Summary
In the following paper, the use of fuzzy models in qualitative rating systems is analyzed in detail. The author works in an Austrian finance institution. There are at the moment two rating systems in use. The main purpose of such a rating system is to analyze company ratios to calculate a rating score, which is a measure for the financial situation and rigidity of a company. The first one is a solely hard fact rating system based on the Quicktest by Kralicek. The second one uses self-organizing maps and neural networks to calculate a rating classification and also offers the possibility to dispose personal appraisal in the calculation process. The following work examines the application spectrum of fuzzy logic and fuzzy models in soft-fact rating systems. We show that the use of fuzzy models in rating systems enables visualization of additional knowledge and offers the possibility to enhance the influence of a company's soft fact rating to the overall rating.
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Extract
Applying Fuzzy Models in Rating Systems
(ProQuest: ... denotes formulae omitted.)
1. PreliminariesA fuzzy subset A on a universal set X is characterized by its membership function μ^sub A^ : X [arrow right] [0, 1]. A support of A is defined as supp(A) = x ∈ X : A(x) > 0}. The height of a fuzzy set A is denoted by hgt(^4), hgt(^4) = supA(x) : x ∈ X}. F(X) denotes the set of all fuzzy subsets of a universe X.Let A ∈ F(X), a e [0, 1]. The a-level of A is the crisp setμ^sup -1^^sub A^(α) = x ∈ X : μ^sub A^(x) = α}. (1)P(X) denotes the set of all subsets of a set X. R^sub A^ is the system of cuts of A, R^sub A^: [0, 1] [arrow right] V(X), which assigns to each a euro [0, 1] the α-cut... (2)A fuzzy interval is a set A ∈ F(R) which satisfies the following conditions:1. supp(A) is a bounded set,2. ∀α ∈ (0, 1] the cut R^sub A^(α) is a closed interval,3. R^sub A^(1) ≠ ∅ (nonempty closed interval).If R^sup A^...See the full content of this document
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