Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

     

Design of polynomial fuzzy observer–controller for nonlinear systems with state delay: sum of squares approach

This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.     

多项式非线性系统的并行分布辨识

在状态空间方程中引入输入和状态的多项式函数,以此多项式函数表示非线性因素.为了辨识多项式非线性系统中的各系统矩阵,对于矢量化各系统矩阵组成的未知参数矢量,分别在无约束和有约束条件下采用两并行分布算法求解.在以状态方程等式为约束条件时,将各状态瞬时刻值与由系统矩阵组成的未知参数矢量合并为一个新的优化矢量.对于优化矢量的辨识,给出了并行分布算法的求解过程和迭代式.最后,通过仿真算例验证了所提出方法的有效性.     

ivnpiv-Neutrosophic soft sets and their decision making based on similarity measure

In recent years, soft sets and neutrosophic sets have become a subject of great interest for researchers and have been widely studied based on decision-making problems. In this paper, we propose a new concept of the soft sets that is called interval-valued neutrosophic parameterized interval-valued neutrosophic soft sets (ivnpivn-soft sets). It is a generalization of the other soft sets such as fuzzy soft sets, intuitionistic fuzzy soft sets, neutrosophic soft sets, fuzzy parameterized soft sets, intuitionistic fuzzy parameterized soft sets, neutrosophic parameterized neutrosophic soft sets. Also, we proposed ivnpivn-soft matrices which are representative of the ivnpivn-soft sets. We then developed a decision-making method on the ivnpivn-soft sets and ivnpivn-soft matrices. Then, we proposed a numerical example to verify validity and feasibility of the developed method. Finally, the proposed method is compared with several different methods to verify its feasibility.

     

基于改进齐次多项式技术的离散时间2-D T-S模糊系统的收敛镇定条件

通过利用改进的齐次多项式技术来研究了Roesser型二维T-S模糊系统的镇定设计问题. 首先, 提出了一种用来镇定该二维T-S模糊系统的一种新型非二次控制率, 并且通过应用两种改进的齐次多项式技术得到了保守性更小的镇定条件. 随着所选用的齐次多项式参数依赖矩阵度数的增加, 所得结果的保守性会越来越小. 其次, 为了继续减少保守性, 提出了一种新的右侧松弛变量引入方法, 该方法适合于齐次多项式情形. 最后, 仿真实验验证了所提方法的有效性.     

考虑专家偏好关联的群决策方法及其应用

通过分析群决策过程,提出使用模糊测度描述专家偏好之间可能存在的关联关系,并给出了一种考虑专家偏好关联的群决策方法.该方法从参评专家知识结构的相似性及判断结果的相似性出发,通过计算得到相应的2-可加模糊测度来描述专家的重要程度,并使用Choquet积分将多个专家的偏好信息聚合为群体的判断结果.最后,通过一个潜艇装备论证的例子验证了所提出方法的可行性和合理性.     

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.     

An optimization framework towards prioritization in fuzzy comparison matrices

Prioritization or eliciting final weights from the pairwise comparison matrices might be a major part of some Multiple Criteria Decision Analysis (MCDA) methods which are based upon these matrices. However, in a fuzzy environment, two other issues, i.e., consistency and reciprocity, are also arisen in such matrices with at least one fuzzy component. In this paper, a single-decision-making optimization model along with two group-decision-making optimization models are developed towards prioritization in fuzzy pairwise comparison matrices. A comprehensive numerical analysis is performed to validate the proposed models. Finally, some conclusions are reported.     

A new design of robust filters for uncertain systems

In this paper, a structured polynomial parameter-dependent approach is proposed for robust H₂ filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with s vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust H₂ filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of s matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples.     

一种基于最优可能满意度的群AHP 判断矩阵集结方法

针对层次分析法(AHP)判断矩阵群决策问题,提出一种新方法：定义可能度和满意度指标,分别衡量属性排序约束下合成矩阵的一致性程度和合成矩阵与群组判断矩阵的差异程度;利用模糊互补判断矩阵的线性和连续性,计算与群组判断矩阵差异最小的最优可能度矩阵和无约束的最优满意度矩阵;采用两个最优矩阵上三角元素的几何平均,获取满足最优可能满意度的群决策合成矩阵。最后通过算例表明了所提出方法的有效性和实用性。     

New stochastic synchronization criteria for fuzzy Markovian hybrid neural networks with random coupling strengths

This paper focuses on the stochastic synchronization problem for a class of fuzzy Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time delays in the mean square. First, a novel free-matrix-based single integral inequality and two novel free-matrix-based double integral inequalities are established. Next, by employing a novel augmented Lyapunov–Krasovskii functional with several mode-dependent matrices, applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the new free-matrix-based integral inequalities, two delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent fuzzy hybrid coupled neural networks. Finally, two numerical examples with simulation are provided to illustrate the effectiveness of the presented criteria.

     

Reliable numerical methods for polynomial matrix triangularization

Numerical procedures are proposed for triangularizing polynomial matrices over the field of polynomial fractions and over the ring of polynomials. They are based on two standard polynomial techniques: Sylvester matrices and interpolation. In contrast to other triangularization methods, the algorithms described in this paper only rely on well-worked numerically reliable tools. They can also be used for greatest common divisor extraction, polynomial rank evaluation, or polynomial null-space computation     

Polynomial Fuzzy Observer Designs: A Sum-of-Squares Approach

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.     

