SMART-or and SMART-and fuzzy average operators: A generalized proposal

In this paper we introduce new average operators for merging any number of fuzzy numbers, without any exogenous components. The proposed n-ary operators are based on a specific adaptation of Marzullo’s algorithm, and depart from the usual fuzzy arithmetic mean according to the degree of agreement or disagreement among the memberships of input fuzzy numbers. Such merging 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. The special case of two fuzzy memberships was the focus of our previous contributions that were elicited in order to estimate the fuzzy volatility parameter in an hybrid fuzzy-stochastic model for option pricing. In this paper we generalize the setting to the case of nfuzzy inputs to be merged and also remove exogenous factors from the definition of the operators. In order to have an application at hand we consider the same example treated in the quoted paper and we compare the outcomes obtained via the new operators, named SMART, with the fuzzy arithmetic mean as a canonical benchmark.