A fuzzy approach to some classification problems

An appropriate algebraic structure was previously defined which can be regarded as a possible alternative to the theory of approximate reasoning, [A. Gisolfi, Fuzzy Sets Syst. 44 , 37–43 (1992)]. In this article we aim at extending the operations of the structure in order to cope with classification problems. the theoretical aspects are emphasized in order to give an adequate background to the possible applications. After defining the basic elements and the related operations, the structure is implemented by means of Prolog. Finally the relationship between the structure and the problems of classification is discussed in some detail. © 1993 John Wiley & Sons, Inc.     

A coloring fuzzy graph approach for image classification

One of the main problems in practice is the difficulty in dealing with membership functions. Many decision makers ask for a graphical representation to help them to visualize results. In this paper, we point out that some useful tools for fuzzy classification can be derived from fuzzy coloring procedures. In particular, we bring here a crisp grey coloring algorithm based upon a sequential application of a basic black and white binary coloring procedure, already introduced in a previous paper [D. Gómez, J. Montero, J. Yáñez, C. Poidomani, A graph coloring algorithm approach for image segmentation, Omega, in press]. In this article, the image is conceived as a fuzzy graph defined on the set of pixels where fuzzy edges represent the distance between pixels. In this way, we can obtain a more flexible hierarchical structure of colors, which in turn should give useful hints about those classes with unclear boundaries.     

A delay partitioning approach to delay-range-dependent stability analysis of fuzzy systems

This paper is concerned with the stability analysis of Takagi-Sugeno (T-S) fuzzy systems with time varying delays in a given range. The delay partitioning approach is proposed to solving the problem of stability analysis for T-S fuzzy systems. By employing a new type of Lyapunov-Krasovskii functionals, delay-range-dependent stability criteria are derived for T-S fuzzy systems. The idea of the approach is that the delay interval is uniformly divided into N segments with N a positive integer, and a proper Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functional. All the sufficient criteria are established in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI algorithm. Finally, numerical example is given to illustrate the less conservatism of the proposed method.     

Supervised methods for regrouping attributes in fuzzy rule-based classification systems

This paper focuses on ensemble methods for Fuzzy Rule-Based Classification Systems (FRBCS) where the decisions of different classifiers are combined in order to form the final classification model. The proposed methods reduce the FRBCS complexity and the generated rules number. We are interested in particular in ensemble methods which cluster the attributes into subgroups of attributes and treat each subgroup separately. Our work is an extension of a previous ensemble method called SIFRA. This method uses frequent itemsets mining concept in order to deduce the groups of related attributes by analyzing their simultaneous appearances in the databases. The drawback of this method is that it forms the groups of attributes by searching for dependencies between the attributes independently from the class information. Besides, since we deal with supervised learning problems, it would be very interesting to consider the class attribute when forming the attributes subgroups. In this paper, we proposed two new supervised attributes regrouping methods which take into account not only the dependencies between the attributes but also the information about the class labels. The results obtained with various benchmark datasets show a good accuracy of the built classification model.     

A CBR-based fuzzy decision tree approach for database classification

Database classification suffers from two well-known difficulties, i.e., the high dimensionality and non-stationary variations within the large historic data. This paper presents a hybrid classification model by integrating a case-based reasoning technique, a fuzzy decision tree (FDT), and genetic algorithms (GAs) to construct a decision-making system for data classification in various database applications. The model is major based on the idea that the historic database can be transformed into a smaller case base together with a group of fuzzy decision rules. As a result, the model can be more accurately respond to the current data under classifying from the inductions by these smaller case-based fuzzy decision trees. Hit rate is applied as a performance measure and the effectiveness of our proposed model is demonstrated experimentally compared with other approaches on different database classification applications. The average hit rate of our proposed model is the highest among others.     

A fuzzy AHP-DEA approach for multiple criteria ABC inventory classification

In order to efficiently control the inventory items and determine the suitable ordering policies for them, multi-criteria ABC inventory classification, which is one of the most common techniques of production and inventory control, is used. In this classification, other criteria in addition to annual dollar usage are taken into account and then the items are classified in three classes with different ordering policies, based on their priority. In this paper, we propose an integrated fuzzy analytic hierarchy process-data envelopment analysis (FAHP-DEA) for multiple criteria ABC inventory classification. The proposed FAHP–DEA methodology uses the FAHP to determine the weights of criteria, linguistic terms such as Very High, High, Medium, Low and Very Low to assess each item under each criterion, the data envelopment analysis (DEA) method to determine the values of the linguistic terms, and the simple additive weighting (SAW) method to aggregate item scores under different criteria into an overall score for each item. The integrated FAHP–DEA methodology is illustrated using a real case study.     

A fuzzy partitioning system

Our system uses fuzzy logic to bipartition cells in VLSI circuits. The system uses fuzzy logic principles to generate net and cell indices and a bottom-up clustering algorithm to produce the two-way partition. We tested our algorithm on eleven ISCAS89 benchmark circuits and compare its performance with that of other implementations. The journal issue contains a concise summary of this article. The complete article is linked to Micro's home page on the World Wide Web (http://www.computer.org/pubs/micro/micro.htm)     

A fuzzy derivative approach to classification of outcomes from the ADRAC database

The Australian Adverse Drug Reaction Advisory Committee (ADRAC) database has been collected and maintained by the Therapeutic Goods Administration. In this paper we study a part of his database (Card2) which contains records having just reactions from the Cardiovascular group. Drug‐reaction relationships are presented by a vector of degrees which shows the degree of association of a drug with each class of reactions. In this work we examine these relationships in the classification of reaction outcomes. A modified version of the fuzzy derivative method (FDM2) is used for classification.     

