Showing papers on "Membership function published in 1991"

Fuzzy min-max neural networks

Abstract: A supervised neural network classifier using a combination of min-max hyperboxes and fuzzy logic is described A min-max hyperbox and its membership function define a fuzzy set Each class in the neural network is a collection of labeled hyperboxes (fuzzy sets) The degree to which an input pattern belongs to a class is determined by the membership function of the winning hyperbox Using multiple hyperbox fuzzy sets to form classes allows arbitrary numbers and shapes of classes and their respective class boundaries The min-max classification learning procedure requires only a single pass through the data and allows online learning The author describes how the fuzzy min-max classifier is implemented as a neural network, explains how min-max classes are produced, and provides two examples of operation >

Design of a cart-pole balancing fuzzy logic controller using a genetic algorithm

Abstract: Scientists at the U.S. Bureau of Mines are currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic affords a mechanism for incorporating the uncertainty inherent in most control problems into conventional expert systems. Although fuzzy logic-based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective and time consuming decision. In this paper, high-performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating a cart-pole balancing system are selected using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions chosen by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the author for the cart-pole balancing problem. Thus, genetic algorithms represent a potentially effective and structured approach for designing fuzzy logic controllers.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Fuzzy control system

Abstract: Disclosed is a fuzzy control system which calculates a membership function concerning a control value of a to-be-controlled object through a fuzzy inference operation in accordance with an input value from the to-be-controlled object and a control rule, and determines the control value from the membership function to control the to-be-controlled object. This fuzzy control system has a plurality of internal states respectively expressed by a plurality of membership functions in addition to the input value and the control value, determines the state of the to-be-controlled object using a rule for evaluating the input value, alters the internal state by fuzzy inference, stores a decision result as a new internal state, and determines the control value of the to-be-controlled object through fuzzy inference from the new internal state and the input value.

Fuzzy set representation of neural network classification boundaries

Abstract: In neural network classification techniques, the uncertainty of a new observation belonging to a particular class is difficult to express in statistical terms. On the other hand, statistical classification techniques are also poor for supplying uncertainty information for new observations. The use of fuzzy sets is a promising approach to providing imprecise class membership information. The monotonic function neural network is a tool that can be used to develop fuzzy membership functions. This research suggests that a multiarchitecture monotonic function neural network can be used for fuzzy set representation of classification boundaries in monotonic pattern recognition. >

Fuzzy control apparatus generating a plurality of membership functions for determining a drive condition of an electric vacuum cleaner

Abstract: A control apparatus of an electrical appliance comprising a sensor for detecting a physical amount; and a fuzzy inferring device for determining the drive condition of a load by fuzzy inference based on a signal outputted from the sensor, and wherein the sensor has at least one normalized membership function to be used by fuzzy inference and achieves a plurality of membership functions which can be expressed by congruent curves by performing a predetermined subtraction or an addition on the signal outputted from the sensor.

Fuzzy choice functions

Abstract: The R-greatest and maximal sets of standard choice theory are extended to fuzzy R-greatest and fuzzy maximal sets. Unlike the precise counterparts of these concepts, these two sets do not in general coincide when preferences are reflexive and connected. A stronger than usual version of connectedness under which the two sets are equal is provided. The concept of a fuzzy choice function is introduced and conditions under which a fuzzy choice function may be rationalized as a fuzzy R-greatest or a fuzzy maximal set are discussed. Rationalizability with transitive and weakly transitive fuzzy preference relations is also considered.

Fuzzy information processing by the Monte Carlo simulation technique

Abstract: This paper presents a new method utilizing the Monte Carlo simulation technique for processing fuzzy information. The method was primarily developed for determining the weighted average of a group of ratings that are represented by fuzzy subsets. By generating a uniform random number, normalizing it with respect to the maximum functional value of the cumulative membership function, and then equating the normalized uniform random number to the cumulative function F(x), a value x can be back-calculated for each fuzzy subset. The resulting value x is a random number representing that fuzzy subset. The weighted average was then calculated with these random numbers. The first through fourth moment parameters were obtained and used to fit the random values of the weighted average with a beta distribution. By normalizing the curve-fitted beta distribution function with respect to its maximum functional value, the membership function of the final fuzzy subset was obtained. Comparison is made between the ...

