# 7.5.3 OPERATORSET

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.