Variable precision rough set for multiple decision attribute analysis

A variable precision rough set (VPRS) model is used to solve the multi-attribute decision analysis (MADA) problem with multiple conflicting decision attributes and multiple condition attributes. By introducing confidence measures and a β-reduct, the VPRS model can rationally solve the conflicting decision analysis problem with multiple decision attributes and multiple condition attributes. For illustration, a medical diagnosis example is utilized to show the feasibility of the VPRS model in solving the MADA problem with multiple decision attributes and multiple condition attributes. Empirical results show that the decision rule with the highest confidence measures will be used as the final decision rules in the MADA problem with multiple conflicting decision attributes and multiple condition attributes if there are some conflicts among decision rules resulting from multiple decision attributes. The confidence-measure-based VPRS model can effectively solve the conflicts of decision rules from multiple decision attributes and thus a class of MADA problem with multiple conflicting decision attributes and multiple condition attributes are solved.

New approach to multiple attribute decision making with interval numbers

In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin＇s approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin＇s approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.

Entropy-based procedures for intuitionistic fuzzy multiple attribute decision making

The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.

Method for multiple attribute decision making based on incomplete linguistic judgment matrix

With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.

Maximizing deviation method for multiple attribute decision making under q-rung orthopair fuzzy environment

Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.

Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making

Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.

Solution to multiple attribute group decision making problems with two decision makers

A kind of multiple attribute group decision making （MAGDM） problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.

Methods of Classification of Ordnance Materials Military-Civilian Joint Support Categories Based on Multiple Attribute Decision

Ordnance material is the physical basis of ordnance equipment maintenance and support. With the increase of technology content and the enhancement of structural complexity of ordnance equipment,the traditional way of military self-independent support is unable to meet the troops' requirements. It has become an inevitable trend to integrate ordnance materials with the militarycivilian joint support. However, there is a problem demanding prompt solution,that is,to distinguish the categories of ordnance material that can be supported by civilian source. Based on the inherent properties of ordnance material, a method to classify ordnance materials military-civilian joint support categories based on multiple attribute decision was proposed. The effectiveness was validated through practical cases.

Man-machine Function Allocation Based on Uncertain Linguistic Multiple Attribute Decision Making

Function allocation is one of the necessary stages in the design course of man-machine systems since appropriate function allocation makes the whole system more effective, reliable and inexpensive. Therefore, our research mainly focuses on the problems of function allocation between man and machine in man-machine systems, analyses each capability advantage of man and machine according to their respective inherent characteristics and makes a comparison between them. In view of highly uncertain characteristics of decision attribute value in the practical process, we introduce the uncertain linguistic multiple attribute decision making （ULMADM） method in the function allocation process. Meanwhile, we also use the uncertain extended weighted arithmetic averaging （UEWAA） method to determine the automation level range of the operator functions. Then, we eventually estab- lish the automation level of man-machine function allocation by using the multi-attribute decision making algorithm, which is combined by UEWAA and uncertain linguistic hybrid aggregation （ULHA） operators. Finally, an example about function allocation is given, that is, fault diagnosis in the cockpit of civil aircraft. The final result of the example demonstrates that the proposed method about function allocation is feasible and effective.

Fuzzy Multiple Attribute Decision Making for Evaluating Aggregate Risk in Green Manufacturing

Industrial risk and the diversification of risk types both increase with industrial development. Many uncertain factors and high risk are inherent in the implementation of new green manufacturing methods. Because of the shortage of successful examples and complete and certain knowledge, decision-making methods using probabilities to represent risk, which need many examples, cannot be used to evaluate risk in the implementation of green manufacturing projects. Therefore, a fuzzy multiple attribute decision-making （FMADM） method was developed with a three-level hierarchical decision-making model to evaluate the aggregate risk for green manufacturing projects. A case study shows that the hierarchical decision-making model of the aggregate risk and the FMADM method effectively reflect the characteristics of the risk in green manufacturing projects.

Expected Value Method for Fuzzy Multiple Attribute Decision Making

This paper presents a fuzzy multiple attribute decision-making （FMADM） method in which the attribute weights and decision matrix elements （attribute values） are fuzzy variables. Fuzzy arithmetic and the expected value operator of fuzzy variables are used to develop the expected value method to solve the FMADM problem. A numerical example is given to demonstrate the feasibility and effectiveness of the method.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

Optimized interval 2-tuple linguistic aggregation operator based on PGSA and its application in MAGDM

This study proposes a multiple attribute group decisionmaking(MAGDM)approach on the basis of the plant growth simulation algorithm(PGSA)and interval 2-tuple weighted average operators for uncertain linguistic weighted aggregation(ULWA).We provide an example for illustration and verification and compare several aggregation operators to indicate the optimality of the assembly method.In addition,we present two comparisons to demonstrate the practicality and effectiveness of the proposed method.The method can be used not only to aggregate MAGDM problems but also to solve multi-granularity uncertain linguistic information.Its high reliability,easy programming,and high-speed calculation can improve the efficiency of ULWA characteristics.Finally,the proposed method has the exact characteristics for linguistic information processing and can effectively avoid information distortion and loss.

