Shortest paths in fuzzy weighted graphs

The task of finding shortest paths in weighted graphs is one of the archetypical problems encountered in the domain of combinatorial optimization and has been studied intensively over the past five decades. More recently, fuzzy weighted graphs, along with generalizations of algorithms for finding optimal paths within them, have emerged as an adequate modeling tool for prohibitively complex and/or inherently imprecise systems. We review and formalize these algorithms, paying special attention to the ranking methods used for path comparison. We show which criteria must be met for algorithm correctness and present an efficient method, based on defuzzification of fuzzy weights, for finding optimal paths. © 2004 Wiley Periodicals, Inc.