Optimally robust H∞ polynomial fuzzy controller design using quantum-inspired evolutionary algorithm

This paper proposes an optimally robust H_∞ polynomial fuzzy controller design using quantum-inspired evolutionary algorithm (QEA) for continuous/discrete time polynomial fuzzy systems with model uncertainties and external disturbances. To improve control performance, QEA is adopted to evolve optimal control gains with a fitness function that is defined by performance requirements. The stability and robustness of the control system are then guaranteed by the proposed robust H_∞ stability conditions, which are formed by the sum of squares (SOS) method. By using the principle of copositivity, novel relaxed SOS-based stability conditions are derived to reduce the conservativeness of solving SOS-based stability conditions, while the feasible solution space is broadened. Four numerical examples demonstrate the effectiveness of the proposed approaches.     

Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems

In this paper, the concept of trapezoidal fuzzy multi-number (TFM-number) is proposed and some desired operational laws with properties are introduced. In the TFM-number, the occurrences are more than one with the possibility of the same or the different membership functions and the TFM-number is an extension of both fuzzy number set and fuzzy set, allowing the repeated occurrences of any element. Also, aim of this paper is to investigate a multiple criteria decision-making (MCDM) method under TFM-number environment. To construct this method, we first introduce some operational laws on TFM-number based on t-norm and s-norm. Then, TFM-number arithmetic and geometric operators are proposed. Finally, we develop an MCDM method and apply to an MCDM problem to verify the introduced decision-making methods.

     

MapReduce based parallel fuzzy-rough attribute reduction using discernibility matrix

Fuzzy-rough set theory is an efficient method for attribute reduction. It can effectively handle the imprecision and uncertainty of the data in the attribute reduction. Despite its efficacy, current approaches to fuzzy-rough attribute reduction are not efficient for the processing of large data sets due to the requirement of higher space complexities. A limited number of accelerators and parallel/distributed approaches have been proposed for fuzzy-rough attribute reduction in large data sets. However, all of these approaches are dependency measure based methods in which fuzzy similarity matrices are used for performing attribute reduction. Alternative discernibility matrix based attribute reduction methods are found to have less space requirements and more amicable to parallelization in building parallel/distributed algorithms. This paper therefore introduces a fuzzy discernibility matrix-based attribute reduction accelerator (DARA) to accelerate the attribute reduction. DARA is used to build a sequential approach and the corresponding parallel/distributed approach for attribute reduction in large data sets. The proposed approaches are compared to the existing state-of-the-art approaches with a systematic experimental analysis to assess computational efficiency. The experimental study, along with theoretical validation, shows that the proposed approaches are effective and perform better than the current approaches.

     

基于事件触发传输机制的非线性系统模糊H∞ 控制

针对离散时间非线性系统, 提出事件触发传输机制下网络化T-S 模糊控制器设计方法. 在事件发生器中引入前提变量偏差触发条件, 从而取消模糊控制器与被控对象的前提变量之间的同步要求. 通过引入一组基于模糊前提变量特性的松弛等式/不等式, 对于无传输时滞和定常传输时滞两种情况, 分别提出具有较小保守性的控制器/事件发生器联合设计算法. 最后, 通过数值算例表明所提出方法的可行性和有效性.

     

FINDING SIMPLIFIED FUZZY IF-THEN RULES FOR FUNCTION APPROXIMATION PROBLEMS USING A FUZZY DATA MINING APPROACH

ABSTRACT

A fuzzy if-then rule whose consequent part is a real number is referred to as a simplified fuzzy rule. Since no defuzzification is required for this rule type, it has been widely used in function approximation problems. Furthermore, data mining can be used to discover useful information by exploring and analyzing data. Therefore, this paper proposes a fuzzy data mining approach to discover simplified fuzzy if-then rules from numerical data in order to approximate an unknown mapping from input to output. Since several pre-specified parameters for deriving fuzzy rules are not easily specified, they are automatically determined by the genetic algorithm with binary chromosomes. To evaluate performance of the proposed method, computer simulations are performed on various numerical data sets, showing that the fitting ability and the generalization ability of the proposed method are comparable to the known fuzzy rule-based methods.     

Generalized Dice measures for multiple attribute decision making under intuitionistic and interval-valued intuitionistic fuzzy environments

This paper proposes Dice measures of intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) and generalized Dice measures of IFSs and IVIFSs, and then indicates the relations of the generalized Dice measures, Dice measures, and projection measures (asymmetric measures) of IFSs and IVIFSs. Furthermore, we develop the generalized Dice measures-based multiple attribute decision-making methods with intuitionistic and interval-valued intuitionistic fuzzy information. Through the weighted generalized Dice measures between each alternative and the ideal solution (ideal alternative) according to some parameter value selected by decision makers’ preference, all the alternatives can be ranked and the best one can be chosen as well. Finally, an actual example about the selection of manufacturing schemes is provided to demonstrate the applications of the proposed decision-making methods under intuitionistic and interval-valued intuitionistic fuzzy environments, and then, a comparison analysis is conducted between the developed approach and other existing methods to verify the effectiveness and flexibility of the proposed method.