A Note on Subsethood Measure of Fuzzy Sets

The main aim of this article is to revisit the definitions of subsethood measure which are predomonant in the literature of fuzzy set theory. It is also intended to revisit the relationship between fuzzy entropy and conditioning as proposed by some authors. We wish to analyze these with the extended definition of complementation of fuzzy sets on the basis of reference function. The existing definition of cardinality of fuzzy sets should have to be changed accordingly and a new definition is proposed hereby. Here efforts have been made to show that those proposed definitions of subsethood measure are not acceptable. Again due to the same reason we would like to mention here that the entropy-subsethood relationship which had been introduced by some authors is also not logical.