fuzzy relational equation

fuzzy relational equation

[¦fəz·ē ri¦lā·shən·əl i′kwā·zhən]
(mathematics)
An equation of the form A · R = B, where A and B are fuzzy sets, R is a fuzzy relation, and A · R stands for the composition of A with R.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Wu, "Minimizing a linear objective function under a max-t-norm fuzzy relational equation constraint," Fuzzy Sets and Systems, vol.
Wu, "Optimizing the geometric programming problem with single-term exponents subject to max-min fuzzy relational equation constraints," Mathematical and Computer Modelling, vol.
Guu, "An efficient procedure for solving a fuzzy relational equation with max-Archimedean t-norm composition," IEEE Transactions on Fuzzy Systems, vol.
Solving a system of fuzzy relational equations is a subject of great scientific interest [1, 2].
Hirota, "Fast solving method of fuzzy relational equation and its application to lossy image compression/reconstruction," IEEE Transactions on Fuzzy Systems, vol.
Solution methods of fuzzy relational equations have been well studied in the literature (cf., e.g., [1-15]) and applied to image processing problems like image compression [16-19] and image reconstruction [7, 8, 20-22].
In a similar way to fuzzy relational equations, when the solution set of problem (1) is not empty, it's in general a non-convex set that can be completely determined by one maximum solution and a finite number of minimal solutions.
For example, these works [22-24] have systematically introduced some theories of fuzzy relational equations. Bourke and Fisher  gave solution algorithms for fuzzy relational equations with max-product composition.
Fisher, "Solution algorithms for fuzzy relational equations with max-product composition," Fuzzy Sets and Systems, vol.
Hirota, "A motion compression/reconstruction method based on max t-norm composite fuzzy relational equations," Information Sciences, vol.
In the Mamdani fuzzy inference methodology, inputs and outputs are represented by fuzzy relational equations in canonical rule-based form.
Hence using the experts opinion for the Fuzzy Relational Equations. The performance that the most of the owners of the street shops choose this as their profession is more profit with reasonable investment and unemployment problem is solved since many owners are from 25 yrs to 35yrs.
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