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Zbl 0898.90134
Furukawa, N.
Parametric orders on fuzzy numbers and their roles in fuzzy optimization problems. (English)
[J] Optimization 40, No.2, 171-192 (1997). ISSN 0233-1934; ISSN 1029-4945/e

The paper introduces and studies two types of parametric order relations for the class of symmetric fuzzy numbers defined as $A(x)= \max(0,L((x- m)/\alpha))$. Here $m$ being a modal value of $A$ and $\alpha$ forming a spread of this fuzzy number; furthermore (i) $L(x)= L(- x)$, (ii) $L(x)= 1$ iff $x= 0$, (iii) $L(x)$ is nonincreasing on $[0,\infty)$. It is shown that the proposed order relations introduce a parametric total order. A number of additional properties are also discussed. An application of these order relations is given to the fuzzy shortest route problem (giving rise to a generalized Dijkstra algorithm).
[W.Pedrycz (Edmonton)]

MSC 2000:: *90C70 Fuzzy programming

Keywords: ranking of fuzzy numbers; parametric order; fuzzy shortest route problem; generalized Dijkstra algorithm

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