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: In this article, the authors define cl∞-monoids, which are used to measure the degree of membership of points in sets, and define L- or "fuzzy" sets are defined, and suitable collections of these are called L-topological spaces.
247 citations
TL;DR: Experimental results show that better control can be achieved using a type-2 FLC with fewer fuzzy sets/rules so one benefit of type-1 FLC is a lower trade-off between modeling accuracy and interpretability.
246 citations
26 Jun 1994
TL;DR: A new version of ID3 algorithm is proposed to generate an understandable fuzzy decision tree using fuzzy sets defined by a user to be applied to diagnosis for potential transformers by analyzing gas in oil.
Abstract: A popular and particularly efficient method for making a decision tree for classification from symbolic data is ID3 algorithm. Revised algorithms for numerical data have been proposed, some of which divide a numerical range into several intervals or fuzzy intervals. Their decision trees, however, are not easy to understand. We propose a new version of ID3 algorithm to generate an understandable fuzzy decision tree using fuzzy sets defined by a user. We apply it to diagnosis for potential transformers by analyzing gas in oil. >
244 citations
TL;DR: The present work characterizes membership functions by the conditions of sum normalization (SN), nonnegativeness (NN), and normality (NO).
Abstract: Introduces a singular value-based method for reducing a given fuzzy rule set. The method conducts singular value decomposition of the rule consequents and generates certain linear combinations of the original membership functions to form new ones for the reduced set. The present work characterizes membership functions by the conditions of sum normalization (SN), nonnegativeness (NN), and normality (NO). Algorithms to preserve the SN and NN conditions in the new membership functions are presented. Preservation of the NO condition relates to a high-dimensional convex hull problem and is not always feasible in which case a closed-to-NO solution may be sought. The proposed method is applicable regardless of the adopted inference paradigms. With product-sum-gravity inference and singleton support fuzzy rule base, output errors between the full and reduced fuzzy set are bounded by the sum of the discarded singular values. The work discusses three specific applications of fuzzy reduction: fuzzy rule base with singleton support, fuzzy rule base with nonsingleton support (which includes the case of missing rules), and the Takagi-Sugeno-Kang (TSK) model. Numerical examples are presented to illustrate the reduction process.
242 citations
TL;DR: The indicator of the grade of inclusion for interval-valued fuzzy sets is used as an element that selects from the diAerent methods of inference studied, the one that will be executed in each case.
242 citations