Application Of Fuzzy Set Theory Research Articles

Fuzzy set theory applied to bend sequencing for sheet metal bending

Brake forming is widely applied in the high variety and small batch part manufacturing of sheet metal components, for the bending of straight bending lines. Currently, the planning of the bending sequences is a task that has to be performed manually, involving many heuristic criteria. However, set-up and bend sequencing procedures and knowledge have to be formally formalized and modeled, for the development of computer-aided process planning systems for sheet metal forming. This paper describes the application of fuzzy set theory for the normalization and modeling of the set-up and bend sequencing process for sheet metal bending. A fuzzy-set based methodology is used to determine the optimal bending sequences for the brake forming of sheet metal components, taking into account the relative importance of handling and accuracy.

Fuzzy relational calculus in land evaluation

In recent years, methods of fuzzy reasoning were developed for situations akin to those found in land evaluation, in which a decision about land suitability must often be based upon imprecise information. The accuracy of such land evaluations depends on the quality of weighing land qualities with respect to their effect on crop production. The advantage of the fuzzy set approach is that class boundaries are not sharply defined, thus allowing the possibility of partial membership to a class. However, the application of fuzzy set theory in land evaluation is often limited to the use of membership functions and has weaknesses with regard to the way weights are attributed to the land qualities considered. Fuzzy relational calculus is introduced to overcome these problems. This new approach is based on fuzzy relations between land qualities and land units. Such a relation mathematically describes the suitability for a particular crop. Relational calculus offers the possibility to construct new relations from those defined previously. It allows to introduce weight coefficients that account for the importance of each land quality considered.

Fault diagnosis of power transformers: application of fuzzy set theory, expert systems and artificial neural networks

The application of fuzzy set theory, expert systems and artificial neural networks to fault diagnosis of power transformers is introduced, and uncertain reasoning and the combination between ES and ANN are studied. Uncertain reasoning is the main diagnostic method. The ES/ANN combination, called the consultative mechanism, can help to improve the correctness of the diagnosis and ensure the accuracy of the knowledge base. Experimental results are given which verify the proposed method.

An application of fuzzy set theory to the individual investor problem

This study reviews the problem of the individual investor and applies to it a methodology based on fuzzy sets and the theory of possibility. The investment decision is characterized by uncertainty, imprecision and complexity, which lessen the effectiveness of conventional calculus and probability tools. In contrast, fuzzy set theory and its modeling language provide objects of analysis and algebra that are well suited to this problem. New concepts such as “fuzzy portfolio weights” are introduced. The result of our research is a qualitative, general, and practical model for individual investors' decision making, which is based on Smith's (1974) asset-mix model.

Knowledge Representation in Fuzzy and Rough Controllers

Alternative approaches to data processing, e.g., fuzzy set theory, rough set theory and neural networks, known collectively as ‘soft computing,’ have drawn significant interest from the scientific community. They have already found numerous applications to real-world problems and will certainly become even more important in the future. This paper concentrates on two important classes of soft computing methods, i.e., fuzzy sets and rough sets. In particular, knowledge acquisition and representation in fuzzy and rough controllers is discussed and compared. The paper is concluded with an illustrative example, showing the application of fuzzy and rough set theory to the control of the ‘inverted pendulum.’

Applications of fuzzy sets theory in power systems planning and operation: a critical review to assist in implementation

A critical review of publications that apply the principles of fuzzy sets theory to power systems planning and operation is presented. An assessment of the costs and benefits associated with the use of fuzzy sets theory is performed to assist both researchers and utility engineers in evaluating its suitability for specific applications that they might encounter. While fuzzy sets theory has seen relatively little use in power systems planning and operation, it has gained widespread popularity in other industries. The use of fuzzy sets theory should be considered in all applications where attempts are made to model the behaviour of soft systems, consider multiple conflicting objectives, or require interpretation of qualitative information.

Does a single response category in a scale completely capture a response?

The objective of this article is to suggest the application of fuzzy set theory to issues in scale development in marketing by conceptualizing response categories of a scale as fuzzy sets. Respondents' natural responses to scales are argued to have degrees of membership in more than one response category when a response scale does not match natural responses. In contrast to traditional scales, which only allow the choice of a single category as a response, a new scale, which allows responses with degrees of membership in more than one response category, is developed. This scale is used in an expository study conducted to demonstrate implications of the conceptualization for issues in scale development. Specifically, norms are suggested for use in evaluating traditional scales during scale development in terms of the optimal number of response categories and appropriate category descriptors. Implications of this methodology for marketers are discussed relating to the use of the proposed methodology in (a) the development of response scales, (b) the development of questions/items in questionnaire design, and (c) the measurement of phenomena that are inherently imprecise. © 1996 John Wiley & Sons, Inc.

