Alternative fuzzy operations: A critical approach and applications in social and economic sciences

The applications of fuzzy numbers to Social Sciences, Economy, and Natural Sciences request, in various cases that the spreads, i. e. the region of indeterminateness, of the results of the operations between fuzzy numbers be less than the ones expected by the Zadeh’s extension principle. Moreover, it appears to be necessary to consider operations that save the shapes of fuzzy numbers. To this aim fuzzy operations are dealt with, alternatives to the operations induced by the extension principle. Critical analyses of logical principles which support the various operations are carried out. Some application to Social Sciences and Economy are considered.