A systematic fuzzy rule based approach for fault classification in transmission lines

The paper presents a new approach for fault classification in transmission line using a systematic fuzzy rule based approach. Fault classification is one of the important requirements in distance relaying for identifying the accurate phases involved in the fault process. The proposed technique starts with preprocessing the fault current signal using advanced time–frequency transform such as S-transform to compute various statistical features. After the required features are extracted, the Decision Tree (DT), a knowledge representation method, is used for initial classification. From the DT classification boundaries, the fuzzy membership functions (MFs) and corresponding fuzzy rule-base is developed for final classification. Thus a systematic fuzzy rule base is developed for fault classification, reducing the redundancies and complexities involved compared to Heuristic fuzzy rule-based approach. Also a qualitative comparison is made between S-transform and Wavelet transform, where S-transform based DT-fuzzy provides highly improved results compared to the later during simulation as well as experimental tests.     

Applying fuzzy logic to codesign partitioning

We propose a tool that will allow designers using the codesign approach to partially automate the development of embedded systems. The framework takes advantage of tools already available on the market for VLSI CAD as well as soft computing techniques. We focus our work mainly on evaluation of cost and partitioning, because this is the area in which soft computing seems to have great advantages over traditional approaches. The main novelty of our approach is our use of artificial intelligence techniques to imitate the behavior of a human in defining a system's partitioning. We hope to devote further studies to techniques to optimize the genetic algorithm, in both the representation and processing of data. We are also working on the use of formal techniques to describe our system     

A thread partitioning approach for speculative multithreading

Speculative multithreading (SpMT) is a thread-level automatic parallelization technique, which partitions sequential programs into multithreads to be executed in parallel. This paper presents different thread partitioning strategies for nonloops and loops. For nonloops, we propose a cost estimation based on combined run-time effects of various speculation factors to predict the resulting performance of candidate threads to guide the thread partitioning. For loops, we parallelize all the profitable loops that can potentially offer additional performance benefits by multilevel spawning in loop bodies, loop iterations, and inner loops. Then we select a proper thread boundary located in the front of loop branch instruction to reduce invalid spawning threads that waste core resources. Experimental results show that the proposed approach can obtain a significant increase in speedup and Olden benchmarks reach a performance improvement of 6.62 % on average.     

Optimal fuzzy controller design in continuous fuzzy system: globalconcept approach

We propose a design method for a global optimal fuzzy controller to control and stabilize a continuous fuzzy system with free- or fixed-end point under finite or infinite horizon (time). A linear-like global system representation of continuous fuzzy system is first proposed by viewing a continuous fuzzy system in global concept and unifying the individual matrices into synthetical matrices. Based on this, the optimal control law which can achieve global minimum effect is developed theoretically. The nonlinear segmental two-point boundary-value problem is derived for the finite-horizon problem and a forward Riccati-like differential equation for the infinite-horizon problem. The stability of the closed-loop fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal closed-loop fuzzy system cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant closed-loop fuzzy system possesses an infinite gain margin     

A fuzzy approach to analogical reasoning

 We address the problem of the representation of resemblances involved in analogical reasoning. We use fuzzy relations to compare situations. We provide constructive methods to adapt the solution of an already solved situation to a similar new situation according to the degree of resemblance between these two situations. We give a general definition of analogical scheme which can be considered from a more or less constrained point of view.     

基于模糊集的风险聚类预测方法

复杂社会技术系统存在许多不确定性的因素,这些因素给社会决策、项目过程管理带来了巨大的障碍和风险,因此有效的风险预测方法变得十分重要.根据风险项目的风险因素向量,利用模糊等价类的方法,对风险项目的历史数据进行模糊聚类,进而通过对新的风险项目和历史数据的模糊匹配实现了项目的风险聚类预测方法.分析和实践表明,该模型有效地解决了风险项目中诸多不确定性因素分类问题.该方法适合于政府决策、电子商务、软件项目管理等方面的风险管理应用.     

A fuzzy approach to strategic games

A game is a decision-making situation with many players, each having objectives that conflict with each other. The players involved in the game usually make their decisions under conditions of risk or uncertainty. In the paper, a fuzzy approach is proposed to solve the strategic game problem in which the pure strategy set for each player is already defined. Based on the concepts of fuzzy set theory, the approach uses a multicriteria decision-making method to obtain the optimal strategy in the game, a method which shows more advantages than the classical game methods. Moreover, with this approach, some useful conclusions are reached concerning the famous “prisoner's dilemma” problem in game theory     

A formal approach to fuzzy modeling

A formalism for coding fuzzy models of dynamical systems is presented. It is shown that the formalism is rich enough to capture the performance of arbitrary conventional discrete time dynamical systems whose transition maps are polynomials with rational coefficients. The proof of this fact provides a constructive algorithm for generating fuzzy models to arbitrarily closely approximate an arbitrary map on a compact set. Our modeling formalism highlights the similarities between fuzzy systems and hybrid control systems. We hope to be able to exploit these similarities by extending results from the area of hybrid systems to the fuzzy domain and vice versa     

A generalized approach to fuzzy optimization

A new approach to fuzzy optimization based on the generalization of Bellman-Zadeh's (BZ) concept is proposed in this article. It consists of a parametric generalization of intersection of fuzzy sets and a generalized defuzzification method. This approach allows the solving of a fuzzy mathematical programming (FMP) problem without transformation to a crisp one. It takes into account all possible fuzzy decisions and allows the degree of conjunction of criteria and constraints to vary. BZ method can be considered a special case of the approach proposed here. A simple algorithm for noniterative solving FMP problem is proposed whereas well-known Zimmermann's approach uses numerical methods. an illustrative example is presented. © 1994 John Wiley & Sons, Inc.