By Bernd Reusch
This e-book constitutes the refereed complaints of the ninth Dortmund Fuzzy Days, held in Dortmund, Germany, 2006. the bushy Days convention has verified itself as a world discussion board for the dialogue of recent ends up in the sphere of Computational Intelligence. all of the papers needed to suffer an intensive evaluate making certain a high-quality caliber of the programme. The papers are dedicated to foundational and useful matters in fuzzy structures, neural networks, evolutionary algorithms, and computing device studying and hence conceal the full variety of computational intelligence.
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Extra resources for Computational Intelligence, Theory and Applications: International Conference 9th Fuzzy Days in Dortmund, Germany, Sept. 18-20, 2006 Proceedings
The summarizers S and qualiﬁers P refer to features of either individuals or options and linguistic terms expressing degrees of preferences, importance of individuals, and relevance of options. First, the summarized objects Y may be identiﬁed with the individuals E, and their attributes A are preference degrees for particular pairs of options as well as their importance degrees. Then, the summaries of the following type may be useful and helpful for running a consensus reaching session: Most individuals deﬁnitely prefer o1 to o2 , moderately prefer o3 to o4 , .
Pakes  considered patents as options. Siegel et al.  discussed the option valuation of oﬀshore oil properties. Majd and Pindyck  analyzed the optimal time and computed the option value of building operations in investment decisions. A fundamental book on managerial ﬂexibility and strategy in resource allocation, written by Trigeorgis , presented a theory of real options. Abel et al.  discussed a theory of option valuation of real capital and investments. Faulkner  discussed the application of real options to the valuation of R&D projects at Kodak.
Of course, this decision rule has to be reapplied each time when new information arrives during the deferral period to see how the optimal investment strategy changes in light of the new information. From a real option perspective, it can be worthwhile to undertake R&D investments with a negative net present value (NPV), when early investment can provide information about future beneﬁts or losses of the whole investment program. 3 A Hybrid Approach to Real Option Valuation A fuzzy set A˜ on the real line R is called a trapezoidal fuzzy number with core [a, b], left width α ≥ 0 and right width β ≥ 0, if its membership function is of the following form: ⎧ a−t ⎪ ⎪ 1− if a − α < t < a, ⎪ ⎪ ⎪ α ⎪ ⎪ ⎨1 if a ≤ t ≤ b, ˜ = A(t) ⎪ ⎪ ⎪ 1 − t − b if b < t < b + β, ⎪ ⎪ ⎪ β ⎪ ⎩ 0 otherwise, and we use the notation A˜ = (a, b, α, β).