Priority approach based on quadratic programming model to fuzzy preference relation

We investigate the decision-making problem with a finite set of alternatives,in which the decision information takes the form of a fuzzy preference relation. We develop asimple and practical approach to obtaining the priority vector of a fuzzy preference relation. Theprominent characteristic of the developed approach is that the priority vector can generally beobtained by a simple formula, which is derived from a quadratic programming model. We utilize theconsistency ratio to check the consistency of fuzzy preference relation. If the fuzzy preferencerelation is of unacceptable consistency, then we can return it to the decision maker to reconsiderstructuring a new fuzzy preference relation until the fuzzy preference relation with acceptableconsistency is obtained. We finally illustrate the priority approach by two numerical examples. Thenumerical results show that the developed approach is straightforward, effective, and can easily beperformed on a computer.

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 unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express their linguistic preference information over alternatives.The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncertain multiplicative linguistic preference relations into a collective one,and then a simple approach is developed to determine the experts＇ weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference relations.Furthermore,a practical interactive procedure for group decision making is proposed based on uncertain multiplicative linguistic preference relations,in which a possibility degree formula and a complementary matrix are used to rank the given alternatives.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.

New approach to determine the priorities from interval fuzzy preference relations

An approach is proposed to solve the problem how to obtain the priorities from interval fuzzy preference relations. Firstly, another expression of interval numbers is given. Then, some basic definitions on consistency and weak transitivity of real and interval fuzzy preference relations are described. Based on these definitions, a two-phase process for determining the priorities from interval fuzzy preference relations is presented. Finally, two exam- ples are used to illustrate the use of the proposed approach.

A group decision making method based on double hesitant linguistic preference relations

A simple decision method is proposed to solve the group decision making problems in which the weights of decision organizations are unknown and the preferences for alternatives are provided by double hesitant linguistic preference relations. First, double hesitant linguistic elements are defined as representing the uncertain assessment information in the process of group decision making accurately and comprehensively, and the double hesitant linguistic weighted averaging operator is developed based on the defined operational laws for double hesitant linguistic elements. Then, double hesitant linguistic preference relations are defined and a means to objectively determine the weights of decision organizations is put forward using the standard deviation of scores of preferences provided by the individual decision organization for altematives. Finally the correlation coefficient between the scores of preferences and the scores of preferences are provided by the other decision organizations. Accordingly, a group decision method based on double hesitant linguistic preference relations is proposed, and a practical example of the Jiudianxia reservoir operation alternative selection is used to illustrate the practicability and validity of the method. Finally, the proposed method is compared with the existing methods. Comparative results show that the proposed method can deal with the double hesitant linguistic preference information directly, does not need any information transformation, and can thus reduce the loss of original decision information.

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

Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). 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.

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

The group decision making problem with linguistic pref- erence 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 eigenvec- tor 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.

Cost Sensitive Multi-Granulation Preference Relation Rough Set for Ordinal Decision System

The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference analysis problems,this paper improves the preference relation rough set model and expands it to multi-granulation cases.Cost is also an important issue in the field of decision analysis.Taking the cost into consideration,we also expand the model to the cost sensitive multi-granulation preference relation rough set.Some theorems are represented,and the granule structure selection based on approximation quality is investigated.The experimental results show that the multi-granulation preference rough set approach with the consideration of cost has a better performance in granule structure selection than that without cost consideration.

Group Decision-Making Method with Incomplete Intuitionistic Fuzzy Preference Relations Based on a Generalized Multiplicative Consistent Concept

Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.

Selection method of risk response schemes for mining project based on fuzzy preference relations

To overcome the subjectivity of experts in the process of risk response scheme selection, according to the theory of group decision making, a selection method and flow of the risk response schemes for a mining project was proposed based on fuzzy preference relation and consistency induced ordered weighted averaging (C-IOWA) operator,which can overcome the loss of information in the process of group decision making to a great degree, and improve its efficiency and quality.A numeric example was introduced to illustrate the application of the method, also validating the method as scientific and practicable.

