The shortest path (SP) problem constitutes one of the most prominent topics in graph theory and has practical applications many research areas such as transportation, network communications, emergency services, fire stations to name just a few. In real-world applications, arc weights corresponding SP problems are represented by fuzzy numbers. current paper presents fuzzy-based Ant Colony Optimi...

the importance as well as the difficulty of the problem of ranking fuzzy numbers is pointed out. here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are defined as the middle-point and the spread of each $gamma$-cut of a fuzzy number, respectively. we use the va...

A signed graph is a simple with two types of edges. Switching vertex v corresponds to changing the type each edge incident v. homomorphism from G another H mapping φ:V(G)→V(H) such that, after switching any number vertices G, φ maps every an same in H. The chromatic χs(G) order smallest that there We show triangular grids at most 10 and hexagonal 4.