Alternative fuzzy operations and applications to social sciences

Some humanistic systems find a suitable method of representation of their features in fuzzy numbers. This is due to the properties of fuzzy numbers that are used to describe indeterminateness. The applications of fuzzy numbers to Social Sciences request, in some cases, that the region of indeterminateness, called spreads, in the results of the operations between fuzzy numbers be less than the ones expected by Zadeh's extension principle. Furthermore, it is important to consider operations that save the shapes of fuzzy numbers for reasons of simplicity and clearness of modeling. To this aim, fuzzy operations are dealt with as possible alternatives to the operations induced by the extension principle. An application to Social Sciences is considered. Finally, the need for defining algebraic structures of fuzzy numbers (e.g., to extend to the fuzzy environment the de Finetti's concept of coherent prevision) leads to considerations for operations defined up to equivalence relations. Some fuzzy extensions of the coherent prevision are introduced. © 2009 Wiley Periodicals, Inc.