The Importance of Learning In Fuzzy Systems

2000

Abstract Nowadays, Linguistic Modeling is considered to be one of the most important areas of application for Fuzzy Logic. Linguistic Mamdani-type Fuzzy Rule-Based Systems (FRBSs), the ones used to perform this task, provide a human-readable description of the model in the form of linguistic rules, which is a desirable characteristic in many problems.

Expert Systems, 2002

Fuzzy logic has been used as a means of interpreting vague, incomplete and even contradictory information into a compromised rule base in artificial intelligence such as machine decision-making. Within this context, fuzzy logic can be applied in the field of expert systems to provide additional flexibilities in constructing a working rule base: different experts' opinions can be incorporated into the same rule base, and each opinion can be modeled in a rather vague notion of human language. As some illustrative application examples, this paper describes how fuzzy logic can be used in expert systems. More precisely, it demonstrates the following applications: (i) a healthcare diagnostic system, (ii) an autofocus camera lens system and (iii) a financial decision system. For each application, basic rules are described, the calculation method is outlined and numerical simulation is provided. These applications demonstrate the suitability and performance of fuzzy logic in expert systems.

American Journal of Computational and Applied Mathematics, 2012

In the present paper we use principles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainty. For this, the main stages of the corresponding process are represented as fuzzy subsets of a set of linguistic labels characterizing the system's performance at each stage. We also introduce three alternative measures of a fuzzy system's effectiveness connected to our general model. These measures include the system's total possibilistic uncertainty, the Shannon's entropy properly modified for use in a fuzzy environment and the "centroid" method in which the coordinates of the center of mass of the graph of the membership function involved provide an alternative measure of the system's performance. The advantages and disadvantages of the above measures are discussed and a combined use of them is suggested for achieving a worthy of credit mathematical analysis of the corresponding situation. An application is also developed for the Mathematical Modelling process illustrating the use of our results in practice.

Data Management, Analytics and Innovation

It has become essential to develop machine learning techniques due to the automation of various tasks. At present, several tasks need manual intervention for better reliability of the system. In this work, fuzzy-based approach has been proposed where systems are trained based on initial data sets. In several data sets, the data is either partially available or unavailable. When data sets need to be used on real time systems, the non-availability of data may lead to catastrophe. In this approach, a fuzzy-based rule set is formulated. The rule strength is used to determine the effectiveness. Rules with similar strengths are clustered together. The learning is carried out by determining a threshold for the formulated rule set. Based on the threshold computed, a modified rule set is formulated with rule strengths greater than the computed threshold. A semi-supervised learning approach that uses an activation function is employed. The fuzzy learning approach proposed in this work reduces the error by 20% compared to conventional approaches.

The definition of the Fuzzy Rule Base is one of the most important and difficult tasks when designing Fuzzy Systems. This paper discusses the results of two different hybrid methods, previously investigated, for the automatic generation of fuzzy rules from numerical data. One of the methods, named DoC-based, proposes the creation of Fuzzy Rule Bases using genetic algorithms in association with a heuristic for preselecting candidate rules based on the degree of coverage. The other, named BayesFuzzy, induces a Bayesian Classifier using a dataset previously granulated by fuzzy partitions and then translates it into a Fuzzy Rule Base. A comparative analysis between both approaches focusing on their main characteristics, strengths/weaknesses and easiness of use is carried out. The reliability of both methods is also compared by analyzing their results in a few knowledge domains.

Fuzzy Sets and Systems, 1996

Most fuzzy controllers and fuzzy expert systems must predefine membership functions and fuzzy inference rules to map numeric data into linguistic variable terms and to make fuzzy reasoning work. In this paper, we propose a general learning method as a framework for automatically deriving membership functions and fuzzy if-then rules from a set of given training examples to rapidly build a prototype fuzzy expert system. Based on the membership functions and the fuzzy rules derived, a corresponding fuzzy inference procedure to process inputs is also developed.

Fuzzy Sets and Systems, 1997

In this paper, we propose a simple but powerful heuristic method for automatically generating fuzzy i~then rules from numerical data. Fuzzy i~then rules with nonfuzzy singletons (i.e., real numbers) in the consequent parts are generated by the proposed heuristic method. The main advantage of the proposed heuristic method is its simplicity, i.e., it involves neither time-consuming iterative learning procedures nor complicated rule generation mechanisms. We also suggest a linguistic representation method for deriving linguistic rules from fuzzy if-then rules with consequent real numbers. The proposed linguistic approximation method consists of two linguistic rule tables, which can realize exactly the same nonlinear mapping as an original system based on fuzzy if-then rules with consequent real numbers. Using computer simulations on rice taste data, we demonstrate the high performance of the proposed heuristic method and illustrate the proposed linguistic representation method. @ 1997 Elsevier Science B.V.

Proceedings of IEEE 5th International Fuzzy Systems

System modelling is an important subject in engineering, both from a research point of view and from a practical perspective. Models have an important role in several intelligent systems and, as it is observed from the research developed in the last years, fuzzy logic is relevant to this topic. This is mainly due to the expressiveness of fuzzy logic that permits the treatment of some kinds of uncertainty largely present in real systems. Also, the if-then rule mechanism is easy to manipulate and, in a certain extent, domain independent. A modelling procedure must produce good models in an effective way. This is the main concern of this paper. 1. No special assumption is made about the system, except that it must be causal.

OR Spektrum, 2001

Hierarchies of criteria and fuzzy rule systems represent an approach which effectively portrays the problem of multiple objectives found in classic decision-making scenarios such as order sequencing or the evaluation of various corporate strategies. They further help the decision-maker to select a concrete course of action. The relevant decision criteria are formalized with the help of linguistic variables. A hierarchy of criteria is then used to relate them to one another and to combine them by rule-bases. Evaluation using fuzzy sets leads to an aggregated rating of the individual alternatives. A problem of such fuzzy systems is the large number of required parameters and their influence on the evaluation results. This article will use the example of a simple criteria hierarchy for a sequencing problem to analyze the effects of individual parameters and their relationships amongst one another in a fuzzy system.

1999

The paper discusses the concept of intelligent expert systems and suggests tools for building adaptable, in an on-line or in an off-line mode, rule base during the system operation in a changing environment. It applies evolving fuzzy neural networks EFuNNs as associative memories for the purpose of dynamic storing and modifying a rule base. Algorithms for rule extraction and rule insertion from EFuNNs are explained and applied to a case study using gas furnace data and the iris data set.