论文信息 - Unattainable solutions of a fuzzy relation equation

Unattainable solutions of a fuzzy relation equation

In a fuzzy relation equation, the properties of the solution set have been investigated especially when the basic spaces are all finite sets. However, when the basic spaces are infinite, a few properties are known. In this paper, we use the concepts of attainability and unattainability of a solution to clarify some properties of the solution set and show the condition for existence of a partially attainable solution and an unattainable one.

Hideyuki Imai | Masaaki Miyakoshi | Ken Kikuchi

[1] G. Klir,et al. Resolution of finite fuzzy relation equations , 1984 .

[2] Hung T. Nguyen,et al. A note on the extension principle for fuzzy sets , 1978 .

[3] M. Wagenknecht,et al. On the existence of minimal solutions for fuzzy equations with tolerances , 1990 .

[4] M. Miyakoshi,et al. Sets of solution-set equivalent coefficient matrices of fuzzy relation equations , 1990 .

[5] M. Miyakoshi,et al. Sets of solution-set-invariant coefficient matrices of simple fuzzy relation equations , 1987 .

[6] Luo Cheng-Zhong. Reachable solution set of a fuzzy relation equation , 1984 .

[7] Elie Sanchez,et al. Resolution of Composite Fuzzy Relation Equations , 1976, Inf. Control..

[8] Hideyuki Imai,et al. Some properties of minimal solutions for a fuzzy relation equation , 1997, Fuzzy Sets Syst..