A Practical Approach to Nonlinear Fuzzy Regression

Abstract: This paper presents a new method of mathematical modeling in an uncertain environment. The uncertainties of data and model are treated using concepts of fuzzy set theory. The model fitting principle is the minimization of a least squares objective function. A practical modeling procedure is obtained by restricting the type of data and parameter fuzziness to conical membership functions. Under this restriction, the model fitting problem can be solved numerically with the aid of any least squares software for regression with implicit constraint equations. The paper contains a short discussion of the geometry of fuzzy point and function spaces with conical membership functions, and illustrates the application of fuzzy regression with an example from terminal ballistics.

Control parameter tuning unit and a method of tuning parameters for a control unit

Abstract: A fuzzy control unit includes a fuzzy inference unit forming a manipulated variable for controlling a plant such that a control response from the plant is made equal to a previously set target value, based on fuzzy control knowledge. An automatic tuning unit corrects the fuzzy control rules in accordance with the control response from the plant. The automatic tuning unit includes a response waveform memory storing a control response value from the plant, a rule grade memory for storing grade values of the fuzzy control rules for the control response from the plant, an ideal waveform memory for storing ideal control response values to be attained by the plant under control by the fuzzy control unit, and a control evaluating circuit evaluating the control operation of the fuzzy control unit based on the ideal response value and the control response value. The automatic tuning unit also includes a circuit for correcting a membership function of a consequent portion of the fuzzy control rules in accordance with the amount of correction and the rule grade.

Bridge condition assessment using fuzzy weighted averages

Abstract: This paper describes a bridge condition assessment model that is based upon the simplification of a computational technique called resolution identity of fuzzy sets. The proposed model utilizes a fuzzy weighted average to combine fuzzy bridge condition ratings. The procedure is based on the decomposition of fuzzy sets into non-fuzzy level-sets or intervals. The utility and effectiveness of this procedure are illustrated with an example of the bridge condition assessment problem.

An exponential membership function for fuzzy multiple objective linear programming

Abstract: The operator “min” is one of the most frequently used aggregation operators in fuzzy decision. However, this operator is the softest operator and no allowance is made for any compensation. The “product” and other operators, some of them may be compensatory, are seldom used because of the nonlinearity of the resulting problem. In this paper, an exponential, instead of linear membership function is proposed. The advantages of using exponential membership are two fold. First, the resulting problems can be transformed to linear ones when the “product” and several other nonlinear aggregate operators are used. Secondly, exponential representation is more realistic than the linear ones usually used for some practical applications.

A decision support system for robot selection

Abstract: This paper presents a decision support robot selection system which applies the fuzzy set method to this multicriteria decision making problem. The objective robot attributes are evaluated via marginal value functions while the subjective robot attributes are evaluated via fuzzy set membership function. Data from both evaluations are finally processed such that a fuzzy set decision vector is obtained. Viewpoints of several members of a decision making body are integrated. Sensitivity analysis has shown that final choices can be varied when the weight assignments are changed.

Method and system for evaluating and modifying fuzzy knowledge

Abstract: A fuzzy evaluation and modification system evaluates and modifies the fuzzy knowledge in a fuzzy reasoning system. The fuzzy knowledge includes fuzzy rules, each described in an "if . . . , then . . ." format, and membership functions defining meanings of propositions described in the "if . . . , then" parts. Results of the fuzzy reasoning are monitored and compared with real data of a plurality of real test cases to evaluate the fuzzy knowledge. An influence power of each of the fuzzy rules with respect to the fuzzy reasoning results is attained for all the cases. Superpositional display of real data on the membership functions of the "if . . ." part and reasoning results on the membership functions of the "then . . ." part indicates a relationship between the membership function and the real data. The system includes units for obtaining a grade of rule representing adequacy of the fuzzy rule based on the membership functions associated with the "if" part, attaining defuzzification values of the membership functions related to the "then" part and obtaining differences between the defuzzification values and the real data. A relationship between the grade of rule and the difference thus obtained between the defuzzification values and the real data is outputted to an output unit. The fuzzy knowledge is modified by an operator in association with the output.