• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.10
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• pp.77-85
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• 1993

In this paper, we present a method to solve a convexly combined fuzzy relational equation with generalized connectives. For this, we propose a neural network whose structure represents the fuzzy relational equation. Then we derive a learning algorithm by using the concept of back-propagation learning. Since the proposed method can be used for a general form of fuzzy relational equations, such fuzzy max-min or min-max relational equations can be treated as its special cases. Moreover, the relational structure adopted in the proposed neurocomputational approach can work in a highly parallel manner so that real-time applications of fuzzy sets are possibles as in fuzzy logic controllers, knowledge-based systems, and pattern recognition systems.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.1
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• pp.38-42
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• 2002

A fast iterative solving method of fuzzy relational equation is proposed. It is derived by eliminating a redundant comparison process in the conventional iterative solving method (Pedrycz, 1983). The proposed method is applied to image reconstruction, and confirmed that the computation time is decreased to 1 / 40 with the compression rate of 0.0625. Furthermore, in order to make any initial solution converge on a reconstructed image with a good quality, a new cost function is proposed. Under the condition that the compression rate is 0.0625, it is confirmed that the root mean square error of the proposed method decreases to 27.34% and 86.27% compared with those of the conventional iterative method and a non iterative image reconstruction method, respectively.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.207-220
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• 2004

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idem-potency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.