The OPERATORSET class aggregates the operators and methods necessary to do calculations with a FUZZYVAR. There are four important steps to achieve results from a rulebase: these are aggregation, certification, inference and accumulation. In the aggregation step the match values of all instantiated membership functions are aggregated to an overall match value by applying the selected AND/OR operators. In the next step the overall certified match value is calculated by applying the selected CERTAINTY operator to the overall match value and the certainty value. The inference step calculates a new match value by applying the INFERENCE operator to the overall certified match value and the old match value. Finally the crisp value of a FUZZYVAR is calculated through the defuzzification process (center of gravity: COG).
OPERATRORSET
IMPORTANCE FuzzyOp
AND FuzzyOp
OR FuzzyOp
CERTAINTY FuzzyOp
INFERENCE FuzzyOp
ACCUMULATE FuzzyOp
DEFUZZIFICATION DefuzzyOp
GAMMA [0..1]
ACCURACY [0..10]
END
At the moment FLIP++ and CSI(C&F) support the following fuzzyfication and defuzzification operators:
DefuzzyOp = COG
NO_DFOP
FuzzyOp = MAXIUMUM
MINIMUM
FUZZY_AND
FUZZY_OR
ASS_COMP_AND
ASS_COMP_OR
NO_FOP
where COG stands for "center of gravity"-defuzzification method, NO_DFOP stand for "no defuzzification operator", MAXIMUM and MINIMUM stand for that what we suggest them to do, FUZZY_AND is realized with a T-Norm calculation, FUZZY_OR is realized with a T-CoNorm calculation, ASS_COMP_AND stands for "associative compensatory and", ASS_COMP_OR stands for "associative compensatory or", and finally NO_FOP stands for "no fuzzy operator". Further mathematical and set theoretical discussion on these operators can be found in Chapter 4 or in the bibliography indicated there.