CADIAG-2/PANCREAS: An Artificial Intelligence System Based on Fuzzy Set Theory to Diagnose Pancreatic Diseases

1984 ◽  
pp. 396-399 ◽  
Author(s):  
K.-P. Adlassnig ◽  
W. Scheithauer ◽  
G. Grabner
Keyword(s):  
Artificial Intelligence ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Artificial Intelligence System ◽  
Pancreatic Diseases ◽  
Intelligence System

Fuzzy Decision Trees

2011 ◽  
pp. 696-703
Author(s):  
Malcolm J. Beynon
Keyword(s):  
Artificial Intelligence ◽  
Decision Tree ◽  
Decision Trees ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Entropy Measure ◽  
Fuzzy Decision ◽  
Fuzzy Environment ◽  
Fuzzy Decision Trees

The inductive learning methodology known as decision trees, concerns the ability to classify objects based on their attributes values, using a tree like structure from which decision rules can be accrued. In this article, a description of decision trees is given, with the main emphasis on their operation in a fuzzy environment. A first reference to decision trees is made in Hunt et al. (1966), who proposed the Concept learning system to construct a decision tree that attempts to minimize the score of classifying chess endgames. The example problem concerning chess offers early evidence supporting the view that decision trees are closely associated with artificial intelligence (AI). It is over ten years later that Quinlan (1979) developed the early work on decision trees, to introduced the Interactive Dichotomizer 3 (ID3). The important feature with their development was the use of an entropy measure to aid the decision tree construction process (using again the chess game as the considered problem). It is ID3, and techniques like it, that defines the hierarchical structure commonly associated with decision trees, see for example the recent theoretical and application studies of Pal and Chakraborty (2001), Bhatt and Gopal (2005) and Armand et al. (2007). Moreover, starting from an identified root node, paths are constructed down to leaf nodes, where the attributes associated with the intermediate nodes are identified through the use of an entropy measure to preferentially gauge the classification certainty down that path. Each path down to a leaf node forms an ‘if .. then ..’ decision rule used to classify the objects. The introduction of fuzzy set theory in Zadeh (1965), offered a general methodology that allows notions of vagueness and imprecision to be considered. Moreover, Zadeh’s work allowed the possibility for previously defined techniques to be considered with a fuzzy environment. It was over ten years later that the area of decision trees benefited from this fuzzy environment opportunity (see Chang and Pavlidis, 1977). Since then there has been a steady stream of research studies that have developed or applied fuzzy decision trees (FDTs) (see recently for example Li et al., 2006 and Wang et al., 2007). The expectations that come with the utilisation of FDTs are succinctly stated by Li et al. (2006, p. 655); “Decision trees based on fuzzy set theory combines the advantages of good comprehensibility of decision trees and the ability of fuzzy representation to deal with inexact and uncertain information.” Chiang and Hsu (2002) highlight that decision trees has been successfully applied to problems in artificial intelligence, pattern recognition and statistics. They go onto outline a positive development the FDTs offer, namely that it is better placed to have an estimate of the degree that an object is associated with each class, often desirable in areas like medical diagnosis (see Quinlan (1987) for the alternative view with respect to crisp decision trees). The remains of this article look in more details at FDTs, including a tutorial example showing the rudiments of how an FDT can be constructed.

scholarly journals Problems of Teaching Future Teachers of Humanities the Basics of Fuzzy Logic and Ways to Overcome Them

2021 ◽  
Vol 13 (2) ◽  
pp. 844-854
Author(s):  
Ivan Bakhov ◽  
Yuliya Rudenko ◽  
Andriy Dudnik ◽  
Nelia Dehtiarova ◽  
Sergii Petrenko
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Logic ◽  
Knowledge Representation ◽  
Information And Communication Technologies ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rapid Development ◽  
Pedagogical Practice ◽  
Future Teachers

The rapid development of computer technology has led to the use of fuzzy set theory in the medical, financial, economic, commercial and other fields as one of the basic components of artificial intelligence. This is due to its universal mechanism designed to analyze research in the field of humanities research. The mathematical apparatus of fuzzy set theory allows them to be performed with unformalized data, and the development and improvement of information and communication technologies make it possible to automate this process. Unformalized, abstract, "blurred" statistics, which are difficult to analyze, are also common in pedagogy. But in pedagogical practice, fuzzy logic has not been widely used. The article proves the importance and expediency of teaching students, future teachers of computer science, skills in the application of fuzzy set theory. The ability to use the mechanisms of fuzzy logic in applied programs will allow future teachers in their further pedagogical activities to conduct multi-criteria analysis of various characteristics of their students, analysis of pedagogical methods, comprehensive assessment of competencies and more. The article presents the experience of teaching fuzzy set theory, the logic of teaching and its sequence, as well as the results of such training at a pedagogical university. The necessity of the step-by-step study of fuzzy set theory is proved - from acquaintance with its basic concepts, giving examples of its application in expert systems, neural networks and artificial intelligence systems to independent construction of fuzzy knowledge representation model, development of linguistic variables and use of spreadsheet or specialized programs. The results of the experimental introduction of the topic "Fuzzy model of knowledge representation" in a training course of computer disciplines are shown. Examination of learning outcomes reveals a positive attitude of the students toward mastering the skills of using fuzzy set theory and willingness to apply it in their further pedagogical activities.

GENERALIZED COMONOTONICALLY ADDITIVE OPERATORS: REPRESENTATIONS BY CHOQUET INTEGRALS

2002 ◽  
Vol 10 (04) ◽  
pp. 329-346
Author(s):  
HEINZ J. SKALA
Keyword(s):  
Artificial Intelligence ◽  
Decision Theory ◽  
Banach Spaces ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Integral Representations ◽  
Representation Theorems ◽  
Projection Property ◽  
Choquet Integrals

Operators which behave (sub-, super-) additive on comonotonic functions occur quite naturally in many contexts, e.g. in decision theory, artificial intelligence, and fuzzy set theory. In the present paper we define comonotonicity for Riesz spaces with the principal projection property and obtain integral representations (in terms of Bochner integrals) for comonotonically additive operators acting on Riesz with the principal projection property and taking values in certain Riesz- or Banach spaces. As easy corollaries we obtain essential generalizations of representation theorems à la schmeidler, Proc. Am. Math. Soc. 97 (1986), 255 – 261. The existence of the necessary convergence theorems makes it possible to extend our results to set-valued operators. This is the topic of a further paper.

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