Exact inversion of decomposable interval type-2 fuzzy logic systems

It has been demonstrated that type-2 fuzzy logic systems are much more powerful tools than ordinary (type-1) fuzzy logic systems to represent highly nonlinear and/or uncertain systems. As a consequence, type-2 fuzzy logic systems have been applied in various areas especially in control system design and modelling. In this study, an exact inversion methodology is developed for decomposable interval type-2 fuzzy logic system. In this context, the decomposition property is extended and generalized to interval type-2 fuzzy logic sets. Based on this property, the interval type-2 fuzzy logic system is decomposed into several interval type-2 fuzzy logic subsystems under a certain condition on the input space of the fuzzy logic system. Then, the analytical formulation of the inverse interval type-2 fuzzy logic subsystem output is explicitly driven for certain switching points of the Karnik–Mendel type reduction method. The proposed exact inversion methodology driven for the interval type-2 fuzzy logic subsystem is generalized to the overall interval type-2 fuzzy logic system via the decomposition property. In order to demonstrate the feasibility of the proposed methodology, a simulation study is given where the beneficial sides of the proposed exact inversion methodology are shown clearly.     

A fuzzy random forest

When individual classifiers are combined appropriately, a statistically significant increase in classification accuracy is usually obtained. Multiple classifier systems are the result of combining several individual classifiers. Following Breiman’s methodology, in this paper a multiple classifier system based on a “forest” of fuzzy decision trees, i.e., a fuzzy random forest, is proposed. This approach combines the robustness of multiple classifier systems, the power of the randomness to increase the diversity of the trees, and the flexibility of fuzzy logic and fuzzy sets for imperfect data management. Various combination methods to obtain the final decision of the multiple classifier system are proposed and compared. Some of them are weighted combination methods which make a weighting of the decisions of the different elements of the multiple classifier system (leaves or trees). A comparative study with several datasets is made to show the efficiency of the proposed multiple classifier system and the various combination methods. The proposed multiple classifier system exhibits a good accuracy classification, comparable to that of the best classifiers when tested with conventional data sets. However, unlike other classifiers, the proposed classifier provides a similar accuracy when tested with imperfect datasets (with missing and fuzzy values) and with datasets with noise.     

基于Nie-Tan算法的区间二型模糊集质心计算:改变主变量采样个数

计算区间二型模糊集的质心(也称降型)是区间二型模糊逻辑系统中的一个重要模块。Karnik-Mendel(KM)迭代算法通常被认为是计算区间二型模糊集质心的标准算法。尽管如此,KM算法涉及复杂的计算过程,不利于实时应用。在各种改进类算法中,非迭代的Nie-Tan(NT)算法可节省计算消耗。此外,连续版本NT(CNT,continuous version of NT)算法被证明是计算质心的准确算法。本文比较了离散版本NT算法中求和运算和连续版本NT算法中求积分运算,通过四个计算机仿真例子证实了当适度增加区间二型模糊集主变量采样个数时,NT算法的计算结果可以精确地逼近CNT算法。     

Credit rating analysis using adaptive fuzzy rule-based systems: an industry-specific approach

This paper presents an analysis of credit rating using fuzzy rule-based systems. The disadvantage of the models used in previous studies is that it is difficult to extract understandable knowledge from them. The root of this problem is the use of natural language that is typical for the credit rating process. This problem can be solved using fuzzy logic, which enables users to model the meaning of natural language words. Therefore, the fuzzy rule-based system adapted by a feed-forward neural network is designed to classify US companies (divided into the finance, manufacturing, mining, retail trade, services, and transportation industries) and municipalities into the credit rating classes obtained from rating agencies. Features are selected using a filter combined with a genetic algorithm as a search method. The resulting subsets of features confirm the assumption that the rating process is industry-specific (i.e. specific determinants are used for each industry). The results show that the credit rating classes assigned to bond issuers can be classified with high classification accuracy using low numbers of features, membership functions, and if-then rules. The comparison of selected fuzzy rule-based classifiers indicates that it is possible to increase classification performance by using different classifiers for individual industries.     

Indirect adaptive fuzzy observer and controller design based on interval type-2 T-S fuzzy model

This paper presents the design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T-S fuzzy model. The nonlinear systems can be well approximated by IT2 T-S fuzzy model, in which the fuzzy rules’ antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The proposed IT2 T-S fuzzy model is a combination of IT2 fuzzy system and T-S fuzzy model, and also inherits the benefits of type-2 fuzzy logic systems, which is able to directly handle uncertainties and can minimize the effects of uncertainties in rule-based fuzzy system. These characteristics can improve the accuracy of the system modeling and reduce the number of system rules. The proposed method using feedback control, adaptive laws, and on-line object parameters are adjusted to ensure observation error bounded. In addition, using Lyapunov synthesis approach and Lipschitz condition, the stability analysis is conducted. The simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.     

