Fuzzy Logic – Quantification

Spread the love

Fuzzy Logic – Quantification

In modeling pure language statements, quantified statements play an essential function. It signifies that NL closely is determined by quantifying building which frequently consists of fuzzy ideas like “virtually all”, “many”, and so forth. Following are a number of examples of quantifying propositions −

  • Each pupil handed the examination.
  • Each sport automotive is pricey.
  • Many college students handed the examination.
  • Many sports activities automobiles are costly.

Within the above examples, the quantifiers “Each” and “Many” are utilized to the crisp restrictions “college students” in addition to crisp scope “(one who)handed the examination” and “automobiles” in addition to crisp scope ”sports activities”.

Fuzzy Occasions, Fuzzy Means and Fuzzy Variances

With the assistance of an instance, we will perceive the above ideas. Allow us to assume that we’re a shareholder of an organization named ABC. And at current the corporate is promoting every of its share for ₹40. There are three totally different corporations whose enterprise is just like ABC however these are providing their shares at totally different charges – ₹100 a share, ₹85 a share and ₹60 a share respectively.

Now the chance distribution of this worth takeover is as follows −

Worth ₹100 ₹85 ₹60
Chance 0.3 0.5 0.2

Now, from the usual chance idea, the above distribution provides a imply of anticipated worth as beneath −

100×0.3+85×0.5+60×0.2=84.5100×0.3+85×0.5+60×0.2=84.5

And, from the usual chance idea, the above distribution provides a variance of anticipated worth as beneath −

(10084.5)2×0.3+(8584.5)2×0.5+(6084.5)2×0.2=124.825(100−84.5)2×0.3+(85−84.5)2×0.5+(60−84.5)2×0.2=124.825

Suppose the diploma of membership of 100 on this set is 0.7, that of 85 is 1, and the diploma of membership is 0.5 for the worth 60. These will be mirrored within the following fuzzy set −

{0.7100,185,0.560,}{0.7100,185,0.560,}

The fuzzy set obtained on this method is named a fuzzy occasion.

We wish the chance of the fuzzy occasion for which our calculation provides −

0.7×0.3+1×0.5+0.5×0.2=0.21+0.5+0.1=0.810.7×0.3+1×0.5+0.5×0.2=0.21+0.5+0.1=0.81

Now, we have to calculate the fuzzy imply and the fuzzy variance, the calculation is as follows −

Fuzzy_mean =(10.81)×(100×0.7×0.3+85×1×0.5+60×0.5×0.2)=(10.81)×(100×0.7×0.3+85×1×0.5+60×0.5×0.2)

=85.8=85.8

Fuzzy_Variance =7496.917361.91=135.27