A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.     

Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems: Survey and Challenges

Three-way decision (T-WD) theory is about thinking, problem solving, and computing in threes. Behavioral decision making (BDM) focuses on effective, cognitive, and social processes employed by humans for choosing the optimal object, of which prospect theory and regret theory are two widely used tools. The hesitant fuzzy set (HFS) captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades. Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together, this paper reviews and examines advances in three-way behavioral decision making (TW-BDM) with hesitant fuzzy information systems (HFIS) from the perspective of the past, present, and future. First, we provide a brief historical account of the three topics and present basic formulations. Second, we summarize the latest development trends and examine a number of basic issues, such as one-sidedness of reference points and subjective randomness for result values, and then report the results of a comparative analysis of existing methods. Finally, we point out key challenges and future research directions.      

A dual‐tree complex wavelet transform‐based approach for recognition of power system transients

The present paper proposes a dual‐tree complex wavelet transform (DTCWT) based approach for recognition of power system transients. Several researchers, all over the world, have so far attempted to solve the problems of recognition of power system transients, hybridizing transform‐based techniques with popular computational intelligence based tools, for example, using wavelet transform and S‐transform for feature extraction, followed by artificial neural networks (ANN) or fuzzy logic‐based classifiers. The proposed method of hybridizing DTCWT‐based feature extraction with ANN‐based classification could efficiently detect several commonly occurring power quality (PQ) disturbance events. The PQ disturbance events considered include four different transient conditions, namely transients due to capacitor switching, transformer inrush currents, transients due to motor switching and transients due to short circuit faults. A detailed performance comparison with several contemporary, competing methods existing in the literatures for similar problems aptly demonstrates the suitability of the proposed method.     

Knowledge-based parameter identification of TSK fuzzy models

Linear/1st order Takagi–Sugeno–Kang (TSK) fuzzy models are widely used to identify static nonlinear systems from a set of input–output pairs. The synergetic integration of TSK fuzzy models with artificial neural networks (ANN) has led to the emergence of hybrid neuro-fuzzy models that can have excellent adaptability and interpretability at the same time. One drawback of these hybrid models is that they tend to have more black-box characteristics of ANN than the transparency of fuzzy systems. If the quality of training data is questionable then it may lead to a fuzzy model with poor interpretability. In an attempt to remediate this problem, we propose a parameter identification technique for TSK models that relies on a-priori available qualitative domain knowledge. The technique is devised for rule-centered TSK models in which the consequent polynomial can be interpreted as the 1st order Taylor series approximation of the underlying nonlinear function that is being modeled. The resulting neuro-fuzzy model is named as a-priori knowledge-based fuzzy model (APKFM). We have shown that besides being reasonably accurate, APKFM has excellent interpretability and extrapolation capability. The effectiveness of APKFM is shown using two examples of static systems. In the first example, a toy nonlinear function is chosen for approximation by an APKFM. In the second example, a real world problem pertaining to the maintenance cost estimation of electricity distribution networks is addressed.     

A new result on state feedback robust stabilization for discrete‐time fuzzy singularly perturbed systems

This paper presents the novel results for stabilizing uncertain standard discrete‐time fuzzy singularly perturbed systems (SPSs) via a state feedback control law. Two standard discrete‐time fuzzy SPSs are constructed firstly by using the Takagi‐Sugeno (T‐S) fuzzy model. Based on a matrix spectral norm approach, two new ε‐dependent stability conditions are derived, which guarantee the resulting closed‐loop systems are asymptotically stable. The gains of controllers are obtained by solving a set of ε‐dependent linear matrix inequalities (LMIs). In contrast to the existing results, the proposed methods have two advantages: (i) the designed controllers can overcome the external disturbances and parameter uncertainty; and (ii) the upper bound of ε is improved, especially it is not required to be smaller than one. Examples are provided to illustrate the reduced conservatism of our results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An efficient methodology for robust control of dynamic systems with interval matrix uncertainties

