12 research outputs found
Plots and Their Applications - Part I: Foundations
The primary goal of this paper is to abstract notions, results and
constructions from the theory of categories to the broader setting of plots.
Loosely speaking, a plot can be thought of as a non-associative non-unital
category with a "relaxed" composition law: Besides categories, this includes as
a special case graphs and neocategories in the sense of Ehresmann, Gabriel's
quivers, Mitchell's semicategories, and composition graphs, precategories and
semicategories in the sense of Schr\"oder. Among other things, we formulate an
"identity-free" definition of isomorphisms, equivalences, and limits, for which
we introduce regular representations, punctors, -connections, and
-factorizations. Part of the material will be used in subsequent
work to lay the foundation for an abstract theory of "normed structures"
serving as a unifying framework for the development of fundamental aspects of
the theory of normed spaces, normed groups, etc., on the one hand, and measure
spaces, perhaps surprisingly, on the other.Comment: Not intended for publicatio
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc