In the case the implication used in a fuzzy inference system is the MINIMUM, and we have rule that have the AND operator, the AND is specified as the MINIMUM also, the result membership function is simply the minimum of the antecedents. But when we have the operator OR (MAXIMUM), the implication also takes the minimum. I can't really understand the rule of MINIMUM implication method here.
For example:
IF ( temperature is warm) AND ( humidity is average) THEN (ventilation is strong).
For example, the degree of membership of each premise:
IF ( temperature is warm (0.7)) AND ( humidity is average (0.5)) THEN (ventilation is strong (???)).
Since the AND conjunction operator is the minimum we will take 0.5 and so we will cut the output membership function (strong) in 0.5.
If the conjunction operator was OR instead of AND, then we cut in 0.7. So I do not really see the minimum involvement in all this.
They refer to the concatenation of operations.
For the antecedent and consequence.
Min or the Product
Mas or sum
Erik Cuevas Thank you for your answer.
Sohel Rana Thank you for your answer. For the AND operator it is obvious. I'm only confused when we have the OR operator. Since it is Maximum in this case, 0.5 OR 0.7 gives 0.7. But since the implication in this case is the 'minimum', as a result we will get 0.7. So I don't really see the role of Then (minimum) operator here.
Could you explain in a bit more detail
Sohel Rana Thank you so much, now I understand that we look for the minimum of (0.7 and 1). I understood AND and OR perfectly, i was just confused about the implication. But now it is clear the role of the Minimum implication. Thank you so much
This paper will give you a very clear answer: https://www.researchgate.net/publication/344638760_Dimensioning_and_Power_Management_of_Hybrid_Energy_Storage_Systems_for_Electric_Vehicles_with_Multiple_Optimization_Criteria
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