Interval models are frequently used for dealing with uncertainties of control systems. However, it is well known that direct analysis and synthesis of a controlled dynamic system with interval matrix uncertainties may be a NP-hard problem. In this work, an efficient methodology for robustness analysis and robust control design of dynamic systems with interval matrix uncertainties is presented systematically, in which the uncertainties appearing in the controlled plant and controller realisation are taken into account simultaneously in an integrated framework. The fundamental problems, such as quadratic stability, guaranteed cost control and H_∞ control of uncertain systems are taken as examples to show the methodology. Necessary and sufficient conditions for linear dynamic systems with interval matrices are derived by transforming all the interval matrices into some more tractable forms. The whole reasoning process is logical and rigorous, and NP-hard problem is successfully avoided. The presented formulations are within the framework of linear matrix inequality and can be implemented conveniently. In contrast to existing vertex-set methods, in which the vertices of interval matrices need to be constructed and checked, the presented methods are more efficient. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.     

T-S模糊系统的基于观测器的H∞控制设计

研究了T-S(Takagi-Sugeno)模糊系统H∞控制设计问题.放宽了Kim E等的T-S模糊 系统可二次稳定的条件.给出了T-S模糊系统新的观测器设计方法.然后给出了T-S模糊系统 基于观测器的H∞控制存在的两个新的充分条件.新方法不但简单,而且充分考虑了模糊子系统 间的相互作用.最后通过例子,应用LMI技术,说明了本文给出的T-S模糊系统的基于观测器 的H∞控制器的设计方法简便易行.     

Applying fuzzy mathematical programming approach to optimize a multiple supply network in uncertain condition with comparative analysis

Supply chain design problems have recently raised a lot of interest since the opportunity of an integrated management of the supply chain can reduce the propagation of undesirable events through the network and can affect decisively the profitability of the members. Often uncertainties may be associated with demand and relevant costs. In most of the existing models uncertainties are treated as randomness and are handled by appealing to probability theory. Here, we propose a fuzzy mathematical programming model for a supply chain which considers multiple depots, multiple vehicles, multiple products, multiple customers, and different time periods. In this work not only demand and cost but also decision variables are considered to be fuzzy. We apply two ranking functions for solving the model. The aim of the fuzzy mathematical program is to select the appropriate depots among candidate depots, the allocation of orders to depots and vehicles, also the allocation of the returning vehicles to depots, to minimize the total costs. To validate the model some numerical experiments are worked out and a comparative analysis is investigated. Also, a regression model is considered to analyze the applied fuzzy ranking methods.     

A hybrid model through the fusion of type-2 fuzzy logic systems and extreme learning machines for modelling permeability prediction

Extreme learning machines (ELM), as a learning tool, have gained popularity due to its unique characteristics and performance. However, the generalisation capability of ELM often depends on the nature of the dataset, particularly on whether uncertainty is present in the dataset or not. In order to reduce the effects of uncertainties in ELM prediction and improve its generalisation ability, this paper proposes a hybrid system through a combination of type-2 fuzzy logic systems (type-2 FLS) and ELM; thereafter the hybrid system was applied to model permeability of carbonate reservoir. Type-2 FLS has been chosen to be a precursor to ELM in order to better handle uncertainties existing in datasets beyond the capability of type-1 fuzzy logic systems. The type-2 FLS is used to first handle uncertainties in reservoir data so that its final output is then passed to the ELM for training and then final prediction is done using the unseen testing dataset. Comparative studies have been carried out to compare the performance of the proposed T2-ELM hybrid system with each of the constituent type-2 FLS and ELM, and also artificial neural network (ANN) and support Vector machines (SVM) using five different industrial reservoir data. Empirical results show that the proposed T2-ELM hybrid system outperformed each of type-2 FLS and ELM, as the two constituent models, in all cases, with the improvement made to the ELM performance far higher against that of type-2 FLS that had a closer performance to the hybrid since it is already noted for being able to model uncertainties. The proposed hybrid also outperformed ANN and SVM models considered.     

