Critical path analysis in the network with fuzzy activity times.

*(English)*Zbl 1015.90096Summary: A natural generalization of the criticality notion in a network with fuzzy activity times is given. It consists in direct application of the extension principle of Zadeh to the notion of criticality of a path (an activity, an event) treated as a function of the activities duration times in the network. There are shown some relations between the notion of fuzzy criticality, introduced in the paper, and the otion of interval criticality (criticality in the network with interval activity times) proposed by the authors in another paper [Eur. J. Oper. Res. 136, 541-550 (2002; Zbl 1008.90029)]. Two methods of calculation of the path degree of criticality (according to the proposed concept of fuzzy criticality) are presented.

##### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C35 | Programming involving graphs or networks |

03E72 | Theory of fuzzy sets, etc. |

90B10 | Deterministic network models in operations research |

##### Keywords:

decision analysis; fuzzy CPM; fuzzy PERT; critical path; critical path method; fuzzy criticality; interval criticality
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\textit{S. Chanas} and \textit{P. Zieliński}, Fuzzy Sets Syst. 122, No. 2, 195--204 (2001; Zbl 1015.90096)

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##### References:

[1] | J.J. Buckley, Fuzzy PERT, in: G.W. Evans, W. Karwowski, M.R. Wilhelm(Eds.), Applications of Fuzzy Set Methodologies in Industrial Engineering, Elsevier,Amsterdam, 1989,, pp. 103-114. |

[2] | S. Chanas, Fuzzy sets in few classical operational research problems,in: M.M. Gupta, E. Sanchez (Eds,). Approximate Reasoning in Decision Analysis, North-Holland, Amsterdam, 1982,,pp. 351-363. |

[3] | Chanas, S.; Kamburowski, J., The use of fuzzy variables in PERT, Fuzzy sets and systems, 5, 1-19, (1981) · Zbl 0451.90076 |

[4] | S. Chanas, E. Radosiński, A model of activity performance time in the light of fuzzy sets theory, Problemy Organizacji 2 (1976) 68-76 (in Polish). |

[5] | S. Chanas, P. Zieliński, Computational complexity of interval critical path method, European J. Oper. Res., submitted. |

[6] | Chang, I.S.; Tsujimura, Y.; Gen, M.; Tozawa, T., An efficient approach for large scale project planning based on fuzzy delphi method, Fuzzy sets and systems, 76, 277-288, (1995) |

[7] | Dubois, D.; Prade, H., Operations on fuzzy numbers follows, Internat. J. systems sci., 30, 613-626, (1978) · Zbl 0383.94045 |

[8] | Gazdik, I., Fuzzy network planning, IEEE trans. reliability, R-32 3, 304-313, (1983) · Zbl 0526.90053 |

[9] | J. Kamburowski, Fuzzy activity duration times in critical path analyses, International Symposium on Project Management, New Delhi, 1983, pp. 194-199. |

[10] | Kelley, J.E., Critical path planning and scheduling – mathematical basis, Oper. res., 9, 296-320, (1961) · Zbl 0098.12103 |

[11] | Lootsma, F.A., Stochastic and fuzzy PERT, European J. oper. res., 43, 174-183, (1989) · Zbl 0681.90039 |

[12] | Malcolm, D.G.; Roseboom, J.H.; Clark, C.E; Fazar, W., Application of a technique for research and development project evaluation, Oper. res., 7, 646-669, (1959) · Zbl 1255.90070 |

[13] | McCahon, C.S., Using PERT as an approximation of fuzzy project-network analysis, IEEE trans. eng. management, 40, 146-153, (1993) |

[14] | Mon, D.L.; Cheng, C.H.; Lu, H.C., Application of fuzzy distributions on project management, Fuzzy sets and systems, 73, 227-234, (1995) · Zbl 0855.90056 |

[15] | Nasution, S.H., Fuzzy decisions in critical path method, Second IEEE conf. on fuzzy systems, 2, 1069-1073, (1993) |

[16] | Nasution, S.H., Fuzzy critical path method, IEEE trans. systems man cybernet, 24, 48-57, (1994) |

[17] | Negoită, C.V.; Ralescu, D.A., Applications of fuzzy sets to systems analysis, (1975), Birkhäuser Verlag Basel · Zbl 0326.94002 |

[18] | Prade, H., Using fuzzy sets theory in a scheduling problema case study, Fuzzy sets and systems, 2, 153-165, (1979) · Zbl 0403.90036 |

[19] | Rommelfanger, H., Network analysis and information flow in fuzzy environment, Fuzzy sets and systems, 67, 119-128, (1994) |

[20] | Slyeptsov, A.I.; Tyshchuk, T.A., Fuzzy critical path method for project network planning and control, Cybernet. system anal., 3, 158-170, (1997) |

[21] | A.I. Slyeptsov, T.A. Tyshchuk, Synthesis of generalized fuzzy critical path method, Proc. Internat. Conf. ICAD’99. · Zbl 0999.68207 |

[22] | Yao, J.S.; Lin, F.T., Fuzzy critical path method based on signed distance ranking of fuzzy numbers, IEEE trans. syst. man cybernet., 20, 76-82, (2000) |

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