Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities

Abstract: A possibility measure can encode a family of probability measures. This fact is the basis for a transformation of a probability distribution into a possibility distribution that generalises the notion of best interval substitute to a probability distribution with prescribed confidence. This paper describes new properties of this transformation, by relating it with the well-known probability inequalities of Bienayme-Chebychev and Camp-Meidel. The paper also provides a justification of symmetric triangular fuzzy numbers in the spirit of such inequalities. It shows that the cuts of such a triangular fuzzy number contains the “confidence intervals” of any symmetric probability distribution with the same mode and support. This result is also the basis of a fuzzy approach to the representation of uncertainty in measurement. It consists in representing measurements by a family of nested intervals with various confidence levels. From the operational point of view, the proposed representation is compatible with the recommendations of the ISO Guide for the expression of uncertainty in physical measurement.

Fuzzy sets and applications : selected papers

Abstract: Coping with the Imprecision of the Real World: An Interview with L.A Zadeh Fuzzy Sets Probability Measures of Fuzzy Events Decision Making in a Fuzzy Environment Similarity Relations and Fuzzy Orderings Outline of a New Approach to the Analysis of Complex Systems and Decision Processes A Fuzzy-Algorithmic Approach to the Definition of Complex or Imprecise Comcepts Fuzzy Sets as a Basis for a Theory of Possibility The Concept of a Linguistic Variable and Its Application to Approximate Reasoning (Part 1) The Concept of a Linguistic Variable and Its Application to Approximate Reasoning (Part 2) The Concept of a Linguistic Variable and Its Application to Approximate Reasoning (Part 3) A Theory of Approximate Reasoning The Role of Fuzzy Logic in the Management of Uncertainty in Expert Systems Syllogistic Reasoning in Fuzzy Logic and its Application to Usuality and Reasoning with Dispositions A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges PRUF-A Meaning Representation Language for Natural Languages A Computational Approach to Fuzzy Quantifiers in Natural Language A Theory of Commonsense Knowledge Test-Score Semantics as a Basis for a Computational Approach to the Representation of Meaning.

Fuzzy min-max neural networks - Part 2: Clustering

Abstract: In an earlier companion paper (56) a supervised learning neural network pattern classifier called the fuzzy min- max classification neural network was described. In this sequel, the unsupervised learning pattern clustering sibling called the fuzzy min-max clustering neural network is presented. Pattern clusters are implemented here as fuzzy sets using a membership function with a hyperbox core that is constructed from a min point and a max point. The min-max points are determined using the fuzzy min-max learning algorithm, an expansion-contraction process that refines the author's earlier Fuzzy Adaptive Reso- nance Theory neural network (50). The fuzzy min-max clustering neural network stabilizes into pattern clusters in only a few passes through a data set; it can be reduced to hard cluster boundaries that are easily examined without sacrificing the fuzzy boundaries; it provides the ability to incorporate new data and add new clusters without retraining; and it inherently provides degree of membership information that is extremely useful in higher level decision making and information processing. This paper will provide some background concerning the development of the fuzzy min-max clustering neural network and provide a comparison with similar work that has recently emerged. A brief description of fuzzy sets, pattern clustering, and their synergistic combination is presented. The fuzzy min- max clustering neural network will be explained in detail and examples of its clustering performance will be given. The paper will conclude with a description of problems that need to be addressed and a list of some potential applications.