Solution

The correct answer is option 2.

Important Points

Certainty Factor (CF) is a numeric value that tells us how likely an event or a statement is supposed to be true.

This value is similar to probability, but with only probability value of any event agent cannot decide what to do. This certainty factor is decided through which the agent can decide whether to declare the statement true or false based on the probability and other knowledge that the agent has.

Dynamic Certainty for a Conclusion :

CF(C) = CF(H) x CF(R) , C is the conclusion

CF(H) = calculated Certainty Factor for Hypothesis.

R = given rule , "if H then C with certainty CF(R)"

Conjunction and Disjunction of Hypotheses:

CF (P1 and P2) = MIN { CF(P1) , CF(P2) }
CF (P1 or P2) = MAX { CF(P1) , CF(P2) }

Here, P1 , P2 are premises.

Given Rule is (P1 and P2) or P3

R1 and R2 are conclusions of rules.

CF(R1)= 0.8 

CF(R2)=0.3

CF(P1)=0.5  , CF(P2)=0.8 , CF(P3)=0.2

Where P1,P2,P3 are premises.

Now the CF of given rule ((P1 and P2) or P3)=   MAX  { MIN{CF(P1),CF(P2)} , CF(P3) } 

= MAX { MIN { 0.5,0.8} ,0.2}

=MAX { 0.5 , 0.2 }

= 0.5

Now, CF of R1 based on premises = 0.5 × CF(R1) =0.5 × 0.8 =0.40

Now, CF of R2 based on premises = 0.5 ×  CF(R2) =0.5 × 0.3 =0.15