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# Described a fuzzy logic implication statement Assignment Help

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

"b is B unless a_{1} is A_{1} AND ... AND an is A_{n},"

That is understood in logic as

"(b is B) unless (a_{1} is A_{1} AND ... AND an is A_{n}),"

Solution

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

"IF (a_{1} is A_{1} AND ... AND an is A_{n}) THEN b is B,"

Name is,

"IF a_{1} is A_{1} OR ... OR an is A_{n} 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 a_{1} is A_{1} THEN b is B,"

(2) "IF a_{2} is A_{2} THEN b is B,"

. . .

A_{n} 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 a_{1} is A_{1} AND ... AND an is A_{n} 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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**Described a fuzzy logic implication statement**

_{1}is A

_{1}AND ... AND an is A

_{n},"

_{1}is A

_{1}AND ... AND an is A

_{n}),"

_{1}is A

_{1}AND ... AND an is A

_{n}) THEN b is B,"

_{1}is A

_{1}OR ... OR an is A

_{n}THEN b is B,"

_{1}is A

_{1}THEN b is B,"

_{2}is A

_{2}THEN b is B,"

_{n}THEN b is B,"

_{1}is A

_{1}AND ... AND an is A

_{n}THEN b is NOT B,"

**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:**

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

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

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