同一水平下模糊规则信息熵的描述

给出了模糊知识系统及模糊决策逻辑公式的定义,在此基础上描述了模糊决策逻辑公式及模糊知识系统下模糊规则的信息熵,讨论了模糊规则信息熵的相关性质;其次,利用模糊规则信息熵对模糊规则进行了分类、评价,从而为建立合理的模糊系统提供了一种有效的判定方法;最后,通过实例验证了所提出理论的正确性.     

A cloud computing based many objective type-2 fuzzy logic system for mobile field workforce area optimization

Large scale optimization problems in the real world are often very complex and require multiple objectives to be satisfied. This applies to industries that employ a large mobile field workforce. Sub-optimal allocation of tasks to engineers in this workforce can lead to poor customer service, higher travel costs and higher CO\(_{2}\) emissions. One solution is to create optimal working areas, which are geographical regions containing many task locations, where the engineers can work. Finding the optimal design of these working areas as well as assigning the correct engineers to them is known as workforce optimization and is a very complex problem, especially when scaled up over large areas. As a result of the vast search space, given by this problem, meta heuristics like genetic algorithms and multi-objective genetic algorithms, are used to find solutions to the problem in reasonable time. However, the hardware these algorithms run on can play a big part in their day-to-day use. This is because the environment in which the engineers are working within is changing on a daily bases. This means that there are severe time-restrictions on the optimization process if the working areas were to be optimized every day. One way to tackle this is to move the optimization system to the cloud where the computing resources available are often far greater than personal desktops or laptops. This paper presents our proposed cloud based many objective type-2 fuzzy logic system for mobile field workforce area optimization. The proposed system showed that utilizing cloud computing with multi-threading capabilities significantly reduce the optimization time allowing greater population sizes, which led to improved working area designs to satisfy the faced objectives.     

Performance evaluation of fuzzy classification methods designed for real time application

This paper proposes a comparative appraisal of the fuzzy classification methods which are Fuzzy C-Means, K Nearest Neighbours, method based on Fuzzy Rules and Fuzzy Pattern Matching method. It presents the results we obtained in applying those methods on three types of data that we present in the second part of this article. The classification rate and the computing times are compared from a method to another. This paper describes the advantages of the fuzzy classifiers for an application to a diagnosis problem. To finish it proposes a synthesis of our study which can constitute a base to choose an algorithm in order to apply it to a process diagnosis in real time. It shows how we can associate unsupervised and supervised methods in a diagnosis algorithm.     

Intelligent systems in finance

Business sectors ranging from banking and insurance to retail, are benefiting from a whole new generation of ‘intelligent’ computing techniques. Successful applications include asset forecasting, credit evaluation, fraud detection, portfolio optimization, customer profiling, risk assessment, economic modelling, sales forecasting and retail outlet location. The techniques include expert systems, rule induction, fuzzy logic, neural networks and genetic algorithms, which in many cases are outperforming traditional statistical approaches. Their key features include the ability to recognize and classify patterns, learning from examples, generalization, logical reasoning from premises, adaptability and the ability to handle data which is incomplete, imprecise and noisy. This paper is the first in a series to appear in Applied Mathematical Finance;here we introduce the reader to the basic concepts of intelligent systems, describe their mode of operation and identify applications of the techniques in real world problem domains. Subsequent papers will concentrate on neural networks, genetic algorithms, fuzzy logic and hybrid systems, and will investigate their history and operation more rigorously.     

Real-time moving object segmentation in H.264 compressed domain based on approximate reasoning

This paper presents a real-time segmentation algorithm to obtain moving objects from the H.264 compressed domain. The proposed segmentation works with very little information and is based on two features of the H.264 compressed video: motion vectors associated to the macroblocks and decision modes. The algorithm uses fuzzy logic and allows to describe position, velocity and size of the detected regions in a comprehensive way, so the proposed approach works with low level information but manages highly comprehensive linguistic concepts. The performance of the algorithm is improved using dynamic design of fuzzy sets that avoids merge and split problems. Experimental results for several traffic scenes demonstrate the real-time performance and the encouraging results in diverse situations.     

Intuitionistic Fuzzy Logic Control for Heater Fans

The concept of intuitionistic fuzzy systems, including intuitionistic fuzzy sets and intuitionistic fuzzy logic, was introduced by Atanassov as a generalization of fuzzy systems. Intuitionistic fuzzy systems provide a mechanism for communication between computing systems and humans. In this paper, we describe the development of an intuitionistic fuzzy logic controller for heater fans, developed on the basis of intuitionistic fuzzy systems. Intuitionistic fuzzy inference systems and defuzzification techniques are used to obtain crisp output (i.e., speed of the heater fan) from an intuitionistic fuzzy input (i.e., ambient temperature). The speed of the heater fan is calculated using intuitionistic fuzzy rules applied in an inference engine using defuzzification methods.     

