www.iaset.us editor@iaset.us AN ALGORITHMIC APPROACH FOR SHORTEST PATH PROBLEM BY POSSIBILITY MEASURE WITH TYPE-2 FUZZY NUMBER V. ANUSUYA 1 & R. SATHYA 2 1 PG and Research Department of Mathematics, Seethalakshmi Ramaswami College, Tiruchirappalli, TamilNadu, India 2 Department of Mathematics, K.S. Rangasamy College of Arts & Science, Tiruchengode, TamilNadu, India ABSTRACT Type-2 fuzzy sets are a generalization of the ordinary sets in which each type-2 fuzzy set is characterized by a fuzzy membership function. In this paper we proposed an algorithm for finding shortest path and shortest path length using possibility measure based on extension principle. In a network each edge have been assigned as discrete type-2 fuzzy number. KEYWORDS: Type-2 Fuzzy Number Possibility Measure Discrete Type-2 Fuzzy Number Extension Principle 1. INTRODUCTION The shortest path problem concentrates on finding the path with minimum distance to find the shortest path from source node to destination node is a fundamental matter in graph theory. The fuzzy shortest path problem was first analyzed by Dubois and Prade [4]. Okada and Soper [9] developed an algorithm based on the multiple labeling approach, by which a number of non dominated paths can be generated. Type-2 fuzzy set was introduced by Zadeh [13] as an extension of the concept of an ordinary fuzzy set. The type-2 fuzzy logic has gained much attention recently due to its ability to handle uncertainty, and many advances appeared in both theory and applications. In general in a directed acyclic network, crisp values are widely used as the weights on edges, but there are many cases when we cannot determine these weights precisely. In these cases, we can use fuzzy weights instead of crisp weights to express the uncertainty, and type-2 fuzzy weights will be more suitable if this uncertainty varies under some conditions. The concept of fuzzy measures was introduced by sugeno [11], Good surveys of various types of measures subsumed under this broad concept were prepared by Dubois and Prade [3], Bacon[2], and Wierzchon [12]. There were many researches using different approaches, but we will mainly focus on an approach based on possibility theory proposed by Okada[10]. The structure of paper is following: In Section 2, we have some basic concepts required for analysis. Section 3, gives an algorithm to find shortest path and shortest path length with type-2 fuzzy number using possibility measure. Section 4 gives the network terminology. To illustrate the proposed algorithm the numerical example is solved in section 5. Finally in section 6, conclusion i included. International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) ISSN(P): 2319-3972; ISSN(E): 2319-3980 Vol. 4, Issue 1, Jan 2015, 1-10 © IASET