Question

Three variables of interest in power transistors are the amount of current that can be switched, the voltage that can be switched, and the cost. The following membership functions for power transistors were developed from a hypothetical components catalog:

Average current (in amps) = I = {0.4/0.8 + 0.7/0.9 + 1.0/1.0 + 0.8/1.1 + 0.6/1.2}

Average voltage (in volts) = V = {0.2/30 + 0.8/45 + 1.0/60 + 0.9/75 + 0.7/90}

Note how the membership values in each set taper off faster toward the lower voltage 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 deal with a general Cartesian relationship between voltage and current, i.e., simply with P = V×I. Keep in mind that the Cartesian product is different from the arithmetic product. The Cartesian product expresses the relationship between Vi and Ij, where Vi and Ij are individual elements in the fuzzy sets V and I.

(1) Find the Fuzzy Cartesian Product P = VI. Now let us define a fuzzy set for the cost
C, in dollars, of a transistor, for example, C = {0.4/0.5 + 1.0/0.6 + 0.5/0.7

(2) Using a fuzzy Cartesian product, find T = I×C. What would this relation, T, represent
physically?

(3) Using max-min composition, find E = PoT. What would this relation, E, represent
physically?

(4) Using max-product composition, find E = PoT. What would this relation, E, represent
physically?

Answer 1