A Geometric Interpretation of the Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set

In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between NS and IFS are underlined.Comment: 9 pages. Presented at the 2003 BISC FLINT-CIBI International Workshop on Soft Computing for Internet and Bioinformatics, University of Berkeley, California, December 15-19, 2003, under the title "Generalization of the Intuitionistic Fuzzy Set to the Neutrosophic Set

About Nonstandard Neutrosophic Logic (Answers to Imamura 'Note on the Definition of Neutrosophic Logic')

In order to more accurately situate and fit the neutrosophic logic into the framework of nonstandard analysis, we present the neutrosophic inequalities, neutrosophic equality, neutrosophic infimum and supremum, neutrosophic standard intervals, including the cases when the neutrosophic logic standard and nonstandard components T, I, F get values outside of the classical real unit interval [0, 1], and a brief evolution of neutrosophic operators. The paper intends to answer Imamura criticism that we found benefic in better understanding the nonstandard neutrosophic logic, although the nonstandard neutrosophic logic was never used in practical applications.Comment: 16 page