AI- firing strength for output with 2 different inputs

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Question:

IF x is A AND y is B THEN z is C
where

A=0.1/1 + 0.4/2 + 0.7/3 + 1.0/4 + 0.6/5 + 0.2/6 + 0.1/7
B=0.3/1 + 0.8/2 + 1.0/3 + 0.6/4 + 0.5/5 + 0.3/6 + 0.2/7
C=0.3/1 + 0.5/2 + 0.7/3 + 1.0/4 + 0.8/5 + 0.4/6 + 0.0/7

Find the fire strength and evaluate output z:
a) for x which is a fuzzy singleton at 4 and y which is a fuzzy singleton at 2
b) for fuzzy inputs
x = 0.1/2 + 0.6/3 + 1.0/4 + 0.6/5 + 0.1/6
y = 0.2/3 + 0.7/4 + 1.0/5 + 0.5/6 + 0.1/7


Now the below is something that I tried, but I'm not sure whether I got it correctly or not.

For part (a)
I used this min(μ(A),μ(B))*C
therefore I have z=0.03/1 + 0.2/2 +0.49/3+0.6/4+0.4/5+0.08/6+0/7

For part (b), I have no idea what is my first step.

If anyone have any idea, just let me know. I'm willing to start the calculation, just let me know what is the first step.

Thanks a lot...

 

[KataKoniK]

Thank you for your question. I would approach this problem by first understanding the concept of fuzzy logic and its application in this scenario. Fuzzy logic is a mathematical approach that deals with uncertainty and imprecision in data. It allows us to use linguistic terms, such as "low", "medium", or "high", to describe a variable rather than precise numerical values. In this case, A, B, and C are fuzzy sets with membership functions that represent the degree of membership of a value in that set.

To find the fire strength and evaluate the output z, we need to first determine the membership values for A, B, and C for the given inputs. For part (a), we are given fuzzy singletons for x and y, which means the membership value for those inputs will be 1 and 0 for all other values. Therefore, for x=4, the membership value for A will be 1, and for y=2, the membership value for B will be 1.

Using the formula z=min(μ(A),μ(B))*C, we can calculate the output z for each value of C. For example, for C=1, we have z=min(1,1)*1=1. Similarly, for C=2, we have z=min(1,1)*2=2. This process can be repeated for all values of C to obtain the output z.

For part (b), we are given fuzzy inputs for x and y, which means we need to calculate the membership values for A and B using the given membership functions. For example, for x=2, the membership value for A will be 0.1/2 + 0.6/3 + 1.0/4 + 0.6/5 + 0.1/6=0.55. Similarly, for y=3, the membership value for B will be 0.2/3 + 0.7/4 + 1.0/5 + 0.5/6 + 0.1/7=0.69.

Once we have the membership values for A and B, we can use the formula z=min(μ(A),μ(B))*C to calculate the output z for each value of C. This process can be repeated for all values of C to obtain the output z.

I hope this helps in understanding how to approach this problem.