Credit Rating Analysis with AFS Fuzzy Logic.
ABSTRACT In this paper, we propose a new machine learning approach based on AFS (Axiomatic Fuzzy Sets) fuzzy logic, in attempt to pro- vide a better model with interpretability. First, we will concisely present the AFS theory. Second, we will propose new membership functions for fuzzy sets and their logic operations. Third, we will design a new machine learning algorithm based on the new membership functions and their logic operations. This algorithm has two advantages. One is that it can mimic the human reasoning comprehensively and offers a far more flex- ible and effective means for the study of large-scale intelligent systems. Another is its simplicity in implementation and mathematical beauty in fuzzy theory. Finally, a credit data example is used to illustrate its effectiveness.
Full-textDOI: · Available from: Wanquan Liu, Jun 25, 2015
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ABSTRACT: In this paper, first the axiomatic fuzzy set (AFS) clustering method [X.D. Liu, W. Wang, T.Y. Chai, The fuzzy clustering analysis based on AFS theory, IEEE Transactions on Systems, Man and Cybernetics Part B 35 (5) (2005) 1013-1027] is investigated further by improving the algorithm to be more applicable, then it is used to analyze the evaluation results of 30 companies which have been studied and analyzed by G.-S. Liang et al. [G.S. Liang, T.Y. Chou, T.C. Han, Cluster analysis based on fuzzy equivalence relation, European Journal of Operational Research 166 (2005) 160-171]. Compared with Liang's algorithm, the proposed method is more transparent, understandable and interpretable. This method can be applied to the management strategic analysis based on the datasets described by mixed features such as real numbers, Boolean logical values, linguistic descriptions. The illustrative examples show that the interpretations of the clustering results of the 30 companies are almost consistent with the expert's intuitions.European Journal of Operational Research 10/2009; 198(1):297-304. DOI:10.1016/j.ejor.2008.08.010 · 1.84 Impact Factor
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ABSTRACT: As moving further into the age of machine intelligence and auto- mated decision-making, we have to deal with both the subjective imprecision of human perception-based information described in natural language and the ob- jective uncertainty of randomness universally existing in the real world. A basic limitation of standard probability theory which cannot deal with information described in natural language becomes a serious problem. With its abilities to represent natural language, the notion of AFS (Axiomatic Fuzzy Set) theory has proven useful in the clustering, classiflcations, concept representations and decision trees. In this paper, we apply AFS theory and probability theory to propose a new interpretation of the membership functions taking both fuzziness (subjective imprecision) and randomness (objective uncertainty) into account. So that uncertainty of randomness and of imprecision can be treated in a uni- fled and coherent manner under the AFS and probability framework. It opens a door to explore the deep mathematical analysis properties of fuzzy set the- ory and to a major enlargement of the role of natural languages in probability theory.01/2007; 3(2).
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ABSTRACT: Many research results of AFS (Axiomatic Fuzzy Set) theory and its applications have been published and reported since Liu proposed it in (20) in 1995. In this paper, an over review of AFS theory is done by both theory analysis and illustrate examples to explain the abstract notations and theorems in order to elicit the potential applications and the further research topics. Many well-known datasets are applied to test the application algorithms and the results show that AFS fuzzy logic system oers a far more flexible and powerful framework for representing human knowledge and studying the large- scale intelligence systems in real world applications.01/2006; 2(3).