Exercise 2. 2(Defining Membership Functions: Multiple Universes of Discourse ) In this problem you will study how to represent various concepts and quantify various relations with membership functions when there is more than one universe of discourse. Use minimum to quantify the"and. For each part below, there is more than one correct answer. Prov ide one of these and justify your choice in each case. Also, in each case draw the three-dimensional plot of the membership function (a) Draw a membership function(and hence def ine a fuzzy set) that quantif ies the set of all people of medium height who are"tan"in color (i.e, tan and medium-height people) Think of peoples colors being on a spectrum from white to black. (b) Draw a membership function(and hence define a fuzzy set)that quantifies the set of all short people who arewhite" in color (i.e, short and white people) (c)Draw a membership function(and hence def ine a fuzzy set) that quantifies the set of all tall people who are"black" " in color(i.e, tall and black people) (d) Draw a membership function that quantif ies the statement"the number x is near 10 and the number y is near 2. (e) Draw a membership function that quantifies the statement"the number x is less than 10 and the number y is near 2. (f) Draw a membership function that quantifies the statement"the number x is greater than 10 and the number y is near 2 (g)Repeat(d)-(f)for-5 rather than 10 and -1 rather than 2 (h) Repeat(d)-(f)using product rather than minimum to represent the " and
Exercise 2.2 (Defining Membership Functions: Multiple Universes of Discourse): In this problem you will study how to represent various concepts and quantify various relations with membership functions when there is more than one universe of discourse. Use minimum to quantify the “and.” For each part below, there is more than one correct answer. Provide one of these and justify your choice in each case. Also, in each case draw the three-dimensional plot of the membership function. (a) Draw a membership function (and hence define a fuzzy set) that quantifies the set of all people of medium height who are “tan” in color (i.e., tan and medium-height people). Think of peoples' colors being on a spectrum from white to black. (b) Draw a membership function (and hence define a fuzzy set) that quantifies the set of all short people who are “white” in color (i.e., short and white people). (c) Draw a membership function (and hence define a fuzzy set) that quantifies the set of all tall people who are “black” in color (i.e., tall and black people). (d) Draw a membership function that quantifies the statement “the number x is near 10 and the number y is near 2.” (e) Draw a membership function that quantifies the statement “the number x is less than 10 and the number y is near 2.” (f) Draw a membership function that quantifies the statement “the number x is greater than 10 and the number y is near 2.” (g) Repeat (d)-(f) for -5 rather than 10 and -1 rather than 2. (h) Repeat (d)-(f) using product rather than minimum to represent the “and.” （a）
(b] white in color po)shd (b) (c)black in color (c)
（ b ） （ c ）
(d)near 10 (d) (e) near 2
（ d ） （ e ）
03 0.1 () near 2 (f) 09 0.8 0.6 [g-d)nea
（f）
09 0.8 0.6 03 0.1 (g-e)near ge) ess than占 1 09 08 0.6 10 5 g-f greater than-5
09 0.8 0.6 4 03 0.1 18 20 4 h可 Oh-d)near 10 09 4 0.3 20 14 Ch-e)ne e)less than 10
09 0.8 0.6 03 0.1 18 4 0-1 near 2