Ingénierie et gestion industrielles

Shortest Path Problem under Fuzziness

Abstract

Luhandjula MK and Strydom MC

The shortest path problem plays a paramount role in a wide spectrum of domains including transportation, communication and networking. The "primum movens" of this paper is to propose a novel approach for solving the shortest path problem with fuzzy parameters. Two key issues need to be addressed in a way to handle the fuzzy path problem. One is how to determine the sum of two edges. The other is how to compare the lengths of two different paths given that the length of each edge is represented by fuzzy numbers.

To solve these problems we resort to the notions of "nearest interval approximation" and average of a fuzzy number.An assessment of our approach, in comparison with extant ones is also provided. A Numerical example is given for the sake of illustration.