2 COMP4033-E1 COMP4033-E1 Question 1: This question relates to type-1 fuzzy sets and their operations. [overall 25 marks] a. Discuss with some brief examples, the inadequacies of classical 2-valued logic in describing the real world. [2 Marks] b. Explain what a fuzzy set is. [2 Marks] c. You are presented with two bottles, X and Y. You are told that the truth value that ‘bottle X is full’ is 0.5, while the probability that ‘bottle Y is full’ is 0.5. Discuss the difference between these two statements, using fuzzy set theory, fuzzy membership values and probabilities to illustrate various scenarios of empty, partially-full and full bottles. [4 Marks] d. Give the informal definition of a linguistic variable, by means of a fully-labelled illustrative example with four associated terms (fuzzy sets). In doing so, give a specific example of the following two concepts: i. An element may have partial membership of a set. ii. An element may be a member of more than one set at the same time. [7 Marks] e. Explain the t-norm and t-conorm operators. Give examples with figures of fuzzy sets to illustrate two common t-norms and two common t-conorms respectively. You need to use R and the FuzzyR toolbox to generate the fuzzy sets and to plot the figures. [10 Marks]