Agricultural Investment Project Decisions Based on an Interactive Preference Disaggregation Model Considering Inconsistency

Agricultural investment project selection is a complex multi-criteria decision-making problem,as agricultural projects are easily influenced by various risk factors,and the evaluation information provided by decisionmakers usually involves uncertainty and inconsistency.Existing literature primarily employed direct preference elicitation methods to address such issues,necessitating a great cognitive effort on the part of decision-makers during evaluation,specifically,determining the weights of criteria.In this study,we propose an indirect preference elicitation method,known as a preference disaggregation method,to learn decision-maker preference models fromdecision examples.To enhance evaluation ease,decision-makers merely need to compare pairs of alternatives with which they are familiar,also known as reference alternatives.Probabilistic linguistic preference relations are employed to account for the presence of incomplete and uncertain information in such pairwise comparisons.To address the inconsistency among a group of decision-makers,we develop a pair of 0-1mixed integer programming models that consider both the semantics of linguistic terms and the belief degrees of decision-makers.Finally,we conduct a case study and comparative analysis.Results reveal the effectiveness of the proposed model in solving agricultural investment project selection problems with uncertain and inconsistent decision information.

The Aviation Technology Two-Sided Matching with the Expected Time Based on the Probabilistic Linguistic Preference Relations

The two-sided matching has been widely applied to the decision-making problems in the field of management.With the limited working experience,the two-sided agents usually cannot provide the preference order directly for the opposite agent,but rather to provide the preference relations in the form of linguistic information.The preference relations based on probabilistic linguistic term sets(PLTSs)not only allowagents to provide the evaluation with multiple linguistic terms,but also present the different preference degrees for linguistic terms.Considering the diversities of the agents,they may provide their preference relations in the form of the probabilistic linguistic preference relation(PLPR)or the probabilistic linguistic multiplicative preference relation(PLMPR).For two-sided matching with the expected time,we first provide the concept of the time satisfaction degree(TSD).Then,we transform the preference relations in different forms into the unified preference relations(u-PRs).The consistency index to measure the consistency of u-PRs is introduced.Besides,the acceptable consistent u-PRs are constructed,and an algorithm is proposed to modify the unacceptable consistent u-PRs.Furthermore,we present the whole two-sided matching decisionmaking process with the acceptable consistent u-PRs.Finally,a case about aviation technology suppliers and demanders matching is presented to exhibit the rationality and practicality of the proposed method.Some analyses and discussions are provided to further demonstrate the feasibility and effectiveness of the proposed method.

AN APPROACH TO GROUP DECISION MAKING BASED ON INTERVAL FUZZY PREFERENCE RELATIONS

In this paper, we investigate group decision making problems where the decision information given by decision makers takes the form of interval fuzzy preference relations. We first give an index to measure the similarity degree of two interval fuzzy preference relations, and utilize the similarity index to check the consistency degree of group opinion. Furthermore, we use the error-propagation principle to determine the priority vector of the aggregated matrix, and then develop an approach to group decision making based on interval fuzzy preference relations. Finally, we give an example to illustrate the developed approach.

Approaches to Improving Consistency of Interval Fuzzy Preference Relations

This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR.By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR,a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency.An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity.The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible.Numerical examples are presented to illustrate how to apply the proposed approaches.

Dynamic Case Retrieval Method With Subjective Preferences and Objective Information for Emergency Decision Making

Case-based reasoning(CBR) is one of the best methods for generating an effective solution in an emergency. In recent years, some methods for generating emergency alternatives have been included in practical CBR applications, but there have been no in-depth studies of these processes. In this study,we propose a new method for dynamic case retrieval with subjective preferences and objective information, which considers the personal preferences of the decision makers and changes in the attributes of the emergency as the situation develops. First,we present a formula for calculating the case similarity and changing trends in the case considered, where similar cases are obtained. Next, we describe a method for measuring the overall assessment value with respect to similar historical cases, which is obtained by aggregating the case similarity, the utility case similarity, the first response time, and the implementation effect.The subjective preferences and objective information are also integrated in the decision-making process. Finally, we present a case study based on the emergency response to a fire in a highrise building, which illustrates the applicability and feasibility of the proposed method.

