Abstract
Activity networks have proved very useful for certain types of project performance evaluations. The purpose of the critical path method (CPM) is to identify the critical activities in the critical path of an activity network. However, the unknowns or vagueness about the time duration for activities in network planning, has led to the development of fuzzy CPM. In this paper, we propose an approach that combines fuzzy mathematics with statistics to solve practical problems in unknown or vague situations. We introduce a fuzzy CPM based on statistical confidence-interval estimates and a signed-distance ranking for (1−α) fuzzy number levels. We not only derive the level (1−α) of fuzzy numbers from (1−α)×100% statistical data confidence-interval estimates, but also use the signed-distance ranking method to define the ordering. The primary result obtained from this study, is a theorem through which the critical path in the fuzzy sense is obtained based on statistical confidence-interval estimates.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. B. Boffey. Graph Theory in Operations Research, The Macmillan Press Ltd., Hong Kong, 1982.
S. Chanas and P. Zielinski. Critical path analysis in the network with fuzzy activity times. Fuzzy Sets and Systems, 122:195-204, 2001.
S. Chanas and J. Kamburowski. The use of fuzzy variables in PERT. Fuzzy Sets and Systems, 5:1-19, 1981.
N. Christofides. Graph Theory an Algorithmic Approach, Academic Press, London, 1975.
I. Gazdik. Fuzzy-Network Planning-FNET. IEEE Transaction on Reliability, R-32(3):304-313, 1983.
P. G. Hoel. Introduction to Mathematical Statistics, John Wiley &; Sons, New York, 1954.
E. Horowitz, S. Sahni, and D. Mehta. Fundamental of Data Structures in C ++, W. H. Freeman and Company, New York, 1995.
A. Kaufmann and M. M. Gupta. Introduction to Fuzzy Arithmetic, Theory and Applications, Van Nostrand Reinhold, New York, 1991.
F. A. Lootsma. Stochastic and fuzzy PERT. European Journal of Operational Research, 43:174-183, 1989.
D. G. Malcolm, J. H. Roseboom, C. E. Clark, and W. Fazar. Application of a technique for research and development program evaluations. Operational Research, 7(5):646-669, 1959.
C. S. McCahon. Using PERT as an approximation of fuzzy project-network analysis. IEEE Transactions on Engineering Management, 40(2):146-153, 1993.
S. H. Nasution. Fuzzy critical path method. IEEE Transactions on Systems, Man, and Cybernetics, 24(1):48-57, 1994.
J. S. Yao and K. M. Wu. Ranking Fuzzy numbers based on decomposition Principle and Signed-distance. Fuzzy Sets and Systems, 116:275-288, 2000.
J. S. Yao and F. T. Lin. Fuzzy critical path method based on signed-distance ranking of fuzzy numbers. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 30(1):76-82, 2000.
H.-J. Zimmermann. Fuzzy Set Theory and Its Applications, 2nd ed., Kluwer Academic Publishers, Boston, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lin, FT., Yao, JS. Fuzzy Critical Path Method Based on Signed-Distance Ranking and Statistical Confidence-Interval Estimates. The Journal of Supercomputing 24, 305–325 (2003). https://doi.org/10.1023/A:1022036931014
Issue Date:
DOI: https://doi.org/10.1023/A:1022036931014