Introduction to neutrosophy and neutrosophic environment

Abstract

Abstract This chapter provides an overview on neutrosophy along with its mathematical developments over the last 2 decades. This will educate the readers about neutrosophy as a generalization of dialectics with its several mathematical algebra, precalculus and calculus. In addition, the nonstandard neutrosophic set (NS), the standard NS, the hesitant NS, and their extension to a complex fuzzy environment are also discussed. Moreover, the neutrosophic aggregation operators; the neutrosophic cognitive maps; the neutrosophic overset, underset, and offset; the neutrosophic crisp set; the refined NS; and the law of included multiple middle are also addressed. Furthermore, this chapter reports the neutrosophic algebraic structures, neutrosophic graphs, neutrosophic triplets, neutrosophic duplets, neutrosophic multisets, and the extension of crisp/fuzzy/intuitionistic fuzzy/NSs to plithogenic sets in detail with their mathematical expressions.