Model for Choosing a Payment Term in Export Business Based on Relative Preference Estimation

To avoid payment risks, 5 widely used payment terms in international trade practice are analyzed quantitatively. The final choice of a payment term in export business is a representation of the transactional ‘Win Win’ principle as well as moderate compromises made by importer and exporter between self protection and acceptability to the other party. The initial assessment is conducted first on decision makers preference and understanding of possible results of each objective. Then, aggregated preference relations are obtained by weighting each objective as per its relative importance and calculating preference indicators. Finally, ranking is made according to the preference indicators.

Multicriteria game approach to air-to-air combat tactical decisions for multiple UAVs

Air-to-air combat tactical decisions for multiple unmanned aerial vehicles(ACTDMU)are a key decision-making step in beyond visual range combat.Complex influencing factors,strong antagonism and real-time requirements need to be considered in the ACTDMU problem.In this paper,we propose a multicriteria game approach to ACTDMU.This approach consists of a multicriteria game model and a Pareto Nash equilibrium algorithm.In this model,we form the strategy profiles for the integration of air-to-air combat tactics and weapon target assignment strategies by considering the correlation between them,and we design the vector payoff functions based on predominance factors.We propose a algorithm of Pareto Nash equilibrium based on preference relations using threshold constraints(PNE-PRTC),and we prove that the solutions obtained by this algorithm are refinements of Pareto Nash equilibrium solutions.The numerical experiments indicate that PNE-PRTC algorithm is considerably faster than the baseline algorithms and the performance is better.Especially on large-scale instances,the Pareto Nash equilibrium solutions can be calculated by PNEPRTC algorithm at the second level.The simulation experiments show that the multicriteria game approach is more effective than one-side decision approaches such as multiple-attribute decision-making and randomly chosen decisions.

Method for multi-attribute group decision-making based on the compromise weights

Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete.In group decision analysis,if preference information about alternatives is provided by participants,it should be verified whether there exist compromise weights that can support all the preference relations.The different compromise weight vectors may differ for the ranking of the alternatives.In the case that compromise weights exist,the method is proposed to find out all the compromise weight vectors in order to rank the alternatives.Based on the new feasible domain of attribute weights determined by all the compromise weight vectors and the incomplete information on value scores of consequences,dominance relations between alternatives are checked by a nonlinear goal programming model which can be transformed into a linear one by adopting a transformation.The checked dominance relations uniformly hold for all compromise weight vectors and the incomplete information on value scores of consequences.A final ranking of the alternatives can be obtained by aggregating these dominance relations.

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

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.

Evaluation of global navigation satellite system spoofing efficacy

The spoofing capability of Global Navigation Satellite System(GNSS)represents an important confrontational capability for navigation security,and the success of planned missions may depend on the effective evaluation of spoofing capability.However,current evaluation systems face challenges arising from the irrationality of previous weighting methods,inapplicability of the conventional multi-attribute decision-making method and uncertainty existing in evaluation.To solve these difficulties,considering the validity of the obtained results,an evaluation method based on the game aggregated weight model and a joint approach involving the grey relational analysis and technique for order preference by similarity to an ideal solution(GRA-TOPSIS)are firstly proposed to determine the optimal scheme.Static and dynamic evaluation results under different schemes are then obtained via a fuzzy comprehensive assessment and an improved dynamic game method,to prioritize the deceptive efficacy of the equipment accurately and make pointed improvement for its core performance.The use of judging indicators,including Spearman rank correlation coefficient and so on,combined with obtained evaluation results,demonstrates the superiority of the proposed method and the optimal scheme by the horizontal comparison of different methods and vertical comparison of evaluation results.Finally,the results of field measurements and simulation tests show that the proposed method can better overcome the difficulties of existing methods and realize the effective evaluation.