A finite element analysis of flat rolling and application of fuzzy set theory

In this work, a model for steady-state plane strain cold rolling of a strain hardening material is proposed. The mixed pressure and velocity formulation is used and front and back tensions are included in the model. Roll deformation is taken into account by Hitchcock's formula and the friction model of Wanheim and Bay is used. Comparisons with the experimental results found in the literature are made to evaluate the accuracy of the present model. In the rolling process, material properties and friction coefficients are not known precisely and hence they can be treated as fuzzy numbers. Analysis with the fuzzy parameters is carried out to highlight the usefulness of such an analysis. A method to assess the reliability of a design is also proposed.

Fuzzy logic in the formulation of decision functions from linguistic specifications

Focuses on the applications of fuzzy set theory as a tool for the construction of multi‐criteria decision functions from specifications expressed in natural language. Starting with the ability to represent individual criteria satisfactions in terms of membership of fuzzy subsets, shows how different types of linguistic specifications are implemented. Consideration is given to the representation of trade‐offs between criteria, quantifier‐guided aggregations, conditioned criteria and possibilistically qualified criteria.

Application of fuzzy set theory to wave optics

In an attempt to apply the fuzzy set theory to optics a fuzzy entropy [A. De Luca and S. Termini: Inf. Control20 (1972) 301] is used as a measure of optical field concentration in transverse dimensions. Unlike the Shannon's information entropy, the fuzzy entropy is based on a nonprobabilistic concept and therefore can be used for characterizing the strength of classical wave localization.

Application of fuzzy set theory and back-propagation neural networks in progressive die design

Fuzzy set theory is introduced to process the design details of the uncertainty portion of die design and assist the designer in transforming design items with fuzziness into definite and reasonable design attributes. For design parameters in die design that possess intermediate features, fuzzy cluster analysis is used to obtain design attributes. For theoretical or empirical formulas possessing uncertainty coefficients ranges or preference design parameters, the fuzzy weighted average method is adopted to obtain the feature parameters that conform to die design requirements. For the design of uncertain operation stations, such as the installation of an idle station, the linguistic fuzziness or linear membership function is matched with the network recall value and learning pattern through neural network learning, and then the designer can decide whether it is necessary to install such an operation station. Finally, this study establishes an expert system prototype to combine the uncertainty problems in three kinds of die design and help the designer obtain a definite design strategy while faced with uncertain design items.

An application of fuzzy sets in students' evaluation

Existing two systems of evaluation of students' answerscripts (grading method and traditional marking method) are considered, and a better method of evaluation called fem is suggested. Fem is a computer based fuzzy approach where a vector valued marking is used. Finally fem is generalized and the generalized method is called gfem in which a matrix-valued marking is adopted. The paper shows a good and successful application of fuzzy set theory initiated by Zadeh in 1965.

Application of fuzzy logic control system for reactor feed-water control

On the occasion of the 2nd World Congress of IFSA held in Tokyo in July, 1987, a small meeting was convened by Prof. Nishiwaki, Ex-deputy director of the Division of Nuclear Safety and Environmental Protection of IAEA, to discuss possible application of fuzzy set theory and fuzzy logic control in nuclear plants. This paper describes successful actual application of fuzzy logic control system (FLCS) to the feed-water control system of the 165 MWe Fugen Advanced Thermal Reactor (ATR). Fugen is a heavy-water moderated, light-water cooled reactor. The introduction of fuzzy logic control system (FLCS) has enabled operators to more effectively control the steam drum water level as compared with a conventional proportional-integral (PI) control system.

Oligopoly and behavioral uncertainty: An application of fuzzy set theory

This paper provides a brief sketch of fuzzy mathematics. It employs this relatively new mathematical tool to define and describe oligopoly markets and to quantitatively establish the impacts of uncertainty on the decision making that is intrinsic to oligopolistic industries. It illustrates how the technique would be used, for example, by applying fuzzy mathematics to the Herfindahl-Hirschman Index.

