Two-phase TOPSIS of uncertain multi-attribute group decision-making

To solve the uncertain multi-attribute group decision-making of unknown attribute weights,three optimal models are built to decide the corresponding ideal solution weights,standard deviation weights and mean deviation weights.The comprehensive attribute weights are gotten through the product of the above three kinds of weights.And each decision maker＇s weighted decision matrices are also received by using the integrated attribute weights.The closeness degrees are also gotten by use of technique for order preference by similarity to ideal solution（TOPSIS） through dealing with the weighted decision matrices.At the same time the group decision matrix and weighted group decision matrix are gotten by using each decision-maker＇s closeness degree to every project.Then the vertical TOPSIS method is used to calculate the closeness degree of each project.So these projects can be ranked according to their values of the closeness degree.The process of the method is also given step by step.Finally,a numerical example demonstrates the feasibility and effectiveness of the approach.

Method for uncertain multi-attribute decisionmaking with preference information in the form of interval numbers complementary judgment matrix

The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.

Multi-attribute group decision making method under 2-dimension uncertain linguistic variables

A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.

Multi-attribute decision-making approach dealing with uncertain linguistic assessment information

An approach is presented to deal with a multi-attribute decision-making problem in which the attribute weights are unknown and the attribute values take the form of uncertain linguistic variables. First, a linguistic assessment standard is set up to deal with the uncertain linguistic attributes, and the operation laws of uncertain linguistic variables and the uncertain linguistic weighting average(ULWA)operator are introduced. Then a ranking formula of uncertain linguistic variables based on expectation-variance is proposed. As for the case without weight information, a goal program based on a warp function is constructed to determine the attribute weights, and the ULWA operator is utilized to aggregate the assessment information of uncertain linguistic variables, and the corresponding alternatives are ranked by a formula based on expectation-variance. Finally, a numerical example is given, and the results demonstrate that it is much easier and faster for the ranking method based on expectation-variance when compared to the existing methods.

A Method of Job Scheduling on SMEs' Key Equipments Based on Hybrid Multi-attribute Decision Making

An analysis of the key factors affecting on the single production process job scheduling of the parts waiting for be- ing processed on the key equipments for SMEs (Small Manufacturing Enterprises) is given in this paper,which include interval number,real number and uncertain linguistic value.A kind of hybrid multi-attribute decision making method for the single pro- duction process job scheduling is presented in this paper,that the parts are firstly sorted about each factor,and then the total evalu- ative attributive value of each part is calculated with the method of weighted arithmetic average,and thus the part with the highest total evaluative attributive value is chosen for being processed firstly.The mathematic model corresponding to the method is set up in this paper.An example is studied in this paper,and the results of the example testify the correctness of this model.

Uncertainty Theory Based Novel Multi-Objective Optimization Technique Using Embedding Theorem with Application to R &D Project Portfolio Selection

This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncertain variables can be embedded into the Banach space C[0, 1] × C[0, 1] isometrically and isomorphically, is developed. Based on this embedding theorem, each objective with uncertain coefficients can be transformed into two objectives with crisp coefficients. The solution of the original m-objectives optimization problem with uncertain coefficients will be obtained by solving the corresponding 2 m-objectives crisp optimization problem. The R & D project portfolio decision deals with future events and opportunities, much of the information required to make portfolio decisions is uncertain. Here parameters like outcome, risk, and cost are considered as uncertain variables and an uncertain bi-objective optimization problem with some useful constraints is developed. The corresponding crisp tetra-objective optimization model is then developed by embedding theorem. The feasibility and effectiveness of the proposed method is verified by a real case study with the consideration that the uncertain variables are triangular in nature.

A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Probabilistic linguistic term sets(PLTSs)are an effective tool for expressing subjective human cognition that offer advantages in the field ofmulti-attribute decision-making(MADM).However,studies have found that PLTSs have lost their ability to accurately capture the views of decision-makers(DMs)in certain circumstances,such as when the DM hesitates between multiple linguistic terms or the decision information is incomplete,thus affecting their role in the decision-making process.Belief function theory is a leading streamof thought in uncertainty processing that is suitable for dealing with the limitations of PLTS.Therefore,the purpose of this study is to extend PLTS to incorporate belief function theory.First,we provide the basic concepts of the extended PLTS(i.e.,belief-based PLTS)through case analyses.Second,the aggregation operator of belief-based PLTS is defined with the ordered weighted average(OWA)-based soft likelihood function,which is improved by considering the reliability of the information source.Third,to measure the magnitude of different belief-based PLTSs,the belief interval of singleton is calculated,and the comparison method of belief-based PLTS is constructed based on probabilities.On the basis of the preceding discussion,we further develop an emergency decision framework that includes several novel techniques,such as attribute weight determination and decision information aggregation.Finally,the usefulness of the framework is demonstrated through a case study,and its effectiveness is illustrated through a series of comparisons.

