Topic
Membership function
About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.
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TL;DR: Two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described, under the restrictive assumption that for any x in X, the membership function of Rχ has a ‘complementary function’.
145 citations
TL;DR: A laser computer output microfilmer wherein vertical and horizontal misalignment errors between the superimposed data character images and a format slide image are electrically corrected by appropriately incrementing or decrementing the presetting inputs of respective vertical andizontal counters pulsed by line scan synchronizing and clock signals.
145 citations
TL;DR: The proposed fuzzy multiple attributes decision making method is more flexible and more intelligent than Chen and Lee’s method due to the fact that it not only uses interval type-2 fuzzy sets, but also considers the decision-maker's attitude towards risks.
144 citations
TL;DR: It turns out that clear decisions can be made outside a certain interval which is determined by the characterizing function of the fuzzy p-values.
Abstract: Statistical hypothesis testing is very important for finding decisions in practical problems. Usually, the underlying data are assumed to be precise numbers, but it is much more realistic in general to consider fuzzy values which are non-precise numbers. In this case the test statistic will also yield a non-precise number. This article presents an approach for statistical testing at the basis of fuzzy values by introducing the fuzzy p-value. It turns out that clear decisions can be made outside a certain interval which is determined by the characterizing function of the fuzzy p-values.
144 citations
TL;DR: The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation.
Abstract: In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. The paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neuro-fuzzy systems, and genetic algorithms.
144 citations