A novel meta-heuristic based method for deriving priorities from fuzzy pairwise comparison judgments

This paper proposes a new method to derive the priority vector from fuzzy pairwise comparison matrices. Unlike several known methods, the proposed method derives crisp weights from consistent and inconsistent fuzzy comparison matrices. Therefore, the crisp weights obviate the need of additional aggregation and ranking procedures. To derive the priority vector, a Modified Fuzzy Logarithmic Least Square Model (MFLLSM) is proposed. In order to solve the MFLLSM, a framework based on genetic algorithm is proposed. In the proposed framework, a heuristic algorithm of population initialization, a heuristic algorithm for simulating fuzzy numbers and a heuristic algorithm of fitness evaluation are proposed.The solution of the prioritization problem requires finding priorities such that their ratio approximately satisfies the initial judgments. Computational results reveal the superiority of the proposed method in comparison with five well known methods of literature from the viewpoint of satisfaction of initial judgments by the obtained priority vector. It is shown by ten different examples that the deviation of the priorities ratio from initial judgments in the proposed method is less than five existing methods of literature. In addition, unlike several methods of literature, the proposed method considers fuzzy judgments represented by both triangular and trapezoidal fuzzy numbers. Furthermore, the proposed method for the first time considers judgments represented by triangular shaped fuzzy numbers and trapezoidal shaped fuzzy numbers which are discussed in the paper.     

集成直觉模糊信息的主观信任模型

针对复杂的在线服务环境下存在的主观性和不确定性,且缺乏从信任程度、不信任程度和不确定性程度三方面描述信任的方法,提出一种集成直觉模糊信息的主观信任模型。首先,给出了一种改进的集成精确数为直觉模糊数的方法,并结合K均值聚类算法,计算实体的直接信任和间接信任;然后,根据基于直觉模糊熵的权重分配策略计算综合信任;最后进行了仿真实验验证。结果表明该方法能有效抑制信用欺诈行为,且当恶意节点达到35%的情况下仍然维持一个较低的误差水平。     

Signed distance ranking based approach for solving bounded interval-valued fuzzy numbers linear programming problems

Fuzzy linear programming (FLP) problems with a wide varietyof applications in sciencesand engineering allow working with imprecise data and constraints, leading to more realistic models. The main contribution of this study is to deal with the formulation of a kind of FLP problems, known as bounded interval-valued fuzzy numbers linear programming (BIVFNLP) problems, with coefficients of decision variables in the objective function, resource vector, and coefficients of the technological matrix represented as interval-valued fuzzy numbers (IVFNs), and crisp decision variables limited to lower and upper bounds. Here, based on signed distance ranking to order IVFNs, the bounded simplex method is extended to obtain an interval-valued fuzzy optimal value for the BIVFNLP problem under consideration. Finally, one illustrative example is given to show the superiority of the proposed algorithm over the existing ones.     

Fuzzy analytic hierarchy process and analytic network process: An integrated fuzzy logarithmic preference programming

This paper proposes a two-stage fuzzy logarithmic preference programming with multi-criteria decision-making, in order to derive the priorities of comparison matrices in the analytic hierarchy pprocess (AHP) and the analytic network process (ANP). The Fuzzy Preference Programming (FPP) proposed by Mikhailov and Singh [L. Mikhailov, M.G. Singh, Fuzzy assessment of priorities with application to competitive bidding, Journal of Decision Systems 8 (1999) 11–28] is suitable for deriving weights in interval or fuzzy comparison matrices, especially those displaying inconsistencies. However, the weakness of the FPP is that it obtains priorities of comparison matrices by additive constraints, and generates different priorities by processing upper and lower triangular judgments. In addition, the FPP solves the comparison matrix individually. By using multiplicative constraints, the method proposed in this paper can generate the same priorities from upper and lower triangular judgments with crisp, interval or fuzzy values. Our proposed method can solve all of the matrices simultaneously by multiple objective programming. Finally, five examples are demonstrated to show the proposed method in more detail.     

