Theory of Fuzzy Sets: An Overview
It is found that the existing definition of complementation as well as the probability - possibility consistency principles is not well defined and the results obtained would be inappropriate fro m the standpoint of the Randomness-Fuzziness consistency principles.
Abstract
In this art icle, we would like to revisit and comment on the definit ion of co mplementation of fu zzy sets and also on some of the theories and formulas associated with this. Furthermore, the existing probability-possibility consistency principles are also revisited and related results are v iewed fro m the standpoint of the Randomness-Fuzziness consistency principles. It is found that the existing definition of complementation as well as the probability - possibility consistency principles is not well defined. Consequently the results obtained from these would be inappropriate fro m our standpoints. Hence we would like to suggest some new defin itions for som e of the terms often used in the theory of fuzzy sets whenever possible.