# Credibilistic Programming: An Introduction to Models and Applications (Uncertainty and Operations Research)

Language: English

Pages: 144

ISBN: 364236375X

Format: PDF / Kindle (mobi) / ePub

It provides fuzzy programming approach to solve real-life decision problems in fuzzy environment. Within the framework of credibility theory, it provides a self-contained, comprehensive and up-to-date presentation of fuzzy programming models, algorithms and applications in portfolio analysis.

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. . . . . . . . . . . . . . . . . . . . . . . . 45 45 61 62 65 70 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii viii Contents 4 Chance-Constrained Programming Model . . 4.1 Optimistic Value . . . . . . . . . . . . . . 4.2 Pessimistic Value . . . . . . . . . . . . . 4.3 Chance-Constrained.

(α) = b. In general, the α-pessimistic value for an equipossible fuzzy variable is ξinf (α) = a, if α ≤ 0.5 b, if α > 0.5 which is shown by Fig. 4.10. Example 4.11 Let ξ = (a, b, c) be a triangular fuzzy credibility inversion theorem that ⎧ 0, ⎪ ⎪ ⎪ ⎨ (r − a)/2(b − a), Cr{ξ ≤ r} = ⎪ (c − 2b + r)/2(c − b), ⎪ ⎪ ⎩ 1, variable. It follows from the if r < a if a ≤ r < b if b ≤ r < c if r ≥ c, which is a strictly increasing and continuous function on interval [a, c]. For any α ≤ 0.5, it is easy to.

Satisfactory approximation for the pessimistic value. Example 4.22 In this example, we take N = 2500 and α = 0.6, and perform Algorithm 4.2 fifty times on fuzzy variable ξ = (−0.3, 1.8, 2.3). The results are recorded by Table 4.4. Compared with the exact value 1.9, the maximum relative error is 0.21 %. 4.5 Applications This section applies the maximax chance-constrained programming model to the fuzzy portfolio selection problem. See Examples 2.4 and 2.5. If the decision-maker prefers a portfolio.

Function defined as T (s, t) = s ln(s/t) + (1 − s) ln (1 − s)/(1 − t) X. Li, Credibilistic Programming, Uncertainty and Operations Research, DOI 10.1007/978-3-642-36376-4_6, © Springer-Verlag Berlin Heidelberg 2013 119 120 6 Cross-Entropy Minimization Model Fig. 6.1 The shape of function T (s, t) with boundary conditions T (s, 0) = 0, +∞, if s = 0 if s > 0, T (s, 1) = 0, if s = 1 +∞, if s < 1. If fuzzy variables ξ and η have credibility functions ν and μ, respectively, then the.

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