%0 Journal Article
%T An Algorithm for Extracting Intuitionistic Fuzzy Shortest Path in a Graph
%A Siddhartha Sankar Biswas
%A Bashir Alam
%A M. N. Doja
%J Applied Computational Intelligence and Soft Computing
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/970197
%X We consider an intuitionistic fuzzy shortest path problem (IFSPP) in a directed graph where the weights of the links are intuitionistic fuzzy numbers. We develop a method to search for an intuitionistic fuzzy shortest path from a source node to a destination node. We coin the concept of classical Dijkstra¡¯s algorithm which is applicable to graphs with crisp weights and then extend this concept to graphs where the weights of the arcs are intuitionistic fuzzy numbers. It is claimed that the method may play a major role in many application areas of computer science, communication network, transportation systems, and so forth. in particular to those networks for which the link weights (costs) are ill defined. 1. Introduction Graphs [1¨C4] are a very important model of networks. There are many real-life problems of network of transportation, communication, circuit systems, and so forth, which are modeled into graphs and hence solved. Graph theory has wide varieties of applications in several branches of engineering, science, social science, medical science, economics, and so forth, to list a few only out of many. Many real-life situations of communication network, transportation network, and so forth cannot be modeled into crisp graphs because of the reason that few or all of the arcs/links have the cost/weight which is ill defined. The weights of the arcs are not always crisp but intuitionistic fuzzy (or fuzzy). One of the first studies on fuzzy shortest path problem (FSPP) in graphs was done by Dubois and Prade [5] and then by Klein [6]. However, few more solutions to FSPP proposed in [7¨C10] are also interesting. Though the work of Dubois and Prade [5] was a major breakthrough, that paper lacked any practical interpretation even if fuzzy shortest path is found, but still this may not actually be any of the path in the corresponding network for which it was found. There are very few works reported in the literature on finding an intuitionistic fuzzy shortest path in a graph. Mukherjee [11] used a heuristic methodology for solving the IF shortest path problem using the intuitionistic fuzzy hybrid geometric (IFHG) operator, with the philosophy of Dijkstra¡¯s algorithm. In [12], Karunambigai et al. in a team work with Atanassov, present a model based on dynamic programming to find the shortest paths in intuitionistic fuzzy graphs. Nagoor Gani and Mohammed Jabarulla in [13] also developed a method on searching intuitionistic fuzzy shortest path in a network. But all these algorithms have both merits and demerits (none is absolutely the best), as all these are
%U http://www.hindawi.com/journals/acisc/2013/970197/