Robust adaptive fuzzy VSS control for a class of uncertain nonlinear systems using small gain design

In this paper, a novel robust adaptive fuzzy variable structure control (RAFVSC) scheme is proposed for a class of uncertain nonlinear systems. The uncertain nonlinear system and gain functions originating from modeling errors and external disturbances are all unstructured (or non-repeatable), state-dependent and completely unknown. The Takagi–Sugeno type fuzzy logic systems are used to approximate uncertain functions in the systems and the RAFVSC is designed by use of the input-to-state stability (ISS) approach and small gain theorem. In the algorithm, there are three advantages which are that the asymptotic stability of adaptive control in the presence of unstructured uncertainties can be guaranteed, the possible controller singularity problem in some of existing adaptive control schemes using feedback linearization techniques can be removed and the adaptive mechanism with minimal learning parameterizations can be achieved. The performance and effectiveness of the proposed methods are discussed and illustrated with two simulation examples.     

Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.     

Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets (SNSs) have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers (SNNs) and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making (MCGDM) problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.     

A fuzzy mid-term single-fab production planning model

Production planning is a complicated task for a semiconductor fabrication plant because of the uncertainties in demand, product prices, cycle times, and product yields. Traditionally, mid-term production planning for a semiconductor fabrication plant is handled with MRP systems or optimized by solving LP or FLP problems. In this study, the philosophy of prioritizing demand classes with higher certainties as proposed by Leachman (1993) is applied to the FLP model of Chen and Wang (1998), and a new FLP model for planning the mid-term production of single wafer fabrication plant is constructed. Parameters in this model are given in the form of trapezoidal fuzzy numbers. Fuzzy comparison is adopted in dealing with the fuzzy objective function and expanding inequalities. The outputs are projected using Chen and Wang's fuzzy dynamic production function. The uncertain demand is classified and satisfied with four successively optimized FLP submodels according to their ascending uncertainties. Chen and Wang's example is adopted to demonstrate the proposed methodology and to make some comparisons. By moving more capacity to demand classes with higher certainties that are usually nearer and have larger discounted revenues, the proposed methodology achieves a higher value of the discounted cash flows than the two referenced models.     

LMI‐based robust sliding control for mismatched uncertain nonlinear systems using fuzzy models

We propose a robust sliding control design method for uncertain Takagi–Sugeno fuzzy models. The uncertain fuzzy systems under consideration have mismatched parameter uncertainties in the state matrix and external disturbances. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel, which is required in the traditional VSS‐based fuzzy control design methods. We derive the existence conditions of linear sliding surfaces guaranteeing the asymptotic stability in terms of constrained LMIs. We present an LMI characterization of such sliding surfaces. Also, an LMI‐based algorithm is given to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give two simulation results to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Neuro fuzzy and punctual kriging based filter for image restoration

In this paper, we present a hybrid, image restoration approach. The proposed approach combines the geostatistical interpolation of punctual kriging, artificial neural networks (ANNs), and fuzzy logic based approaches. Images degraded with Gaussian white noise are restored by first utilizing fuzzy logic for selecting pixels that needs kriging. Three fuzzy systems are employed. Both type-I and type-II fuzzy sets in addition with neuro fuzzy classifier (NFC) have been used for the detection of noisy pixels. To avoid edge pixels, a post processing technique is used to check the edge pixel connectivity up to lag 5. If the pixel under consideration is an edge pixel, it is excluded from the fuzzy map and thus not estimated. The concept of punctual kriging is then used to estimate the intensity of a noisy pixel. ANN is employed to minimize the cost function of the kriging based pixel intensity estimation procedure. ANN, in contrast to analytical methodologies, avoids both matrix inversion failure and negative weights problems. Image restoration performance based comparison has been made against adaptive Weiner filter and existing fuzzy kriging approaches. Experimental results using 450 images are used to validate the effectiveness of the proposed approach. Different image quality measures are used to compare the efficacy of the proposed NFC and fuzzy type-II approaches for detecting noisy pixels in conjunction with ANN and kriging based estimation.     

