We consider here fuzzy quantities, i.e. fuzzy sets without any hypothesis about normality nor convexity. Two main topics are examined: the first one consists in defining the evaluation of a fuzzy quantity, in such a way that it may be applied both in ranking and in defuzzification problems. The definition is based on α-cuts and depends on two parameters: a coefficient connected with the optimistic or pessimistic attitude of the decision maker and a weighting function similar to a density function. The second aim is showing that the proposed definition is suitable for defuzzifying the output of a fuzzy expert system: we treat a classical example discussed in [1], using several t-norms and t-conorms in aggregation procedures.
Evaluation of fuzzy quantities by means of a weighting functions / G., Facchineti; Pacchiarotti, Nicoletta. - ELETTRONICO. - 193:(2009), pp. 194-204. (Intervento presentato al convegno 18th Italian Workshop on Neural Networks: WIRN 2008 tenutosi a Vietri sul Mare nel 22-24 maggio 2008) [10.3233/978-1-58603-984-4-194].
Evaluation of fuzzy quantities by means of a weighting functions
PACCHIAROTTI, Nicoletta
2009
Abstract
We consider here fuzzy quantities, i.e. fuzzy sets without any hypothesis about normality nor convexity. Two main topics are examined: the first one consists in defining the evaluation of a fuzzy quantity, in such a way that it may be applied both in ranking and in defuzzification problems. The definition is based on α-cuts and depends on two parameters: a coefficient connected with the optimistic or pessimistic attitude of the decision maker and a weighting function similar to a density function. The second aim is showing that the proposed definition is suitable for defuzzifying the output of a fuzzy expert system: we treat a classical example discussed in [1], using several t-norms and t-conorms in aggregation procedures.
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