We introduce three important concepts of fuzzy complex numbers, fuzzy distance and fuzzy limit of fuzzy complex numbers, and give some elementary properties of the fuzzy complex numbers and fuzzy distance and fuzzy limit of the fuzzy complex numbers. We also discuss some important theorems of fuzzy complex numbers: nested closed rectangles theorem, Cauchy's criterion for convergence, accumulation principle, etc. © 1992.
Guang-Quan, Z 1992, 'The structural characteristics of the fuzzy number-valued fuzzy measure on the fuzzy σ-algebra and their applications', Fuzzy Sets and Systems, vol. 52, no. 1, pp. 69-81.
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In this paper, some structural characteristics of the fuzzy number-valued fuzzy measure on the fuzzy σ-algebra are discussed. On the fuzzy number-valued fuzzy measure space, the concepts of 'almost' and 'pseudo-almost' are introduced, and Riesz's theorem, Lebesgue's theorem and Egoroff's theorem for sequences of fuzzy measurable functions and some convergence theorems for sequences of fuzzy number-valued fuzzy integrals on fuzzy sets are proved by some structural characteristics of the fuzzy number-valued fuzzy measure. © 1992.
ZHANG, GQ 1992, 'FUZZY NUMBER-VALUED FUZZY MEASURE AND FUZZY NUMBER-VALUED FUZZY INTEGRAL ON THE FUZZY SET', FUZZY SETS AND SYSTEMS, vol. 49, no. 3, pp. 357-376.
ZHANG, GQ 1992, 'ON FUZZY NUMBER-VALUED FUZZY MEASURES DEFINED BY FUZZY NUMBER-VALUED FUZZY INTEGRALS .2.', FUZZY SETS AND SYSTEMS, vol. 48, no. 2, pp. 257-265.
ZHANG, GQ 1992, 'ON FUZZY NUMBER-VALUED FUZZY MEASURES DEFINED BY FUZZY NUMBER-VALUED FUZZY INTEGRALS-I', FUZZY SETS AND SYSTEMS, vol. 45, no. 2, pp. 227-237.
The authors propose a real-time supervised structure and parameter learning algorithm for constructing fuzzy neural networks (FNNs) automatically and dynamically. This algorithm combines the backpropagation learning scheme for the parameter learning and a novel fuzzy similarity measure for the structure learning. The fuzzy similarity measure is a new tool to determine the degree to which two fuzzy sets are equal. The FNN is a feedforward multi-layered network which integrates the basic elements and functions of a traditional fuzzy logic controller into a connectionist structure which has distributed learning abilities. The structure learning decides the proper connection types and the number of hidden units which represent fuzzy logic rules and the number of fuzzy partitions. The parameter learning adjusts the node and link parameters which represent the membership functions. The proposed supervised learning algorithm provides an efficient way for constructing a FNN in real time. Simulation results are presented to illustrate the performance and applicability of the proposed learning algorithm.