By Zhigeng Fang, Hengwu Wei, Baohua Yang, Sifeng Liu, Ye Chen (auth.), Sifeng Liu, Jeffrey Yi-Lin Forrest (eds.)
This booklet comprises contributions via the various top researchers within the quarter of gray structures concept and functions. the entire papers incorporated during this quantity are chosen from the contributions bodily offered on the 2009 IEEE overseas convention on gray structures and clever prone, November eleven – 12, 2009, Nanjing, Jiangsu, People’s Republic of China. This occasion was once together subsidized through IEEE structures, guy, and Cybernetics Society, typical technology beginning of China, and gray structures Society of China. also, Nanjing collage of Aeronautics and Astronautics additionally invested seriously during this occasion with its direct and oblique monetary and administrative supports.
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Extra resources for Advances in Grey Systems Research
1) ( i , j )∈ p 3 The Grey Network and the Critical Path The grey network GN ( A, V ) has the same configuration as the certain net- work G ( A, V ) ; the dissimilarity is the network activity times are grey numbers t ± (i, j ) . In GN ( A, V ) , since the network activity times are grey numbers, ± − + the network total duration is also a grey number. e. 2) ( i , j )∈ p T + = max p∈P ( n ) ∑t ∑t + ( i , j )∈ p GN ( A, V ) has the following properties: Theorem 1. In grey network GN ( A, V ) , let Tα ij be the total duration of the The grey network network schedule.
T − ( p ∗ ) + α [t + ( p ∗ ) − t − ( p ∗ )] ≤ t − ( p) + α [t + ( p) − t − ( p)] . Therefore t ( p ∗ ) = min tα± ( p) . Because Since path α α≥β , we have p∈P ( n ) is a deterministic number for a given t , from Definition 4, the length of p ∗ is a minimum in all the whitening values tα± ( p ) . Therefore, path p ∗ is a critical path. For uncertain problems, if the objective is to solve for the maximum, people’s preference in many cases is to follow two aspects. One is the upper objective value, while the other one is lesser uncertainty.
One is the upper objective value, while the other one is lesser uncertainty. They stand for similarly expectation and variance in terms of the concepts of probability theory. Thus we give the following definitions. Definition 9. 8) 1 + T + +T− [T + T − ] 2 Definition 10. 10) (T + − T − ) 2 Definition 11. 11) p∈P ( n ) ~ ~ ( p ) denotes the expectation of a decision-maker and d ( p ) denotes where m variance of a decision-maker. They reflect objective demands of a decision-maker, and F ( p, t ) reflects subjective demands of a decision-maker.
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