Subtractive clustering attribute weighting (SCAW) to discriminate the traffic accidents on Konya-Afyonkarahisar highway in Turkey with the help of GIS: A case study

A case study including the discrimination of traffic accidents as accident free and accident cases on Konya-Afyonkarahisar highway in Turkey using the proposed hybrid method based on combining of a new data preprocessing method called subtractive clustering attribute weighting (SCAW) and classifier algorithms with the help of Geographical Information System (GIS) technology has been conducted. In order to improve the discrimination of classifier algorithms including artificial neural network (ANN), adaptive network based fuzzy inference system (ANFIS), support vector machine, and decision tree, using data preprocessing need in solution of these kinds of problems (traffic accident case study). So, we have proposed a novel data preprocessing method called subtractive clustering attribute weighting (SCAW) and combined with classifier algorithms. In this study, the experimental data has been obtained by means of using GIS. The obtained GIS attributes are day, temperature, humidity, weather conditions, and month of occurred accident. To evaluate the performance of the proposed hybrid method, the classification accuracy, sensitivity and specificity values have been used. The experimental obtained results are 53.93%, 52.25%, and 38.76% classification successes using alone ANN, ANFIS, and SVM with RBF kernel type, respectively. As for the proposed hybrid method, the classification accuracies of 67.98%, 70.22%, and 61.24% have been obtained using the combination of SCAW with ANN, the combination of SCAW with SVM (radial basis function (RBF) kernel type), and the combination of SCAW with ANFIS, respectively. The proposed SCAW method with the combination of classifier algorithms has been achieved the very promising results in the discrimination of traffic accidents.     

Real time fuzzy scheduling rules in FMS

This paper presents a real-time fuzzy expert system to scheduling parts for a flexible manufacturing system (FMS). First, some vagueness and uncertainties in scheduling rules are indicated and then a fuzzy-logic approach is proposed to improve the system performance by considering multiple performance measures. This approach focuses on characteristics of the system's status, instead of parts, to assign priorities to the parts waiting to be processed. Secondly, a simulation model is developed and it has shown that the proposed fuzzy logic-based decision making process keeps all performance measures at a good level. The proposed approach provides a promising alternative framework in solving scheduling problems in FMSs, in contrast to traditional rules, by making use of intelligent tools.     

An Alternative approach to H∞ control for fuzzy systems

In this paper the problem of H_∞ dynamic feedback control for fuzzy dynamic systems has been studied. First the problem of H_∞ dynamic feedback controller designs for complex nonlinear systems, which can be represented by Takagi‐Sugeno (T‐S) fuzzy systems, is presented. Second, based on a Lyapunov function, four new dynamic feedback H_∞ fuzzy controllers are developed by adequately considering the interactions among all fuzzy sub‐systems and these dynamic feedback H_∞ controllers can be obtained by solving a set of suitable linear matrix inequalities. Finally, two examples are given to demonstrate the effectiveness of the proposed design methods. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay-dependent robust stabilization and H ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.     

Fuzzy logical control based on optical information technologies

This paper is concerned with one problem in creating intellectual control systems: methods and design tools of fuzzy logical devices for building modern efficient and reliable control systems in poorly formalized problems and ill-structured problem domains. Flaws of the available microprocessor devices for fuzzy information processing are indicated and alternative design principles of fuzzy logic control systems based on high-speed spatially distributed wave guide optical structures are considered based on an example of an opto-electronic dephaser. High-speed spatially distributed wave guide optical structures are shown as being advantageous for solving the scientific and engineering problems for developing new design methods of fuzzy logical devices with enhanced technical characteristics for implementation of fuzzy logical control.