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Fuzzy Systems - Fuzzy Set Theory

Fuzzy SystemsFuzzy Set TheoryProf. Dr. Rudolf Kruse Christian University of MagdeburgFaculty of Computer ScienceDepartment of Knowledge Processing and Language EngineeringR. Kruse, C. MoewesFS Fuzzy Set TheoryLecture 2 Outline1. Representation of Fuzzy SetsCantor s TheoryAlpha-cutsProperties based on Alpha-cuts2. Fuzzy Set Operators based on Multi-valued LogicsDefinition of a set By a set we understand every collection made intoa whole of definite, distinct objects of our intuitionor of our thought. (Georg Cantor).For a set in Cantor s sense, the following propertieshold: x6={x}. Ifx XandX Y, thenx/ Y. The Set of all subsets ofXis denoted as 2X. is the empty set and thus very Cantor (1845-1918)R.

Fuzzy Systems Fuzzy Set Theory Prof. Dr. Rudolf Kruse Christian Moewes {kruse,cmoewes}@iws.cs.uni-magdeburg.de Otto-von-Guericke University of Magdeburg Faculty of Computer Science Department of Knowledge Processing and Language Engineering R. Kruse, C. Moewes FS – Fuzzy Set Theory Lecture 2

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