数据中心多维感知的资源联合优化调整策略(英文)

Resource Scheduling is crucial to data centers. However, most previous works focus only on one-dimensional resource models which ignoring the fact that multiple resources simultaneously utilized, including CPU, memory and network bandwidth. As cloud computing allows uncoordinated and heterogeneous users to share a data center, competition for multiple resources has become increasingly severe. Motivated by the differences on integrated utilization obtained from different packing schemes, in this paper we take the scheduling problem as a multi-dimensional combinatorial optimization problem with constraint satisfaction. With NP hardness, we present Multiple attribute decision based Integrated Resource Scheduling (MIRS), and a novel heuristic algorithm to gain the approximate optimal solution. Refers to simulation results, in face of various workload sets, our algorithm has significant superiorities in terms of efficiency and performance compared with previous methods.

The Discussion of Analytic Hierarchy Process for Quantitative Type Multiple Attribute Decision Systems Analysis

In this paper,we discussed quantitative type multiple attribute decision problem with rank scale and Analytic Hierarchy Process. It not only is a reasonable generalization of Analytic Hierarchy Process in multiple attribute decision problem, but also provide a effective method for quantitative type multiple attribute decision problem.

Hesitant Trapezoid Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making

In this paper,we investigate the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant trapezoid fuzzy information.Firstly,inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers,the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed.Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed,such as the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA)operator,the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG)operator,the hesitant trapezoid fuzzy Hamacher Choquet average(HTr FHCA),the hesitant trapezoid fuzzy Hamacher Choquet geometric(HTr FHCG),etc.Furthermore,an approach based on the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA)operator and the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG)operator is proposed for MADM problems under hesitant trapezoid fuzzy environment.Finally,a numerical example for supplier selection is given to illustrate the application of the proposed approach.

UNIFORMIZATION OF MULTIGRANULAR LINGUISTIC LABELS AND THEIR APPLICATION TO GROUP DECISION MAKING

In multiple attribute group decision making （MAGDM） problems based on linguistic information, the granularities of linguistic label sets are usually different due to the differences of thinking modes and habits among decision makers. In order to deal with this inconvenience, the transformation relationships among multigranular linguistic labels （TRMLLs）, which are applied to unify linguistic labels with different granularities into a certain linguistic label set with fixed granularity, are presented in this paper. Furthermore, the reference tables are made according to TRMLLs so that the interrelated calculation will be less complicated, and the method of how to use them is explained in detail. At length, the TRMLLs are illustrated through an application example.

Dynamic Multi-Attribute Decision Analysis on Three-Parameter Interval Grey Number of Upper(Lower)Deviation Quasi-Normal Distribution

Aiming at the dynamic multi-attribute decision making problem where the weight of each decision stage and attribute weight are completely unknown and the attribute value is unknown distributed three-parameter interval grey number,a threeparameter interval grey number dynamic multiattribute grey target decision making method with attribute value following quasi-normal distribution is proposed.Firstly,the position relationship between the“center of gravity”point and the kernel of the threeparameter interval grey number is discussed.According to the characteristicthat the attribute value obeys the quasi-normal distribution,anew weight isgiventothe“centerof gravity”point,and a new distance measure formula of the three-parameter interval grey number is defined.Secondly,according to the principle of maximum entropy,the objective programming model is constructed to determine the stage weight and attributeweight.Then,the schemes aresorted according to thesize of the comprehensive bull's-eye distance Finally an example is given to illustrate the effectiveness of the decision model.

Regression model for estimation of attribute reliability

In this paper,a regression model is developed to estimate attribute reliability in the evidential reasoning(ER)context.By analysing the difference between attribute weight and attribute reliability,a general qualitative definition of attribute reliability is provided.The reliability of an attribute is quantitatively measured in consistence with the qualitative definition in the context of the ER approach.A regression model is then constructed to generate attribute reliabilities by minimising the maximum differences between the real value of attribute reliability and its estimation.Within the post-optimal solution space of attribute reliabilities,an optimisation model is constructed to determine the expected utilities of each alternative in order to generate solutions to multiple attribute decision analysis problems.Asale place selection problem in Qingyang County of Chizhou in Anhui province of China is analysed using the proposed regression model to demonstrate its detailed implementation process,validity and applicability.