Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: A systematic investigation of the cardinality of a fuzzy set is performed which unifies and improves previous attempts and the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized.
187 citations
TL;DR: This paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict-feedback nonlinear systems with time delays and unknown virtual control coefficients, and the adaptive fuzzy tracking controller is designed by using the backstepping technique and Lyapunov-Krasovskii functionals.
187 citations
TL;DR: A vector similarity measure (VSM) is proposed for IT2 FSs, whose two elements measure the similarity in shape and proximity, respectively, which shows that the VSM gives more reasonable results than all other existing similarity measures for IT1 FSs for the linguistic approximation problem.
187 citations
TL;DR: This paper first describes the change values of Pythagorean fuzzy numbers (PFNs), which are the basic components of PFSs, when considering them as variables, and divides all the changevalues into the eight regions by using the basic operations of PFNs.
Abstract: In practical decision-making processes, we can utilize various types of fuzzy sets to express the uncertain and ambiguous information. However, we may encounter such the situations: the sum of the support membership degree and the against nonmembership degree to which an alternative satisfies a criterion provided by the decision maker may be bigger than 1 but their square sum is equal to or less than 1. The Pythagorean fuzzy sets PFS, as the generalization of the fuzzy sets, can be used to effectively deal with this issue. Therefore, to enrich the theory of PFS, it is very necessary to investigate the fundamental properties of Pythagorean fuzzy information. In this paper, we first describe the change values of Pythagorean fuzzy numbers PFNs, which are the basic components of PFSs, when considering them as variables. Then we divide all the change values into the eight regions by using the basic operations of PFNs. Finally, we develop several Pythagorean fuzzy functions and study their fundamental properties such as continuity, derivability, and differentiability in detail.
186 citations
TL;DR: Experimental results show that the proposed SVFNN for pattern classification can achieve good classification performance with drastically reduced number of fuzzy kernel functions.
Abstract: Fuzzy neural networks (FNNs) for pattern classification usually use the backpropagation or C-cluster type learning algorithms to learn the parameters of the fuzzy rules and membership functions from the training data. However, such kinds of learning algorithms usually cannot minimize the empirical risk (training error) and expected risk (testing error) simultaneously, and thus cannot reach a good classification performance in the testing phase. To tackle this drawback, a support-vector-based fuzzy neural network (SVFNN) is proposed for pattern classification in this paper. The SVFNN combines the superior classification power of support vector machine (SVM) in high dimensional data spaces and the efficient human-like reasoning of FNN in handling uncertainty information. A learning algorithm consisting of three learning phases is developed to construct the SVFNN and train its parameters. In the first phase, the fuzzy rules and membership functions are automatically determined by the clustering principle. In the second phase, the parameters of FNN are calculated by the SVM with the proposed adaptive fuzzy kernel function. In the third phase, the relevant fuzzy rules are selected by the proposed reducing fuzzy rule method. To investigate the effectiveness of the proposed SVFNN classification, it is applied to the Iris, Vehicle, Dna, Satimage, Ijcnn1 datasets from the UCI Repository, Statlog collection and IJCNN challenge 2001, respectively. Experimental results show that the proposed SVFNN for pattern classification can achieve good classification performance with drastically reduced number of fuzzy kernel functions.
186 citations