with uncertain data, this paper aims to establish a novel decision-making method for scheme selection from the perspective of Pythagorean fuzzy rough sets. Pythagorean fuzzy numbers (PFNs) are first employed to express fuzzy preference information, and then multi-objective Pythagorean fuzzy information systems are introduced. Subsequently, we develop a new fuzzy rough set using an improved correlation coefficient method to deal with the uncertainty of PFNs. Furthermore, considering the diversified weights, we present a weight calculation method based on approximate accuracies. Meanwhile, a weighted fuzzy rough set model is constructed to achieve multi-objective information fusion. Accordingly, a multi-objective decision-making method is put forward with the help of overlap functions. Finally, we apply the built method to three cases from different decision scenarios to illustrate the applicability of the method. By some comparative analyses, the effectiveness and superiority of the method are also exhibited. Moreover, we discuss the establishment of decision support systems regarding scheme selection. On the whole, the work of this paper is helpful to support the solution of complex multi-objective decision-making problems.

To select suitable supplier for complex equipment military-civilian collaborative design based on fuzzy preference information that from matching perspective

Combine complex equipment collaborative development in military-civilian integration context not only fulfils actual development requirement, but also beneficial to the national economy. Design procedure as first stage of complex equipment military-civilian collaborative development process, select suitable design supplier is significant to whole development process of complex equipment. In order to select suitable design supplier for complex equipment, two aspects done in this paper. One is comprehensive analysis of evaluated influencing factors that affect complex equipment military-civilian collaborative design process, corresponding evaluation indicator constructed and a combination of grey correlation, entropy, DEMATEL (Decision-making Trial and Evaluation Laboratory) and VIKOR analysis theory to obtain grey entropy-DEMATEL-VIKOR, then the combined method is utilized to acquire matching attributes for followed research content. Meanwhile, satisfaction degree for matching side obtained with the help of information aggregation based on power generalized Heronian mean which on the basis of fuzzy preference information. Then, through constructed matching model, suitable design supplier obtained. Finally, a corresponding illustrative example given.

Contingency response decision of network public opinion emergencies based on intuitionistic fuzzy entropy and preference information of decision makers

A multi-attribute group decision-making (MAGDM) method based on intuitionistic fuzzy preference information is proposed for the multi-attribute intuitionistic fuzzy group decision-making problem where the decision-makers weight and attribute weight are completely unknown and the decision-maker has preference information for the scheme. Firstly, an intuitionistic fuzzy interval judgment matrix is established to describe the original data of the key decision indicators for multiple network public opinion emergencies that erupt simultaneously. Secondly, the attribute weights are determined based on the improved intuitionistic fuzzy entropy construction method, and the expert weights are determined by using objective decision information, taking into account the intuitionistic fuzzy entropy of decision matrix. MAGDM can not only synthesize experts' professional experience in different aspects, but also avoid experts' decision-making errors caused by insufficient domain knowledge. It is necessary to continuously adjust the expert weight based on decision-making information to make the comprehensive decision-making information more accurate. Thirdly, a scheme preference model and an attribute weight optimization model are established to determine the ranking method of intuitionistic fuzzy interval values. Then, a modified distance measure of intuitionistic fuzzy sets (IFSs) is introduced to make the evaluation result more accurate and reasonable when it comes to solving the deviation between the evaluation value and ideal solution of each scheme. Finally, the effectiveness and practicability of the proposed decision-making method are verified by an example of emergency crisis severity, It assists decision makers in selecting and implementing the optimal emergency response plan in a timely and efficient manner, which improves the emergency treatment efficiency of network public opinion crisis, helps emergency departments to better deal with the network public opinion crisis, improves the ability of public opinion guidance and control, and provides a new method and idea for multi-attribute intuitionistic fuzzy group decision-making problem.

Research on the optimal aggregation method of fuzzy preference information based on spatial Steiner-Weber point

In view of the present situation that most aggregation methods of fuzzy preference information are extended or mixed by classical aggregation operators, which leads to the aggregation accuracy is not high. The purpose of this paper is to develop a novel method for spatial aggregation of fuzzy preference information. Thus we map the fuzzy preference information to a set of three-dimensional coordinate and construct the spatial aggregation model based on Steiner-Weber point. Then, the plant growth simulation algorithm (PGSA) algorithm is used to find the spatial aggregation point. According to the comparison and analysis of the numerical example, the aggregation matrix established by our method is closer to the group preference matrices. Therefore, the optimal aggregation point obtained by using the optimal aggregation method based on spatial Steiner-Weber point can best represent the comprehensive opinion of the decision makers.

A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.

