Fuzzy Network Flow Problems

By : S.U. Malini , Felbin C. Kennedy

Page No: 1-21

Abstract
The concept of octagonal fuzzy numbers was introduced by the authors in an earlier paper [14]. In this paper, solution to network flow problems using octagonal fuzzy numbers are dealt with. viz, finding the shortest path of the network and project completion time. These problems were dealt with by several authors under different circumstances for different types of fuzzy numbers (to cite a few, [2],[3],[6],[7],[10]). In this paper the duration of activities are defined by octagonal fuzzy numbers which are more realistic and general in nature. Ranking using ?–cut [14] is used to compare octagonal fuzzy numbers. An algorithm is proposed to find fuzzy shortest path and fuzzy critical path of a project. Fuzzy shortest path, fuzzy critical path, fuzzy project completion time, fuzzy earliest start time, fuzzy earliest finish time, fuzzy latest start time, fuzzy latest finish time and fuzzy slack time for all activities are obtained as octagonal fuzzy numbers that captures the problem in a more realistic way.

Authors :
Felbin C. Kennedy : Associate Professor, Department of Mathematics, Stella Maris College (Autonomous), Chennai, Tamilnadu, India.
S.U. Malini : Research Scholar, Department of Mathematics, Stella Maris College Faculty, D.G. Vaishnav College, Chennai, Tamilnadu, India