激励相容理论下再制造绿色供应链网络模糊优化

为探讨政府干预在供应链回收网络中的作用,基于激励相容理论,建立以最低总成本、最少碳排放和最大大数据投资回报为目标的多周期多目标优化模型,采用多目标三角模糊数和改进混合算法进行求解。结果表明:改进混合算法在处理回收网络多周期多目标方面具有较强的求解能力;政府政策能弥补制造业减排能力弱的问题。结论如下:制造业企业运用人工智能技术回收再制造能够提升竞争力;政府引导能够帮助企业实现产业升级。

Multivariable Decoupling Predictive Control Based on QFT Theory and Application in CSTR Chemical Process

A novel method of incorporating generalized predictive control (GPC) algorithms based on quantitative feedback theory (QFT) principles is proposed for solving the feedback control problem of the highly uncertain and cross-coupling plants. The quantitative feedback theory decouples the multi-input and multi-output (MIMO) plant and is also used to reduce the uncertainties of the system, stabilize the system, and achieve tracking performance of the system to a certain extent. Single-input and single-output (SISO) generalized predictive control is used to achieve performance with higher performance. In GPC, the model is identified on-line, which is based on the QFT input and the plant output signals. The simulation results show that the performance of the system is superior to the performance when only QFT is used for highly uncertain MIMO plants.

Approach for uncertain multi-objective programming problems with correlated objective functions under C_(EV) criterion

An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.

On consistency and ranking of alternatives in uncertain AHP

This paper introduces uncertainty theory to deal with non-deterministic factors in ranking alternatives. The uncertain variable method (UVM) and the definition of consistency for uncertainty comparison matrices are proposed. A simple yet pragmatic approach for testing whether or not an uncertainty comparison matrix is consistent is put forward. In cases where an uncertainty comparison matrix is inconsistent, an algorithm is used to generate consistent matrix. And then the consistent uncertainty comparison matrix can derive the uncertainty weights. The final ranking is given by uncertainty weighs if they are acceptable;otherwise we rely on the ranks of expected values of uncertainty weights instead. Three numerical examples including a hierarchical (AHP) decision problem are examined to illustrate the validity and practicality of the proposed methods.

Threat sequencing of multiple UCAVs with incomplete information based on game theory

The threat sequencing of multiple unmanned combat air vehicles(UCAVs) is a multi-attribute decision-making(MADM)problem. In the threat sequencing process of multiple UCAVs,due to the strong confrontation and high dynamics of the air combat environment, the weight coefficients of the threat indicators are usually time-varying. Moreover, the air combat data is difficult to be obtained accurately. In this study, a threat sequencing method of multiple UCAVs is proposed based on game theory by considering the incomplete information. Firstly, a zero-sum game model of decision maker( D) and nature(N)with fuzzy payoffs is established to obtain the uncertain parameters which are the weight coefficient parameters of the threat indicators and the interval parameters of the threat matrix. Then,the established zero-sum game with fuzzy payoffs is transformed into a zero-sum game with crisp payoffs(matrix game) to solve. Moreover, a decision rule is addressed for the threat sequencing problem of multiple UCAVs based on the obtained uncertain parameters. Finally, numerical simulation results are presented to show the effectiveness of the proposed approach.

Uncertainty Weight Generation Approach Based on Uncertainty Comparison Matrices

In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of uncertainty comparison matrix and uncertainty weights are proposed in this paper. It also gives the uncertain variable method to calculate uncertainty weights from uncertainty comparison matrices, which can be either consistent or inconsistent. The proposed uncertain variable method (UVM) is also applicable to interval comparison matrices and fuzzy comparison ma-trices when they are transformed into uncertainty comparison matrices using linear uncertainty distribution or zigzag uncertainty distribution. The proposed approach is computationally efficient as it consists of solving only inverse uncertainty distribution. At the end of this paper, five numerical examples are given to illustrate the method.

Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging （I-IIULHSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric （I-IIULHSG） operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley averaging （I-IIULHλSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric （I-IIULHλSG） operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.

Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.

Robust Stability Criterion for Uncertain Neural Networks with Time Delays

The robust stability of uncertain neural network with time-varying delay was investigated.The norm-bounded uncertainties are included in the system matrices.The constraint on time-varying delays is removed,which means that a fast time-varying delay is admissible.Some new delay-dependent stability criteria were presented by using Lyapunov-Krasovskii functional and linear matrix inequalities(LMIs) approaches.Finally,a numerical example was given to illustrate the effectiveness and innovation nature of the developed techniques.

Multivariable Decoupling Predictive Control Based on QFT Theory and Application in CSTR Chemical Process

A novel method of incorporating generalized predictive control GPC algorithms based on quantitative feedback theory QFT principles is proposed for solving the feedback control problem of the highly uncertain and cross-coupling plants. The quantitative feedback theory decouples the multi-input and multi-output MIMO plant and is also used to reduce the uncertainties of the system, stabilize the system, and achieve tracking performance of the system to a certain extent. Single-input and single-output SISO generalized predictive control is used to achieve performance with higher performance. In GPC, the model is identified on-line, which is based on the QFT input and the plant output signals. The simulation results show that the performance of the system is superior to the performance when only QFT is used for highly uncertain MIMO plants.

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded（polytope type） uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.

Semi entropy of uncertain random variables and its application to portfolio selection

Semi entropy is a measure to characterize the indeterminacy of the uncertain random variable considering the values of the uncertain random variable which are lower than the mean.As important roles of semi entropy in finance,this paper presents the concept of semi entropy for uncertain random variables.In order to compute semi entropy for uncertain random variables,Monte-Carlo approach is provided.As an application of semi entropy,portfolio selection problems are optimized based on mean-semi entropy mode.