Improved Definition of Non Standard Neutrosophic Logic and Introduction to Neutrosophic Hyperreals (Fourth version)

Abstract

Bulletin of Pure and Applied SciencesOn the third version of this response-paper to Imamura’s criticism, we recall that Non(1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tellIextended the Non Standard Analysis byhyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise they would be inapplicable.also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandardunit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introducedby adding theleft monad closed to the right(we introduced in 1998), andunpierced binadStandard Neutrosophic Logicwas never used by neutrosophic community in no application, that the quarter of century oldneutrosophic operatorsmura were never utilized since they were improved shortly after but he omits to telltheir development, and that in real world applications we need to convert/approximate the Non Standard AnalysisWe point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets,Neutrosophic Hyperreals that are indeterminate), whence the transfer principle is questionable. After his criticism,several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such,all these in order to close the newly extendednonstandardaddition,