242 research outputs found
Computer-Aided Discovery and Categorisation of Personality Axioms
We propose a computer-algebraic, order-theoretic framework based on
intuitionistic logic for the computer-aided discovery of personality axioms
from personality-test data and their mathematical categorisation into formal
personality theories in the spirit of F.~Klein's Erlanger Programm for
geometrical theories. As a result, formal personality theories can be
automatically generated, diagrammatically visualised, and mathematically
characterised in terms of categories of invariant-preserving transformations in
the sense of Klein and category theory. Our personality theories and categories
are induced by implicational invariants that are ground instances of
intuitionistic implication, which we postulate as axioms. In our mindset, the
essence of personality, and thus mental health and illness, is its invariance.
The truth of these axioms is algorithmically extracted from histories of
partially-ordered, symbolic data of observed behaviour. The personality-test
data and the personality theories are related by a Galois-connection in our
framework. As data format, we adopt the format of the symbolic values generated
by the Szondi-test, a personality test based on L.~Szondi's unifying,
depth-psychological theory of fate analysis.Comment: related to arXiv:1403.200
Approximation Theory and Related Applications
In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics
Linear logic for constructive mathematics
We show that numerous distinctive concepts of constructive mathematics arise
automatically from an interpretation of "linear higher-order logic" into
intuitionistic higher-order logic via a Chu construction. This includes
apartness relations, complemented subsets, anti-subgroups and anti-ideals,
strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We
also explain the constructive bifurcation of classical concepts using the
choice between multiplicative and additive linear connectives. Linear logic
thus systematically "constructivizes" classical definitions and deals
automatically with the resulting bookkeeping, and could potentially be used
directly as a basis for constructive mathematics in place of intuitionistic
logic.Comment: 39 page
Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications
Tesis por compendioMathematical models have extensively been used in problems related to
engineering, computer sciences, economics, social, natural and medical sciences
etc. It has become very common to use mathematical tools to solve,
study the behavior and different aspects of a system and its different subsystems.
Because of various uncertainties arising in real world situations,
methods of classical mathematics may not be successfully applied to solve
them. Thus, new mathematical theories such as probability theory and fuzzy
set theory have been introduced by mathematicians and computer scientists
to handle the problems associated with the uncertainties of a model. But
there are certain deficiencies pertaining to the parametrization in fuzzy set
theory. Soft set theory aims to provide enough tools in the form of parameters
to deal with the uncertainty in a data and to represent it in a useful
way. The distinguishing attribute of soft set theory is that unlike probability
theory and fuzzy set theory, it does not uphold a precise quantity. This
attribute has facilitated applications in decision making, demand analysis,
forecasting, information sciences, mathematics and other disciplines.
In this thesis we will discuss several algebraic and topological properties
of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued
maps, the study of fixed point theory for multivalued maps on soft
topological spaces and on other related structures will be also explored.
The contributions of the study carried out in this thesis can be summarized
as follows:
i) Revisit of basic operations in soft set theory and proving some new
results based on these modifications which would certainly set a new
dimension to explore this theory further and would help to extend its
limits further in different directions. Our findings can be applied to
develop and modify the existing literature on soft topological spaces
ii) Defining some new classes of mappings and then proving the existence
and uniqueness of such mappings which can be viewed as a positive
contribution towards an advancement of metric fixed point theory
iii) Initiative of soft fixed point theory in framework of soft metric spaces
and proving the results lying at the intersection of soft set theory and
fixed point theory which would help in establishing a bridge between
these two flourishing areas of research.
iv) This study is also a starting point for the future research in the area of
fuzzy soft fixed point theory.Abbas, M. (2014). Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48470TESISCompendi
New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations
This Special Issue puts forward for discussion state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, neutrosophic symmetry, and their applications in the real world. This book leads to the further advancement of the neutrosophic and plithogenic theories of NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, Neutrosophic n-SuperHyperGraph (the most general form of graph of today), Neutrosophic Statistics, Plithogenic Logic as a generalization of MultiVariate Logic, Plithogenic Probability and Plithogenic Statistics as a generalization of MultiVariate Probability and Statistics, respectively, and presents their countless applications in our every-day world
Some fixed point results in the generalized convex metric spaces
In this study, we introduce a new three step iteration process and show that
the iteration process converges to the unique fixed point by two theorems under different
conditions of contractive mappings on the generalized G- convex metric spaces. Also, we
investigate data dependence result for this iterative process in the generalized G- convex
metric spaces
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