On a class of Fuzzy Set Theories

Abstract

This paper studies the main properties of a broad class of Fuzzy Set Theories that we call Minimal Fuzzy Set Theories. We investigate the fulfillment of well-known properties, such as idempotency or the existence of absorbent elements. The paper shows, in particular, that these theories do always verify the Kleene's law, as well as the Non-Contradiction and Excluded-Middle principles when these are understood as in ancient logic.