Time–frequency masking based supervised speech enhancement framework using fuzzy deep belief network

In recent years, deep learning based supervised speech enhancement methods have gained a considerable amount of research attention over the statistical signal processing based methods. In this study, we have considered the time–frequency masking based deep learning framework for speech enhancement and investigated how the performance of these methods can be improved further. We have mainly established that significant performance improvement can be achieved if the deep neural network (DNN) is pre-trained by using Fuzzy Restricted Boltzmann Machines (FRBM) rather than using regular Restricted Boltzmann Machines (RBM). This is mainly because of the fact that the performance of FRBM is more robust and effective when the training data is noisy. In order to train an FRBM, we have adopted a defuzzification method based on the crisp probabilistic mean value of fuzzy numbers. The detailed theory of training strategy of an FRBM with different fuzzy membership functions such as Symmetric Triangular Fuzzy Numbers (STFN) and Asymmetric Triangular Fuzzy Numbers (ATFN) is presented. Furthermore, we have evaluated the performance of the proposed training strategies on different DNN based Speech Enhancement Systems (SES) which are developed based on different training targets such as Complex Ideal Ratio Mask (cIRM), Ideal Ratio Mask (IRM) and Phase-Sensitive Mask (PSM). Experimental results on various noise scenarios have shown that the DNN-based speech enhancement system trained by the proposed approach ensures a consistent improvement in various objective measure scores of perceived speech quality and intelligibility while compared to the conventional DNN-based speech enhancement methods which use regular RBM for unsupervised pre-training.     

A measurement model for experts knowledge-based systems algorithm using fuzzy analytic network process

This study proposes an experts knowledge-based systems measurement model, the model using fuzzy analytic network process (FANP) to resolve the uncertainty and imprecision of evaluations during pre-negotiation stages, where the comparison judgments of a decision maker are represented as fuzzy triangular numbers. A novel fuzzy prioritization method, which derives crisp priorities (criteria weights and scores of alternatives) from consistent and inconsistent fuzzy comparison matrices, is also proposed. The applicability of the proposed model is demonstrated in a government purchase digital video recorder (DVR) system project study. The stability tests indicate the advantages of the proposal model in determining the value of model. Importantly, the proposed model can provide decision makers a reference material, making it highly applicable for academic and commercial purposes.     

An approach to decision-making with triangular fuzzy reciprocal preference relations and its application

Triangular fuzzy reciprocal preference relations (TFRPRs) are powerful tools to denoting decision-makers’ fuzzy judgments, which permit the decision-makers to apply triangular fuzzy ratio rather than real numbers to express their judgements. Consistency analysis is one of the most crucial issues in preference relations that can guarantee the reasonable ranking order. However, all previous consistency concepts cannot well address this type of preference relations. Based on the operational laws on triangular fuzzy numbers, this paper introduces an additive consistency concept for TFRPRs by using quasi TFRPRs, which can be seen as a natural extension of the crisp case. Using this consistency concept, models to judging the additive consistency of TFRPRs and to estimating missing values in complete TFRPRs are constructed. Then, an algorithm to decision-making with TFRPRs is developed. Finally, two numerical examples are offered to illustrate the application of the proposed procedure, and comparison analysis is performed.     

Integrating fuzzy theory and hierarchy concepts to evaluate software quality

This study proposes a software quality evaluation model and its computing algorithm. Existing software quality evaluation models examine multiple characteristics and are characterized by factorial fuzziness. The relevant criteria of this model are derived from the international norm ISO. The main objective of this paper is to propose a novel Analytic Hierarchy Process (AHP) approach for addressing uncertainty and imprecision in service evaluation during pre-negotiation stages, where comparative judgments of decision makers are represented as fuzzy triangular numbers. A new fuzzy prioritization method, which derives crisp priorities from consistent and inconsistent fuzzy comparison matrices, is proposed. The Fuzzy Analytic Hierarchy Process (FAHP)-based decision-making method can provide decision makers or buyers with a valuable guideline for evaluating software quality. Importantly, the proposed model can aids users and developers in assessing software quality, making it highly applicable for academic and commercial purposes.

A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning

In this study a hybrid (including qualitative and quantitative objectives) fuzzy multi objective nonlinear programming (H-FMONLP) model with different goal priorities will be developed for aggregate production planning (APP) problem in a fuzzy environment. Using an interactive decision making process the proposed model tries to minimize total production costs, carrying and back ordering costs and costs of changes in workforce level (quantitative objectives) and maximize total customer satisfaction (qualitative objective) with regarding the inventory level, demand, labor level, machines capacity and warehouse space. A real-world industrial case study demonstrates applicability of proposed model to practical APP decision problems. GENOCOP III (Genetic Algorithm for Numerical Optimization of Constrained Problems) has been used to solve final crisp nonlinear programming problem.     

