Described a fuzzy logic implication statement Assignment Help

Fuzzy Rules And Their Operations - Described a fuzzy logic implication statement

Described a fuzzy logic implication statement

"b is B unless a1 is A1 AND ... AND an is An,"

That is understood in logic as

"(b is B) unless (a1 is A1 AND ... AND an is An),"

 Solution

One can first convert it by utilizing fuzzy logic NOT and OR operations as given below:

"IF (a1 is A1 AND ... AND an is An) THEN b is B,"

Name is,

 "IF a1 is  A1 OR ... OR an is  An THEN b is B,"

 And after that replace all the OR operations by a fuzzy logic rule base in the following form as:

(1)   "IF a1 is A1  THEN b is B,"

(2)   "IF a2 is A2  THEN b is B,"

. . .

An THEN b is B,"

This Equivalent rule base is in the general format, indeed.

However, in this illustration, this should be noted that the specified statement is not equivalent to the following:

"IF a1 is A1 AND ... AND an is An THEN b is NOT B,"

Because the conclusion can be "b has no relation along with B."

At last, note that a fuzzy rule base has to satisfy several properties or requirements as the so-called "3C requirement" - concise, consistent, and complete

Firstly, a fuzzy rule base has to be complete, in this sense no other possible situations are left out. The given rule base is incomplete as:

(a)   IF a > 0 THEN b > 0,

(b)   IF a = 0 THEN b < 0,

As the case of a < 0 is left out

Secondly, a fuzzy rule base has to be consistent; in this sense no conclusions are contradictive. The given rule base is inconsistent as:

(a)   IF a > 0 THEN b > 0,

(b)   IF a >0 THEN b = 0,

(c)    IF a = 0 THEN b < 0,

(d)   IF a <0 THEN b = 0,

As the first two rules contradicts each other. Until now this rule base is complete. Notice the given two rules are consistent as:

(a)   IF a > 0 THEN b > 0,

(b)   IF a = 0 THEN b > 0,

Here two different conditions give the similar conclusion, which is not a conflict, and the given two rules are consistent, as:

(a)   IF a > 0 THEN b > 0,

(b)   IF a > 0 THEN c > 0,

Such are Equivalent to "IF a > 0 THEN b > 0 AND c > 0."

At last, some other requirements may need to be imposed too for a fuzzy rule base in a particular application. Particularly, a rule base should be concise with less or no redundancy.The above 3C requirement provides a guideline for designing a correct, whole and fuzzy rule base in engineering applications.


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