Abstract

A special issue of the International Journal in Information Science and Engineering “Neutrosophic Sets and Systems” (vol. 71/2024) is dedicated to the Conference on NeutroGeometry, NeutroAlgebra, and Their Applications, organized by the Latin American Association of Neutrosophic Sciences. This event, which took place on August 12-14, 2024, in Havana, Cuba, was made possible by the valuable collaboration of the University of Havana, the University of Physical Culture and Sports Sciences "Manuel Fajardo," the José Antonio Echeverría University of Technology, University of Informatics Sciences and the Cuban Academy of Sciences among other institutions. In 2019 Smarandache generalized the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false} and on 2020 he continued to develop them. The NeutroAlgebras & AntiAlgebras are a new field of research, which is inspired from our real world. In classical algebraic structures, all operations are 100% well-defined, and all axioms are 100% true, but in real life, in many cases these restrictions are too harsh, since in our world we have things that only partially verify some operations or some laws. Similarly, a classical Geometry structure has all axioms totally (100%) true. A NeutroGeometry structure has some axioms that are only partially true, and no axiom is totally (100%) false. Whereas an AntiGeometry structure has at least one axiom that is totally (100%) false. And in general, in any field of knowledge one has: Structure, NeutroStructure, and AntiStructure which were inspired from our real world where the laws (axioms) do not equally apply to all people and in the same degree. This special issue aims to highlight the most recent advances and applications in the fields of NeutroGeometry and NeutroAlgebra, two areas that are at the forefront of contemporary mathematical and scientific thought. During the conference, the mathematical foundations and practical applications of these disciplines were explored, as well as their relevance in the MultiAlism system and other interdisciplinary areas. The content of this special issue has been carefully selected to reflect the diversity and depth of the topics discussed at the conference. This event and the subsequent publication of these works underline the growing importance of neutrosophic theories in the current scientific landscape. We are confident that the ideas and discoveries shared in these pages will be of great value to researchers, academics, and professionals interested in these innovative areas of knowledge.