3.5. Three variables of interest in power transistors are the amount of current that can beswitched, the voltage that can be switched, and the cost. The following membershipfunctions for power transistors were developed from a hypothetical componentscatalog:0.40.710.80.6Average current (in amperes) =I =0.80.91.11.2(0.20.610.90.7Average voltage (in volts) = V =3045607590Note how the membership values in each set taper off faster toward the lower volt-age and currents. These two fuzzy sets are related to the "power" of the transistor.Power in electronics is defined by an algebraic operation, P = VI, but let us dealwith a general Cartesian relationship between voltage and current, that is, simplywith P = V x I. Keep in mind that the Cartesian product is different from the arith-metic product. The Cartesian product expresses the relationship between V; and Ij,where V; and Ij are individual elements in the fuzzy sets V and I.4/8(a) Find the fuzzy Cartesian product P = V x I. Now let us define a fuzzy set forthe cost C, in dollars, of a transistor, for example,0.410.8C =0.50.60.7(b) Using a fuzzy Cartesian product, find T I x C. What would this relation, T.represent physically?(c) Using max-min composition, find E= PoT. What would this relation, E,represent physically?(d) Using max-product composition, find E Po T.

Here, I have to provide a solution to the above question.

(a) Find the fuzzy Cartesian product P = V x I. Now let us define a fuzzy set for the cost C, in dollars, of a transistor, for example, 0.4 0.8 0.5 0.6 0.7 (b) Using a fuzzy Cartesian product, find T =I x C. What would this relation, T, represent physically? (c) Using max-min composition, find E= PoT. What would this relation, E, represent physically? (d) Using max-product composition, find E = PoT.

(a) Find the fuzzy Cartesian product P = V x I. Now let us define a fuzzy set for the cost C, in dollars, of a transistor, for example, 0.4 0.8 0.5 0.6 0.7 (b) Using a fuzzy Cartesian product, find T =I x C. What would this relation, T, represent physically? (c) Using max-min composition, find E= PoT. What would this relation, E, represent physically? (d) Using max-product composition, find E = PoT.

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter13: Structures

Section: Chapter Questions

Problem 4PP

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