EECE 664 Midterm, Fall 2013

> PAGEIOF3 EECE 664"- Fuzzy Sets, Logic and Applications Midterm Exam-Fall 2009-2010 AMERICAN t::-IIVERSITY OF BEIRUT FACULTY OF E:-IGINEERING AND ARCHITECTURE ELECTRICAL AND COMPUTER ENGINEERING DEPARTME:-IT EECE 664 - Fuzzy Sets. Logic 80d Applications Midterm Exam FALL TERM 2009-2010 DECEMBER 3, 2009 TIME: 1 J.I HOURS CLOSED BOOK EXAM ALL PROaLE!'ttS ARE EQt:ALLY WEIGHTED IN GARDlNG INSTRUCTOR: DR. JEAN J. SAADE NAME:_________ ID#: ______ Problem # t Give a brief (approximately Slines) definition of an intelligent system or machine. In this definition, include a statement related to "task execution or performance" and another one related to "human experts." Problem #2 When a human expert executes a task requiring a high level of intelligence he or she uses most often an approximate rather than a precise type of reasoning. Explain briefly what is meant by approximate reasoning using the car driving example and then tell how this type of reasoning can be represented mathematically by fuzzy sets and fuzzy logic (do not exceed 10 lines in aU). Problem # 3 For a human being to become able to perform or execute appropriately a task requlring a high level of intelligence, he or she usually needs to be trained by a supervisor or expert in order to gain the needed expertise. Is it possihle to train a machine? Ifso, explain how. • PAGE 2 OF3 EECE 664 ~ Fuzzy Sets. Logic and AppliGations Midtenn Exam-Fall 2009-2010 Problem # 4 Fuzzy set theory can be used to model uncertainty in a manner similar to the theory of probability, Furthennore, the theory of digital communications is usually referred to as the "statistical theory of communications." Is it possible to rebuild the theory of digital communications using fuzzy sets so that it may then be caned the "fuzzy theory of communications?" Whether your answer is positive or negative explain it and give justifications, Problem # 5 Explain the difference between artificial neural networks and fuzzy sets and logic in the setting of inteHlgent machine design. Problem # 6 Specify the rcason for which not all elements in a space over which a fuzzy set is defined can be classified as complete clements or no elements in the fuzzy set. In your answer consider the manner by which a fuzzy Set is defmed and also the manner by which the grades of membership are assigned. Do not consider any type of fonnula for membership functions. Problem # 7 Explain the reason for which a crisp set has a sharply defined boundary whHe a fuzzy set does not. Problem # 8 Omsider the set A=(l,2,4,5) and the crisp relation R from A into A defined by xRy¢?x~y. Give a matrix representation of this relation where the entries of thc matrix arc lhe characteristic values ofR considered as a crisp subset ofAxA. • PAGE30F3 EECE 664 ~ Fuzzy Sets, Logic and Applications Midterm Exam-Fall 2009-2010 Problem #9 Consider the function y=f{x) = xl: mapping the set of real numbers it{ into ~ and the fuzzy sel A defined over 9t such lhat: I 2 -x+- 2';x";l 3 3' 1 4 --x+-,1";x,,;4 3 3 0, elsewhere. Are the conditions needed to make Bo=[f(A)]n=UAa) satisfied by f and A in this problem? State these conditions and tell if they arc satisfied or not. l'rQblem# 10 Consider again Problem Ii 9 and determine Bn for aH ue(O, Ij by assuming that Bu-=tIAu). froblem # 11 Use Bn you obtained in Problem # 10 and drnw an approximate plot of the membership function of fuzzy set B induced from A by function f. You do not need to determine PB(Y)' Problem # 12 Addition of real numbers is known to be a continuous binary operation (function) from 9lxffi. into 91, where ffi is the set of real nwnbers, Consider fuzzy numbers A and B such that these numbers satisfy the properties required under the extension principle to make Cc:=-A«+B,. where C=A+B. (a) What are these properties? State them clearly, (b) What other properties are required to be satisfied by A and B so as to be able to perform their addition using their u cuts? State these properties clearly as wen.