Kybernetika 32 no. 4, 343-351, 1996

Fuzzy zero, algebraic equivalence: yes or no?

Milan Mareš


When some algebraic properties of fuzzy numbers and, more generally, fuzzy quantities are investigated then it appears useful to study more deeply the notion of "fuzzy zero'' and of the additive equivalence derived from it. This was done, e. g. in [2], [3], [4], [5] and in some other related papers. In fact, the idea of fuzzy zero, and especially the concept of additive equivalence evidently provoke some questions. Namely, if exactly this concept of fuzzy zero really reflects the intuitive vision of negligibility, connected with the zero. Further, if the equivalence concept based on such fuzzy zero is distinguishing enough, i. e., if elements equivalent in this sense are also similar regarding the common understanding of similarity. In this contribution we briefly recall the necessary notions and discuss some aspects of the questions mentioned above. In this sense, the following paper does not offer new formal results but it summarizes discussion arguments regarding the usefullness and acceptability of a few notions derived to explain the behaviour of fuzzy quantities as algebraic objects.


04A72, 94D05, 03E72