Liquefaction Susceptibility Evaluation Using Fuzzy Sets

Liquefaction susceptibility is the measure of a soil’s ability to liquefy during earthquakes. Conventionally, liquefaction susceptibility is determined from soil properties and a subjective knowledge of the geologic conditions. There are many uncertainties in this approach because of the subjectivity in evaluating many important factors. An expert is required if the evaluation is to be performed with confidence. The application of fuzzy set theory is proposed to improve this process. The intent was to develop a method of evaluating liquefaction susceptibility that included factors usually evaluated only by an expert. The method could then be used by engineers with little experience with liquefaction. This new approach incorporates expert opinion of the importance of the subjective factors known to affect liquefaction. The engineer inputs the soil profile using linguistic descriptions which are then processed using the theory of fuzzy sets. The resulting fuzzy sets are interpreted by defining the Fuzzy Liquefaction Susceptibility Index ( FLSI ) , a number which can be plotted and contoured to produce a map of liquefaction susceptibility. The new approach was tested by mapping the liquefaction susceptibility of Charleston, South Carolina, and comparing with other published results generated from conventional analysis. The results were quite comparable, indicating the potential for the new method to evaluate liquefaction susceptibility. The new technique is useful in creating maps of relative liquefaction hazard that can be used in municipal planning.

An application of fuzzy set theory for an electronic video camera image stabilizer

An electronic video camera image stabilizer has been developed which eliminates a substantial part of the image instability caused by the involuntary movement of camera holders. For the discrimination between image movement caused by unstable hand-holding and that of moving objects, fuzzy set theory is applied through the following process: 1) dividing the image taken by the camera into four regions, 2) providing two signals to discriminate between the causes of image instability, 3) evaluating these two discriminating signals after they are transformed into reliability values by membership functions, and 4) tuning the membership functions using a simplex method. This image stabilizer has been incorporated into a new compact video camera, and its substantially improved field performance has been confirmed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An index of applicability for the decomposition method of multivariable fuzzy systems

Research on the application of fuzzy set theory to the design of control systems has led to interest in decomposition of multivariable fuzzy systems. Decomposition of multivariable control rules is preferable since it alleviates the complexity of the problem, but the inference error is inevitable because of its approximate nature. In this paper we show that a large inference error is generated when the Gupta's decomposition method (1986) is applied to Exclusive-nor (ENOR) gate model which is used as a counter example. We define an index of applicability which can classify whether the decomposition method can be applied to a multivariable fuzzy system or not.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Overview and literature survey of fuzzy set theory in power systems

Increasing interest has been seen in applying fuzzy set theory to power systems problems from the number of publications on this topic. As a relatively new research topic a need is felt to pay more attention to the understanding of the basic principles of the theory and the identification of problems suitable for solving by this method. This paper presents a survey of publications on applications of fuzzy set theory to power systems and the basic procedures for fuzzy set based methods to solve specific power systems problems. Simple numerical examples are used to show the practical procedures of problem formulation and solution. Theses examples are: generator maintenance scheduling, dynamic programming, and power system stabiliser. >

An application of fuzzy set theory to differentiating the effectiveness of drugs in treatment of inflammation of genital organs

Abstract This paper is an attempt to apply fuzzy set theory to differentiate the effectiveness of action of drugs in a group of patients. The method presented here should give an answer to the question whether it is possible to find the degree of effectiveness of the drug on some determined symptoms which are characteristics of a sample of patients. It can be concluded that the final (minimal and maximal) level of drug action, found theoretically, does not change even if the patients take the drugs for a long time. Such a conclusion is a result of finding eigen-fuzzy sets associated with given fuzzy relations where the basic operation is a max-min composition of them. The theoretical model was tested in a group of women with trichomoniasis. Three drugs (metronidazole, tinidazole, ornidazole) were taken by the patients and the mathematical results obtained were similar when compared with the physicians' observations.

Fuzzy model for fabricating planar gratings

In this paper a fuzzy model for fabricating planar-grating is given. In the model, the diffraction efficiency of the holographic grating (predicted by computer simulation) has a reasonable match with the experimentally verified results. The method can be summarized in three steps: first, a choice of the grating characteristics, which are closely related to the diffraction efficiency factors, is made; secondly, according to our experience, we construct the fuzzy matrix from the grating manufacturing parameters and the grating characteristics; finally, we use the fuzzy matrix composition to obtain the diffraction efficiency factors. Then, coupled wave theory is used to predict the diffraction efficiency. The comparisons between the results of this fuzzy model and experiments are given. It is found that the application of fuzzy set theory in grating manufacturing reduces the cost of the process and improves the quality of the grating.