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Sathyabama Institute of Science and Technology M.Sc - Mathematics SMT5205 Fuzzy Analysis Syllabus DEPARTMENT OF MATHEMATICS SCHOOL OF SCIENCE AND HUMANITIES SMT5205 FUZZY ANALYSIS L T P CREDIT 3 1 0 4 UNIT 1: 12 Hrs From Classical Sets To Fuzzy sets – Fuzzy set: Basic types – Fuzzy sets Versus Crisp sets- Extension Principle for fuzzy sets – Operations on Fuzzy sets – Types of operations – Fuzzy complements. UNIT 2: 12 Hrs Fuzzy Arithmetic – Fuzzy numbers - Linguistic variables – Arithmetic operations on intervals – Arithmetic operations on Fuzzy numbers – Lattice of Fuzzy numbers – Fuzzy equations. UNIT 3: 12 Hrs Fuzzy Logic – Multi-valued Logics – Fuzzy Propositions – Unconditional and Unqualified Fuzzy propositions – Unconditional and qualified Propositions – Conditional and Unqualified propositions – Conditional and Qualified propositions – Linguistic Hedges – Inference from conditional Fuzzy propositions- Inference from conditional and qualified propositions. UNIT 4: 12 Hrs Fuzzy Decision making – Individual decision making – Fuzzy Ranking methods – Fuzzy Linear programming. UNIT 5: 12 Hrs Fuzzy Relations – composition of fuzzy relations – properties of fuzzy relations. Total No of Hours: 60 TEXT BOOK : T.B-1: George J.Klir and Bo Yuan, Fuzzy sets and Fuzzy Logic Theory and Applications, PHI,2004. T.B-2: A.Nagoor Gani and V.J.Chandrasekaran, A first look at Fuzzy Graph Theory, Allied Publishers Pvt. Ltd. UNIT I Chapter 1 - 1.3,2.3 & Chapter 3 - 3.1&3.2 T.B-1 UNIT II Chapter 4 – 4.1,4.2,4.3,4.4,4.5,4.6 T.B-1 UNIT III Chapter 8 – 8.2,8.3,8.5,8.6,8.7 T.B-1 UNIT IV Chapter 15 – 15.2,15.6,15.7 T.B-1 UNIT V Chapter 1 – 1.3,1.4,1. 5 T.B-2 REFERENCE BOOKS: 1. Timothy J.Ross, Fuzzy Logic with Engineering Applications –McGraw-Hill, Inc., H.J. Zimmermann, Fuzzy Set Theory and its Applications, Allied Publishers Limited, 1991. UNIVERSITY EXAM QUESTION PAPER PATTERN: Max. Marks : 70 Exam Duration : 3 Hrs Part A : 4 questions of 5 marks each – No choice - 20 marks Part B : 5 questions from each unit of internal choice, each carrying 10 marks - 50 marks |
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