On Some Results Based on Geometrical Representation of Fuzzy Sets

The main purpose of this article is to highlight the fact that there are some drawbacks in the existing definition of complementation of fuzzy sets and hence the geometrical representation of fuzzy sets on the basis of such definition which itself is defective would have no meaning. As a result the theorems or formulas which were rooted in the geometrical representation would become unacceptable and it is realized that in most cases of practical significance it is desirable to consider an additional requirement in defining fuzzy complement. It is important to mention here the fact that all these existing properties are being seen through the application of complementation of fuzzy sets which is rooted in the reference function. The current definition of complementation would infact remove those drawbacks and cosequently produce the results which seems to be logical. IndexTerms— Reference Function, Membership Function, Entropy of Fuzzy Sets, The RandomnessFuzziness Consistency Principles