22,366 research outputs found
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products
The present paper extends generalized morphisms of relations into the realm
of Monoidal Fuzzy Logics by first proving and then using relational
inequalities over pseudo-associative BK-products (compositions) of relations in
these logics.
In 1977 Bandler and Kohout introduced generalized homomorphism,
proteromorphism, amphimorphism, forward and backward compatibility of
relations, and non-associative and pseudo-associative products (compositions)
of relations into crisp (non-fuzzy Boolean) theory of relations. This was
generalized later by Kohout to relations based on fuzzy Basic Logic systems
(BL) of H\'ajek and also for relational systems based on left-continuous
t-norms.
The present paper is based on monoidal logics, hence it subsumes as special
cases the theories of generalized morphisms (etc.) based on the following
systems of logics: BL systems (which include the well known Goedel, product
logic systems; Lukasiewicz logic and its extension to MV-algebras related to
quantum logics), intuitionistic logics and linear logics.Comment: 13 pages, 4 figures, 4 tables. Invited and refereed paper presented
at JCIS 2003 - 7th Joint Conf. on Information Sciences (Subsection: 9th
Internat. Conf. on Fuzzy Theory and Technology), Cary, North Carolina, USA;
September 200
New type Pythagorean fuzzy soft set and decision-making application
We define the Pythagorean fuzzy parameterized soft set and investigate some
properties of the new set. Further, we propose to the solution of
decision-making application for the Pythagorean fuzzy parameterized soft set
and other related concepts.Comment: 14 pages, 1 figure, 8 table
Representation of Uncertainty for Limit Processes
Many mathematical models utilize limit processes. Continuous functions and
the calculus, differential equations and topology, all are based on limits and
continuity. However, when we perform measurements and computations, we can
achieve only approximate results. In some cases, this discrepancy between
theoretical schemes and practical actions changes drastically outcomes of a
research and decision-making resulting in uncertainty of knowledge. In the
paper, a mathematical approach to such kind of uncertainty, which emerges in
computation and measurement, is suggested on the base of the concept of a fuzzy
limit. A mathematical technique is developed for differential models with
uncertainty. To take into account the intrinsic uncertainty of a model, it is
suggested to use fuzzy derivatives instead of conventional derivatives of
functions in this model
Dialectics of Counting and the Mathematics of Vagueness
New concepts of rough natural number systems are introduced in this research
paper from both formal and less formal perspectives. These are used to improve
most rough set-theoretical measures in general Rough Set theory (\textsf{RST})
and to represent rough semantics. The foundations of the theory also rely upon
the axiomatic approach to granularity for all types of general \textsf{RST}
recently developed by the present author. The latter theory is expanded upon in
this paper. It is also shown that algebraic semantics of classical \textsf{RST}
can be obtained from the developed dialectical counting procedures. Fuzzy set
theory is also shown to be representable in purely granule-theoretic terms in
the general perspective of solving the contamination problem that pervades this
research paper. All this constitutes a radically different approach to the
mathematics of vague phenomena and suggests new directions for a more realistic
extension of the foundations of mathematics of vagueness from both foundational
and application points of view. Algebras corresponding to a concept of
\emph{rough naturals} are also studied and variants are characterised in the
penultimate section.Comment: This paper includes my axiomatic approach to granules. arXiv admin
note: substantial text overlap with arXiv:1102.255
A comparison of techniques for learning and using mathematics and a study of their relationship to logical principles
Various techniques exist for learning mathematical concepts, like experimentation and exploration, respectively using mathematics, like modelling and simulation. For a clear application of such techniques in mathematics education, there should be a clear distinction between these techniques.
A recently developed theory of fuzzy concepts can be applied to analyse the four mentioned concepts. For all four techniques one can pose the question of their relationship to deduction, induction and abduction as logical principles. An empirical study was conducted with 12-13 aged students, aiming at checking the three reasoning processes
Towards combinatorial clustering: preliminary research survey
The paper describes clustering problems from the combinatorial viewpoint. A
brief systemic survey is presented including the following: (i) basic
clustering problems (e.g., classification, clustering, sorting, clustering with
an order over cluster), (ii) basic approaches to assessment of objects and
object proximities (i.e., scales, comparison, aggregation issues), (iii) basic
approaches to evaluation of local quality characteristics for clusters and
total quality characteristics for clustering solutions, (iv) clustering as
multicriteria optimization problem, (v) generalized modular clustering
framework, (vi) basic clustering models/methods (e.g., hierarchical clustering,
k-means clustering, minimum spanning tree based clustering, clustering as
assignment, detection of clisue/quasi-clique based clustering, correlation
clustering, network communities based clustering), Special attention is
targeted to formulation of clustering as multicriteria optimization models.
Combinatorial optimization models are used as auxiliary problems (e.g.,
assignment, partitioning, knapsack problem, multiple choice problem,
morphological clique problem, searching for consensus/median for structures).
Numerical examples illustrate problem formulations, solving methods, and
applications. The material can be used as follows: (a) a research survey, (b) a
fundamental for designing the structure/architecture of composite modular
clustering software, (c) a bibliography reference collection, and (d) a
tutorial.Comment: 102 pages, 66 figures, 67 table
Graph ambiguity
In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved
Hi tech microeconomics and information non-intensive calculi
The article establishes link between the contributions made to the study of hi tech
phenomena. It analyzes the evolution undergone by studies on the topic of the knowledge
economics (HI-TECH) process carried out by different disciplines (hard and soft sciences –
sociology, ecology etc.) from the point of view of the objectives they pursue. The attentions
are concentrated on analysis of applicable mathematical tools used to develop realistic formal
models. Information intensity is defined as the amount of information which is needed for the
realistic application of a corresponding formal tool. High information intensity is desirable
because it influences the model accuracy. Low information intensity is preferred when high
information intensity requires more information items than are available and this is usually
the case in knowledge engineering. Fuzzy models seem to be a useful extension of formal tool
used in hi tech microeconomics. However, even fuzzy sets could be prohibitively information
intensive. Therefore the range of available formal tools must be considerably broader. This
paper introduces qualitative and semiqualitative models and rough sets. Each formal tool is
briefly characterized
- …