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In analysing the project network with uncertain activity duration time, stochastic and fuzzy approaches are well known. Stochastic methods such as PERT and GERT are based on too simplified assumptions and does not always give very accurate results. Fuzzy Set Theory is being used more and more frequently for network scheduling because of its simplicity and similarity to human reasoning. The majority of the research in the field of network scheduling using fuzzy set theory is devoted to Fuzzy PERT.
Fuzzy Set Theory:
Fuzzy Set Theory was developed my Zadeh in 1965. The notion central to fuzzy systems is that the truth values (in fuzzy logic) or membership values are indicated by a value in the range [0. ... The concepts of fuzzy sets differ to the conventional crisp sets mainly in the degree by which an object belong to that set. ... On the other hand in the fuzzy set theory, the objects are assigned a member ship value in the range from 0. ...
It is important to point out the distinction between fuzzy system and probability. ... 8 shows the probability of an even to happen is 80% but in fuzzy set theory 0. ...
Mathematically, a crisp set can be defined as:
1, x belongs to A,
χA (x) =
0, x does not belong to A ------ 1
And in the case of fuzzy sets:
0 ≤ μA(x) ≤ 1, for any x Є A ------ 2
Where the truth value μA(x) represents the degree of truth, subjectively designed by human referee, of the statement x belongs to A.
Approximate Word count = 1064
Approximate Pages = 4.3
(250 words per page double spaced)
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