Two SMART Fuzzy Aggregation Operators

In this paper we introduce new disjunction and conjunction (named SMART) for merging, without any exogenous components, any number of fuzzy memberships. The present proposals are n-ary operators, based on a specific adaptation of Marzullo’s algorithm, that depart from the usual fuzzy mean on the base of the agreement/disagreement among the different memberships. These different operators are suitable to be applied in any model where the same quantity (usually a parameter) can be measured (estimated) through different fuzzy memberships stemming by different sources of information. In our previous contributions we have considered the special case of two fuzzy memberships that were elicited for the volatility parameter in an hybrid fuzzy-stochastic model for option pricing. Here we adopt the same example to have an application at hand and to compare our new proposed operators with the ordinary fuzzy mean; nevertheless, the operators can be applied to merge any n memberships which are candidates to represent the same fuzzy number.