Showing papers on "Fuzzy number published in 1970"

Decision-making in a fuzzy environment

Abstract: By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of alternatives whose boundaries are not sharply defined. An example of a fuzzy constraint is: “The cost of A should not be substantially higher than α,” where α is a specified constant. Similarly, an example of a fuzzy goal is: “x should be in the vicinity of x0,” where x0 is a constant. The italicized words are the sources of fuzziness in these examples. Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value. The use of these concepts is illustrated by examples involving multistage decision processes in which the system under control is either deterministic or stochastic. By using dynamic programming, the determination of a maximizing decision is reduced to the solution of a system of functional equations. A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.

An Algorithm for Detecting Unimodal Fuzzy Sets and Its Application as a Clustering Technique

Abstract: An algorithm is presented which partitions a given sample from a multimodal fuzzy set into unimodal fuzzy sets. It is proven that if certain assumptions are satisfied, then the algorithm will derive the optimal partition in the sense of maximum separation.

Dynamic Programming and Fuzzy Allocation Processes.

Abstract: : The modeling and computational aspects of certain allocation processes are studied through a new concept in systems theory -- fuzzy decision making. The use of these concepts will generally provide models of better proximity to the systems modelled than the traditional deterministic and stochastic approaches. Some concepts of fuzzy systems theory are first introduced. Fuzzy dynamic programming models with their corresponding flow charts are then provided for an allocation problem arising in R and D systems. The computational problems in fuzzy algorithms are discussed. An extensive bibliography on fuzzy decision theory is included. (Author)

Edge Detection By Fuzzy Neural Network

Abstract: In this paper, the edge detection using fuzzy neural network is described. The input features are fuzzy sets and a learning algorithm employs fuzzified delta rule. To increase the efficiency during the training, the varied learning rate and the momentum is applied instead of fixed values. In addition, instead of pixel-based inputs, the texture-based inputs are fed into the fuzzy neural network to facilitate and determine the quality of an edge feature. Experimental results have been tested for the case of both step edges and real world images with noise. The performance of a fuzzy neural network edge detector is compared with the neural network and the traditional techniques such as Sobel, LoG, Gabor function, and relaxation.

A Fuzzy Recurrent Neural Network Of BinaryNeurons For Content Addressable Memory

Abstract: This paper is concerned with a proposal for a recurrent neural network of fuzzy neurons which may be used as a content addressable memory. The behavior of the fuzzy unit in the network is based on fuzzy logic in that each component of the binary input vector to the fuzzy neuron is compared to a number which represents the membership value for a 0 in that position. The results of the comparisons are then combined using a generalized mean function to produce a single number which is compared to a threshold. A training algorithm is developed based on an algorithm for linear inequalities described by Ho and Kashyap in a paper titled “ An Algorithm for Linear Inequalities and its Applications”. The results obtained by simulation of this content addressable memory look promising enough to warrant further investigation.

Adjustment of membership functions, generation and reduction of fuzzy rule base from numerical data

Abstract: In this paper we introduce a new approach for adjustment of membership functions, generation, and reduction of fuzzy rule base from data in the same time. The proposed approach consists of five steps: First, generate fuzzy rules from data using Mendel & Wang Method introduced in [1]. Second, calculate the degree of similarity between rules. Third, measure the distance between the numerical values which induces similar rules. Four, if the distance is greater than base value then merge membership functions. Finally, regenerate rules from data with new fuzzy sets. This approach is applied to truck backer-upper control and Liver trauma diagnostic. A comparative study with a simple Mendel Wang method shows the advantages of the developed approach.