An integrated logarithmic fuzzy preference programming based methodology for optimum maintenance strategies selection

Selecting optimum maintenance strategies plays a key role in saving cost, and improving the system reliability and availability. Analytic hierarchical process (AHP) is widely used for maintenance strategies selection in the Multiple Criteria Decision-Making (MCDM) field. But the traditional or hybrid AHP methods either produce multiple, even conflict priority results, or have complicated algorithm structures which are unstable to obtain the optimum solution. Therefore, this paper proposes an integrated Logarithmic Fuzzy Preference Programming (LFPP) based methodology in AHP to solve the optimum maintenance strategies selection problem. The multiplicative constraints and deviation variables are applied instead of additive ones to utilize both qualitative and quantitative data, and process the upper and lower triangular fuzzy judgments to obtain the same priorities. The proposed methodology can produce the unique normalized optimal priority vector for fuzzy pairwise comparison matrices, and it is capable of processing all comparison matrices to obtain the global priorities simultaneously and directly in the form of super-matrix according to the different requirements and judgments of decision-makers. Finally, an example is provided to demonstrate the feasibility and validity of the proposed methodology.     

A constrained non-linear optimization model for fuzzy pairwise comparison matrices using teaching learning based optimization

Non-linear optimization models have been recently proposed to derive crisp weights from fuzzy pairwise comparison matrices. In this paper, a TLBO (Teaching Learning Based Optimization) based solution is presented for solving an optimization model as a system of non-linear equations to derive crisp weights from fuzzy pairwise comparison matrices in AHP (Analytic Hierarchy Process). This fuzzy-AHP method is named as TLBO-1. It has been found that TLBO-1 can lead to inconsistent or less consistent weights. To solve the problem of inconsistent weights, a new constrained non-linear optimization model is proposed in this paper. This model is based on the min-max approach for fuzzy pairwise comparison ratios of weights. TLBO is again used to solve this optimization model, and crisp weights are derived. This fuzzy AHP method is named as TLBO-2. The effectiveness of the proposed model is illustrated by three examples. For each example, the consistency of the derived crisp weights is compared with other optimization models. The results show that the TLBO-2 method can derive more consistent weights for the fuzzy AHP based Multi-Criteria Decision Making (MCDM) systems as compared to the other optimization models.     

Fuzzy nonparametric regression based on local linear smoothing technique

In a great deal of literature on fuzzy regression analysis, most of research has focused on some predefined parametric forms of fuzzy regression relationships, especially on the fuzzy linear regression models. In many practical situations, it may be unrealistic to predetermine a fuzzy parametric regression relationship. In this paper, a fuzzy nonparametric model with crisp input and LR fuzzy output is considered and, based on the distance measure for fuzzy numbers suggested by Diamond [P. Diamond, Fuzzy least squares, Information Sciences 46 (1988) 141-157], the local linear smoothing technique in statistics with the cross-validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit this model. Some simulation experiments are conducted to examine the performance of the proposed method and three real-world datasets are analyzed to illustrate the application of the proposed method. The results demonstrate that the proposed method works quite well not only in producing satisfactory estimate of the fuzzy regression function, but also in reducing the boundary effect significantly.     

Preference ratio-based maximum operator approximation and its application in fuzzy flow shop scheduling

Maximum operator distorts the shape(s) of Triangular Fuzzy Numbers (TFNs) and Trapezoidal Fuzzy Numbers (TrFNs) in many problems such as Flow shop scheduling, job-shop scheduling and project scheduling. In this paper, we introduce an appropriate approximation for the maximum operator, in which the weak-dominance fuzzy numbers are ranked based on the concept of preference ratio. Since in most practical cases the due dates and the processing time of scheduling are not deterministic, we consider the scheduling problems with fuzzy processing time. Finally we develop a novel fuzzy CDS algorithm in fuzzy flow shop scheduling by applying the preference ratio concept through an example.     

Applying fuzzy hierarchy multiple attributes to construct an expert decision making process

The main objective of this paper is to propose an approach within the AHP framework for tackling the uncertainty and imprecision of service evaluations during pre-negotiation stages, where the expert’s comparison judgments are represented as fuzzy triangular numbers. A fuzzy prioritization method, which derives crisp priorities from consistent and inconsistent fuzzy comparison matrices, is described. The fuzzy analytic hierarchy process (FAHP)-based decision-making method can provide decision makers or buyer a valuable reference for evaluating software quality. A case study demonstrates the effectiveness of the proposed scheme. Importantly, the proposed scheme can assist decision makers in assessing the feasibility of digital video recorder system to management public space, making it highly applicable for academic and commercial purposes.     

