Title :
On shortest paths in free spaces including obstacles with fuzzy boundaries
Author :
Saito, Seiji ; Ishii, Hiroaki ; Yeh, Kuang-Yih ; Hsia, Hao-Ching
Author_Institution :
Dept. of Sci. & Eng., Doshisha Univ., Kyotanabe
Abstract :
In this paper we introduce definitions of norms and gauges in linear spaces in order to find shortest paths in free spaces with obstacles. Secondly, Euler-Lagrange equations in the calculus of variation give the optimal solutions for the problems of shortest paths. Thirdly we consider a linear structure in a sets of fuzzy numbers and also introduce norms in fuzzy linear spaces. Finally we discuss shortest paths in free spaces including obstacles, with fuzzy boundaries. It is useful in finding shortest paths in realistic environment with natural damage, for example, earthquakes etc.
Keywords :
fuzzy set theory; graph theory; optimisation; variational techniques; Euler-Lagrange equations; free spaces; fuzzy boundaries; fuzzy linear spaces; fuzzy numbers; fuzzy set theory; fuzzy shortest path problem; optimisation; variational calculus; Bismuth; Calculus; Earthquakes; Equations; Fuzzy sets; Urban planning;
Conference_Titel :
Fuzzy Information Processing Society, 2008. NAFIPS 2008. Annual Meeting of the North American
Conference_Location :
New York City, NY
Print_ISBN :
978-1-4244-2351-4
Electronic_ISBN :
978-1-4244-2352-1
DOI :
10.1109/NAFIPS.2008.4531289
