This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. For the first time, we now introduce:
— Neutrosophic Duplets and the Neutrosophic Duplet Structures;
— Neutrosophic Multisets (as an extension of the classical multisets);
— Neutrosophic Spherical Numbers;
— Neutrosophic Overnumbers / Undernumbers / Offnumbers;
— Neutrosophic Indeterminacy of Second Type;
— Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations);
— Neutrosophic Triplet Loop;
— Neutrosophic Triplet Function;
— Neutrosophic Modal Logic;
— and Neutrosophic Hedge Algebras.
The Refined Neutrosophic Set / Logic / Probability were introduced in 2013 by F. Smarandache. Since year 2016 a new interest has been manifested by researchers for the Neutrosophic Triplets and their corresponding Neutrosophic Triplet Algebraic Structures (introduced by F. Smarandache & M. Ali). Subtraction and Division of Neutrosophic Numbers were introduced by F. Smarandache - 2016, and Jun Ye – 2017.
We also present various new applications in: neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function (the equatorial virtual line), neutrosophic probability in target identification, neutrosophic dynamic systems, neutrosophic quantum computers, neutrosophic theory of evolution, and neutrosophic triplet structures in our everyday life.
Several theorems and their proofs, together
with some definitions from the world first publication on neutrosophic triplets are improved (see Section VII.3, pages 76-78) in this first book that dedicates two chapters (VII - VIII) to the neutrosophic triplets and the neutrosophic triplet algebraic structures
neutrosophy, neutrosophic duplets, neutrosophic duplet structures, neutrosophic multisets, neutrosophic hedge algebras, neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function, neutrosophic probability in target identification, neutrosophic dynamic systems, neutrosophic quantum computers, neutrosophic theory of evolution, neutrosophic triplet structures, neutrosophic duplet structures, neutrosophic multiset structures.
Smarandache, Florentin. "Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications (second extended and improved)." (2017). https://digitalrepository.unm.edu/math_fsp/27