Two-sided matching decision-making model with hesitant fuzzy preference information for configuring cloud manufacturing tasks and resources

Owing to the complexity of socio-economic environments and the fuzziness of human cognition, information of cognitive preference provided by decision-making organizations composed of many experts is often hesitant and fuzzy. In consequence, for the sake of addressing the hesitance and fuzziness of preference information for the configuration of tasks and resources in cloud manufacturing, a decision-making model of a two-sided matching considering a bidirectional projection under preference information of hesitant fuzzy is put forward. Primarily, this paper describes the problem of two-sided matching and introduces the hesitant fuzzy set. Afterwards, according to preference information given by matching agents using the hesitant fuzzy element, the evaluation matrix is constructed. Meanwhile, the bidirectional projection technology and TOPSIS method are combined to calculate the closeness degree matrix. Further, by introducing the constraint of the stable matching, a decision-making model of a two-sided matching for maximizing the closeness degree of two-sided matching agents is constructed, and the optimal configuration results are obtained by the solving of the model. Subsequently, the illustrative case is provided to validate the rationality and effectiveness of the presented model in solving the configuration for cloud manufacturing tasks and resources. Also, the stability in the proposed configuration results is illustrated by making a sensitivity analysis. Further, the reliability in the given solving process is demonstrated through performing a comparative analysis, as well as the advantages in the proposed model is also discussed. It shows that this developed model can give stable configuration results and also provide a matching approach for different agents under an uncertain environment.

Two-sided matching model for complex product manufacturing tasks based on dual hesitant fuzzy preference information

Due to the increasing complexity in socioeconomic environments and the fuzziness in human cognition, the cognitive information over alternatives provided by a decision organization consisting of several experts is usually uncertain and hesitant. Consequently, in order to solve the fuzziness and uncertainty of preference information in the matching process of complex product manufacturing tasks on the cloud manufacturing platform, a novel two-sided matching model based on dual hesitant fuzzy preference information is proposed. Firstly, the two-sided matching problem and the dual hesitant fuzzy set (DHFS) are described. Then, the dual hesitant fuzzy preference information evaluation matrix is constructed and normalized according to the preference information provided by agents on both sides. Sequentially, the dual hesitant fuzzy preference information evaluation matrix is transformed into the satisfaction degree matrix by the projection technology. Simultaneously, considering the stable matching constraint, a multi-objective two-sided matching optimization model which maximizes the satisfaction degree and minimizes the difference degree of two-sided agents is established. Further, the matching relative competition degree is used to convert the multi-objective optimization model into a single-objective optimization model, and the matching algorithm is designed for solving the model. Moreover, an illustrative example is employed to demonstrate the practicality and feasibility of the developed model. Subsequently, the sensitivity analysis is performed to validate the stability of the proposed matching results, and the comparative analysis is carried out to illustrate the reliability of the proposed matching algorithm and the merits of the developed model. It reveals that the proposed model can not only obtain stable matching results but also give more choices in matching methods.

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.

Research on Fuzzy Multiple Attribute Route Evaluation Decision Method

The route evaluation is an important basis for airlines to make route decisions. In order to solve the fuzzy multiple attribute route decision problem, route attribute weight was completely unknown, and the route evaluation fuzzy language information was given, the fuzzy language and preference information were converted into trapezoidal fuzzy numbers. A programming model was constructed by minimizing the total deviation between trapezoidal fuzzy numbers to determining the weight of each attribute in the route decision, By weighting the average of the route attribute value and the weights value, compared the expected value of fuzzy comprehensive evaluation for each route, and ranking alternatives by using the expected value operator of fuzzy variable. Finally, a numerical example was used to illustrate the proposed method. The results show that the method can be used by air-lines to solve multiple attribute route decision problems with unknown weights, and the method is scientific and effective.

An Algorithm for Interval-Valued Intuitionistic Fuzzy Preference Relations in Group Decision Making Based on Acceptability Measurement and Priority Weight Determination

Group decision making with intuitionistic fuzzy preference information contains two key issues: acceptability measurement and priority weight determination. In this paper, we investigate the above two issues with respect to multiplicative interval-valued intuitionistic fuzzy preference relation (IVIFPR). Firstly, a consistency index is defined to measure the multiplicative consistency degree of IVIFPR and an optimization model is established to improve the consistency degree of IVIFPR to an acceptable one. Next, in terms of priority weight determination, an error-analysis-based extension method is proposed to obtain priority weight vector from the acceptable IVIFPR. For GDM problems, decision makers’ weights are derived by the proposed multiplicative consistency index. Subsequently, the collective IVIFPR is obtained by using an interval-valued intuitionistic fuzzy (IVIF) weighted averaging operator. Finally, a step-by step algorithm for GDM with IVIFPRs is given, and an example of enterprise innovation partner selection is analyzed, and comparative analyses with existing approaches are performed to demonstrate that the proposed algorithm is both effective and practical in dealing with GDM problems.

Sequential funding the venture project or not? A prospect consensus process with probabilistic hesitant fuzzy preference information

Sequential investment problem is a widespread issue in venture capital (VC) process and it is an important key for the success of VC as well. Not only the basic information of projects but also the sunk cost, the network of venture capitalists (VCs), etc., should be considered in the sequential decision-making. In this paper, we study the sequential investment from building a decision-making index system firstly. Then, because of complex and uncertain decision-making circumstance, it is hard for the VCs to give their evaluation information for each alternative as crisp numbers, but it may be easy for them to provide their preferences over each pair of alternatives. Motivated by which, the probabilistic hesitant fuzzy preferences (P-HFPs) are adopted by the VCs in their evaluation process. Moreover, considering the bounded rational psychological characteristic of the VCs in decision-making, the prospect theory has been introduced. Therefore, a prospect consensus with P-HFPs has been constructed due to the grouping of sequential decision-making. It has been applied to a practical case, and an expected consensus under rational framework has been used to analyze the case. The superiority of prospect consensus with P-HFPs has been correspondingly demonstrated in this paper through the comparative analyses of the expected consensus with P-HFPs, the prospect consensus with HFPs and the expected consensus with HFPs.

