Annals of Communications in Mathematics

AbstractIn this paper, a new approach is introduced to find the shortest path between two given vertices on interval-valued fuzzy hypergraphs. When only crisp numbers are not sufficient to measure a real world parameter, fuzzy numbers are considered. But, there are many types of fuzzy numbers available in literature. Most useful fuzzy number is trapezoidal fuzzy numbers. Throughout this paper the interval-valued trapezoidal fuzzy number is used as the arc length of the interval-valued fuzzy hypergraph. We have measured similarity between two interval-valued fuzzy numbers to find the shortest path. An algorithm is also designed to find all possible hyperpaths in a hypergraph and calculated its time complexity

AbstractIn this article, the notion of a new kind of derivation is introduced for a lattice L called symmetric bi-(T, F)-derivations on L as a generalization of derivation of lattices and characterized some of its related properties. Some equivalent conditions provided for a lattice L with greatest element 1 by the notion of isotone symmetric bi- (T, F)-derivation on L. By using the concept of isotone derivation, we characterized the modular and distributive lattices by the notion of isotone symmetric bi-(T, F)-derivation