Real-time moving object segmentation in H.264 compressed domain based on approximate reasoning

This paper presents a real-time segmentation algorithm to obtain moving objects from the H.264 compressed domain. The proposed segmentation works with very little information and is based on two features of the H.264 compressed video: motion vectors associated to the macroblocks and decision modes. The algorithm uses fuzzy logic and allows to describe position, velocity and size of the detected regions in a comprehensive way, so the proposed approach works with low level information but manages highly comprehensive linguistic concepts. The performance of the algorithm is improved using dynamic design of fuzzy sets that avoids merge and split problems. Experimental results for several traffic scenes demonstrate the real-time performance and the encouraging results in diverse situations.     

Simulation and evaluation of dual fully fuzzy linear systems by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate solution of fuzzy linear systems of the form Ax = Bx + d, where A and B are two square matrices of fuzzy coefficients, x and d are two fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution, a simple and fast algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

一类模糊逻辑系统幺半群与同态映射

首先利用代数中幺半群的概念给出了模糊逻辑系统专业领域的概念, 建立专业领域概念的目的是为了规范模糊逻辑系统中语言变量的取值范围, 从而将模糊逻辑系统看作是某个笛卡儿乘积幺半群的有限子集. 然后利用这个笛卡儿乘积幺半群的乘积运算构造了模糊逻辑系统幺半群. 最后, 在一定的约定条件下证明了通常使用的一类Mamdani形模糊逻辑系统的输出可以看作是从模糊逻辑系统幺半群到连续函数域的同态映射.     

Fuzzy neural network modeling for product development

A fairly general product development model is formulated and analyzed based on multiple attribute decision making with emphasis on the treatment of the linguistic and vague aspects by fuzzy logic and up-dating or learning by neural network. Due to the representative ability of fuzzy set theory and the learning or intelligent ability of neural network, the proposed approaches appear to be an effective tool for handling vague and not well-defined systems.     

Implicational (semilinear) logics I: a new hierarchy

In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives they possess. It yields a new classification of logics expanding Leibniz hierarchy: the hierarchy of implicational logics. In this framework the notion of implicational semilinear logic can be naturally introduced as a property of the implication, namely a logic L is an implicational semilinear logic iff it has an implication such that L is complete w.r.t. the matrices where the implication induces a linear order, a property which is typically satisfied by well-known systems of fuzzy logic. The hierarchy of implicational logics is then restricted to the semilinear case obtaining a classification of implicational semilinear logics that encompasses almost all the known examples of fuzzy logics and suggests new directions for research in the field.     

Evaluation of fuzzy regression models by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

Historical reflections and new positions on perceptual computing

This paper traces the historical origins of perceptual computing and credits Tong and Bonissone (IEEE Trans Syst Man Cybern 10:716–723, 1980) as being the first to originate it but under a different name. It also takes the position that interval type-2 fuzzy sets, and not type-1 fuzzy sets, should be used in perceptual computing. Finally, it proposes some testable guidelines for when a solution (e.g., perceptual computing) may be branded computing with words.     

Comment on “Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems”

In this comment, we point out the inappropriateness of Theorem 1 in the article [Tsung-Chih Lin, Mehdi Roopaei. Based on interval type-2 adaptive fuzzy H^∞ tracking controller for SISO time-delay nonlinear systems. Commun Nonlinear Sci Numer Simulat 2010;15:4065–75]. For solving this problem, some formular mistakes are corrected and novel parameter adaptive laws of interval type-2 fuzzy neural network system are given.     

Ten questions and one problem on fuzzy logic

Recently, I had a very interesting friendly e-mail discussion with Professor Parikh on vagueness and fuzzy logic. Parikh published several papers concerning the notion of vagueness. They contain critical remarks on fuzzy logic and its ability to formalize reasoning under vagueness [10,11]. On the other hand, for some years I have tried to advocate fuzzy logic (in the narrow sense, as Zadeh says, i.e. as formal logical systems formalizing reasoning under vagueness) and in particular, to show that such systems (of many-valued logic of a certain kind) offer a fully fledged and extremely interesting logic [4, 5]. But this leaves open the question of intuitive adequacy of many-valued logic as a logic of vagueness. Below I shall try to isolate eight questions Parikh asks, add two more and to comment on all of them. Finally, I formulate a problem on truth (in)definability in Łukasiewicz logic which shows, in my opinion, that fuzzy logic is not just “applied logic” but rather belongs to systems commonly called “philosophical logic” like modal logics, etc.