On a class of Fuzzy Set Theories
21 Citations•2007•
E. Trillas, C. Alsina, A. Pradera
2007 IEEE International Fuzzy Systems Conference
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.
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.