ALGEBRAIC EQUIVALENCES OVER FUZZY QUANTITIES

Fuzzy numbers and fuzzy quantities do not generally fulfil some fundam ental algebraic properties valid for crisp numbers, as shown e.g. in [ 1]. But it is possible to avoid this discrepancy if the strict equalit y between fuzzy quantities is substituted by rather weaker equivalence relations (cf. [5, 8, 9]) more respecting the natural vagueness of fu zzy phenomena. The equivalence relations suggested in the referred pap ers are based on analogous principles, however they are modified for t he specific cases of addition and multiplication relations. Here we su ggest a generalized equivalence model covering both previous equivalen ces (additive and multiplicative) as its special cases, and show its a pplicability to adequate description of certain class of algebraic tre atments of fuzzy numbers and fuzzy quantities.