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation U+0028 IFPR U+0029 is a suitable technique to express fuzzy preference information by decision makers U+0028 DMs U+0029. This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR, by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly, a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.

Multi-criteria decision making method based on analytic hierarchy process with intuitionistic fuzzy preference information

An extension method of multi-criteria decision making (MCDM) is proposed in the thesis for selection and assessment of parting line in mould design. First of all, linguistic variable is used to express grade of alternative parting line scheme and weight of criterion significance; and then, the membership function of final fuzzy assessed value is determined based on these linguistic values; in the end, a new ordering method of maximum and minimum sets will be adopted for normalisation of weight grading and defuzzification to clear value and for strength and weakness ordering of alternative scheme. The verification and contrast experiment show effectiveness of the method in the thesis and the comparison with traditional fuzzy multi-criteria decision making method shows the method in the thesis is more applicable.

Multi-criteria decision making method based on analytic hierarchy process with intuitionistic fuzzy preference information

An extension method of multi criteria decision making (MCDM) is proposed in the Thesis for selection and assessment of parting line in mold design. First of all, linguistic variable is used to express grade of alternative parting line scheme and weight of criterion significance; and then, the membership function of final fuzzy assessed value is determined based on these linguistic values; in the end, a new ordering method of maximum and minimum sets will be adopted for normalization of weight grading and defuzzification to clear value and for strength and weakness ordering of alternative scheme. The verification and contrast experiment show effectiveness of the method in the Thesis and the comparison with traditional fuzzy multi criteria decision making method shows the method in the Thesis is more applicable.

A Method for Group Decision Making Based on Interval-Valued Intuitionistic Fuzzy Geometric Distance Measures

In this paper, at first, we develop some new geometric distance measures for interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, an illustrative example with interval-valued intuitionistic fuzzy information is given.

Managing interval-valued multiplicative hesitant fuzzy information in GDM problems

Inspired by the idea of multiplicative preference relation as well as interval-valued hesitant fuzzy set, we introduce a new preference relation called interval-valued multiplicative hesitant fuzzy preference structure. It is a powerful technique to describe the preference information assessed by different appraise subjective. The predominant feature of it was allows decision makers to use the interval-valued hesitant fuzzy information in describing the preference structure. We focus on the information aggregation methods for interval-valued multiplicative hesitant fuzzy preference information and proposed a series of useful aggregation operators. Moreover, we propose a group decision making (GDM) method based on proposed aggregation operators under interval-valued multiplicative hesitant fuzzy environment. Real case about college application problem is presented to show the useful and effectiveness of our proposed method.

MULTIATTRIBUTE WAREHOUSE LOCATION SELECTION IN HUMANITARIAN LOGISTICS USING HESITANT FUZZY AHP

Deploying warehouses at strategic locations becomes an important issue for humanitarian relief organizations in order to improve their relief aid capability and rescue plan. The delivery of sufficient technical equipment and provision of shelter and reinforcement to victims is a significant event during relief operations. Warehouse location selection in humanitarian logistics (HL) is a challenging process because choosing a non-optimal location may cause additional problems during rescue activities. The conventional decision making tools used for a warehouse location selection problem tend to be less effective in dealing with the imprecise or vague nature of the linguistic assessment. In many situations, the values of the qualitative attributes are often incompletely determined by the decision-makers. The fuzzy set theory can capture this type of uncertainty. In this paper, a recent extension of ordinary fuzzy sets, namely hesitant fuzzy sets, is used for considering the decision makers hesitancy in the evaluation. To solve the HL warehouse location selection problem, we propose a new hesitant fuzzy Analytic Hierarchy Process (AHP) method. We also present a HL warehouse location selection case study for a Turkish humanitarian relief organization by using hesitant fuzzy preference information.

A group decision making model considering both the additive consistency and group consensus of intuitionistic fuzzy preference relations

Group decision making with intuitionistic fuzzy preference information involves three steps: the consistency checking process, the consensus checking process and the selection process. In this paper, we investigate the above three steps with respect to additive intuitionistic fuzzy preference relation (IFPR). Firstly, a consistency index is introduced to measure the additive consistency level of IFPR and an automated approach is developed to improve the consistency level with respect to IFPR to an acceptable level. Meanwhile, the group consensus index of IFPR is defined and one algorithm for reaching acceptable level of consensus is developed. Secondly, after implementing this modified algorithm, consistency index and group consensus index are investigated. And we prove that they can hold on, even receive better levels. Thirdly, a framework for group decision making is developed based on IFPR with additive consistency and group consensus. Finally, an illustrative example is presented to demonstrate the effectiveness and applicability of the proposed approach.