Option valuation model with adaptive fuzzy numbers

In this paper, we consider moment properties for a class of quadratic adaptive fuzzy numbers defined in Dubois and Prade [D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980]. The corresponding moments of Trapezoidal Fuzzy Numbers (Tr.F.N’s) and Triangular Fuzzy Numbers (T.F.N’s) turn out to be special cases of the adaptive fuzzy number [S. Bodjanova, Median value and median interval of a fuzzy number, Information Sciences 172 (2005) 73–89]. A numerical example is presented based on the Black–Scholes option pricing formula with quadratic adaptive fuzzy numbers for the characteristics such as volatility parameter, interest rate and stock price. Our approach hinges on a characterization of imprecision by means of fuzzy set theory.     

Multi-attribute Group Decision-making Based on Hesitant Bipolar-valued Fuzzy Information and Social Network

Fuzzy sets have undergone several expansions and generalisations in the literature, including Atanasov’s intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets, to name a few. They can be regarded as fuzzy multisets from a formal standpoint; nevertheless, their interpretation differs from the two other approaches to fuzzy multisets that are currently available. Hesitating fuzzy sets (HFS) are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships. However, these possible memberships can be not only crisp values in [0,1], but also interval values during a practical evaluation process. Hesitant bipolar valued fuzzy set (HBVFS) is a generalization of HFS. This paper aims to introduce a general framework of multi-attribute group decision-making using social network. We propose two types of decision-making processes: Type-1 decision-making process and Type-2 decision-making process. In the Type-1 decision-making process, the experts’ original opinion is proces for the final ranking of alternatives. In Type-2 decision making processs, there are two major aspects we consider. First, consistency tests and checking of consensus models are given for detecting that the judgments are logically rational. Otherwise, the framework demands (partial) decision-makers to review their assessments. Second, the coherence and consensus of several HBVFSs are established for final ranking of alternatives. The proposed framework is clarified by an example of software packages selection of a university.     

Multi-objective solid transportation problems with budget constraint in uncertain environment

This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.     

机会约束下贷款组合优化决策的方差最小化模型

通过把贷款的收益率刻画为模糊变量,提出了机会约束下贷款组合优化决策的方差最小化模型。针对贷款收益率是特殊的三角模糊变量的情况,给出模型的清晰等价类,对等价类模型用传统的方法进行求解。对于贷款收益率的隶属函数比较复杂的情况,应用集成模糊模拟、神经网络、遗传算法和同步扰动随机逼近算法的混合优化算法求解模型。数值算例验证了模型和算法的有效性。     

Nature-inspired optimal tuning of input membership functions of Takagi-Sugeno-Kang fuzzy models for Anti-lock Braking Systems

This paper suggests a synergy of fuzzy logic and nature-inspired optimization in terms of the nature-inspired optimal tuning of the input membership functions of a class of Takagi-Sugeno-Kang (TSK) fuzzy models dedicated to Anti-lock Braking Systems (ABSs). A set of TSK fuzzy models is proposed by a novel fuzzy modeling approach for ABSs. The fuzzy modeling approach starts with the derivation of a set of local state-space models of the nonlinear ABS process by the linearization of the first-principle process model at ten operating points. The TSK fuzzy model structure and the initial TSK fuzzy models are obtained by the modal equivalence principle in terms of placing the local state-space models in the rule consequents of the TSK fuzzy models. An operating point selection algorithm to guide modeling is proposed, formulated on the basis of ranking the operating points according to their importance factors, and inserted in the third step of the fuzzy modeling approach. The optimization problems are defined such that to minimize the objective functions expressed as the average of squared modeling errors over the time horizon, and the variables of these functions are a part of the parameters of the input membership functions. Two representative nature-inspired algorithms, namely a Simulated Annealing (SA) algorithm and a Particle Swarm Optimization (PSO) algorithm, are implemented to solve the optimization problems and to obtain optimal TSK fuzzy models. The validation and the comparison of SA and PSO and of the new TSK fuzzy models are carried out for an ABS laboratory equipment. The real-time experimental results highlight that the optimized TSK fuzzy models are simple and consistent with both training data and validation data and that these models outperform the initial TSK fuzzy models.     

一种基于支持向量机的模糊分类系统研究

提出一种基于支持向量机学习的模糊分类束纯模型．通过将支持向量机映射成等价的模糊分类系统,支持向量机的稀疏性表示等特性使得相应的模糊分类系统避免了“维数灾难”问题,并具有良好的泛化能力．另一方面,模糊系统的一些理论和应用成果也可用来进一步改善分类系统的性能．本文根据模糊集合的贴近度概念对模糊系统的语言变量进行约简,合并冗余的和不一致的模糊规则,然后采用粒子群优化方法改善模糊分类系统性能．该方法增强了系统的泛化能力,并可以理解为解决支持向量机中难以确定的系统参数问题的一种辅助方法．实验结果表明了该方法的可行性和有效性．