Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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08 Mar 1992
TL;DR: The Stone-Weierstrass theorem is used to prove that fuzzy systems with product inference, centroid defuzzification, and a Gaussian membership function are capable of approximating any real continuous function on a compact set to arbitrary accuracy.
Abstract: The author proves that fuzzy systems are universal approximators. The Stone-Weierstrass theorem is used to prove that fuzzy systems with product inference, centroid defuzzification, and a Gaussian membership function are capable of approximating any real continuous function on a compact set to arbitrary accuracy. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems. >
1,075 citations
TL;DR: It is noted that as q increases the space of acceptable orthopairs increases and thus gives the user more freedom in expressing their belief about membership grade, and introduces a general class of sets called q-rung orthopair fuzzy sets in which the sum of the ${\rm{q}}$th power of the support against is bonded by one.
Abstract: We note that orthopair fuzzy subsets are such that that their membership grades are pairs of values, from the unit interval, one indicating the degree of support for membership in the fuzzy set and the other support against membership. We discuss two examples, Atanassov's classic intuitionistic sets and a second kind of intuitionistic set called Pythagorean. We note that for classic intuitionistic sets the sum of the support for and against is bounded by one, while for the second kind, Pythagorean, the sum of the squares of the support for and against is bounded by one. Here we introduce a general class of these sets called q-rung orthopair fuzzy sets in which the sum of the ${\rm{q}}$ th power of the support for and the ${\rm{q}}$ th power of the support against is bonded by one. We note that as q increases the space of acceptable orthopairs increases and thus gives the user more freedom in expressing their belief about membership grade. We investigate various set operations as well as aggregation operations involving these types of sets.
1,056 citations
TL;DR: The definition of fuzzy time series is given, some properties of fuzzyTime series are explored, and procedures to develop fuzzy timeseries models are discussed.
1,048 citations
TL;DR: It is shown that the proposed representation exists for certain families of the conjugate pairs of t-norms and t-conorms and resolves some of the difficulties associated with particular interpretations of conjunction, disjuntion, and implication in fuzzy set theories.
1,041 citations
TL;DR: A fuzzy neural network model based on the multilayer perceptron, using the backpropagation algorithm, and capable of fuzzy classification of patterns is described, and the results are compared with those of the conventional MLP, the Bayes classifier, and other related models.
Abstract: A fuzzy neural network model based on the multilayer perceptron, using the backpropagation algorithm, and capable of fuzzy classification of patterns is described. The input vector consists of membership values to linguistic properties while the output vector is defined in terms of fuzzy class membership values. This allows efficient modeling of fuzzy uncertain patterns with appropriate weights being assigned to the backpropagated errors depending upon the membership values at the corresponding outputs. During training, the learning rate is gradually decreased in discrete steps until the network converges to a minimum error solution. The effectiveness of the algorithm is demonstrated on a speech recognition problem. The results are compared with those of the conventional MLP, the Bayes classifier, and other related models. >
1,031 citations