5,069 research outputs found
Join and Meet Operations for Interval-Valued Complex Fuzzy Logic
DMU Interdisciplinary Group in Intelligent Transport SystemsInterval-valued complex fuzzy logic is able to handle scenarios where both seasonality and uncertainty feature. The interval-valued complex fuzzy set is defined, and the interval valued
complex fuzzy inferencing system outlined. Highly pertinent to complex fuzzy logic operations is the concept of rotational invariance, which is an intuitive and desirable characteristic. Interval-valued complex fuzzy logic is driven by interval-valued join and meet operations. Four pairs of alternative algorithms for these operations are specified; three pairs possesses the attribute of rotational invariance, whereas the other pair lacks this characteristic
Fuzzy in 3-D: Contrasting Complex Fuzzy Sets with Type-2 Fuzzy Sets
CCIComplex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, applications, definitions, and structures. In addition, pure complex fuzzy sets are compared with type-2 fuzzy sets in relation to their inferencing operations.
Complex fuzzy sets and type-2 fuzzy sets differ in their roles and applications. Their definitions differ also, though there is equivalence between those of a pure complex fuzzy set and a type-2 fuzzy set. Structural similarity is evident between these three-dimensional sets. Complex fuzzy sets are represented by a line, and type-2 fuzzy sets by a surface, but a surface is simply a generalisation of a line. This similarity is particularly evident between pure complex fuzzy sets and type-2 fuzzy sets, which are both mappings from the domain onto the unit square. Type-2 fuzzy sets were found not to be isomorphic to pure complex fuzzy sets
Variable sets over an algebra of lifetimes: a contribution of lattice theory to the study of computational topology
A topos theoretic generalisation of the category of sets allows for modelling
spaces which vary according to time intervals. Persistent homology, or more
generally, persistence is a central tool in topological data analysis, which
examines the structure of data through topology. The basic techniques have been
extended in several different directions, permuting the encoding of topological
features by so called barcodes or equivalently persistence diagrams. The set of
points of all such diagrams determines a complete Heyting algebra that can
explain aspects of the relations between persistent bars through the algebraic
properties of its underlying lattice structure. In this paper, we investigate
the topos of sheaves over such algebra, as well as discuss its construction and
potential for a generalised simplicial homology over it. In particular we are
interested in establishing a topos theoretic unifying theory for the various
flavours of persistent homology that have emerged so far, providing a global
perspective over the algebraic foundations of applied and computational
topology.Comment: 20 pages, 12 figures, AAA88 Conference proceedings at Demonstratio
Mathematica. The new version has restructured arguments, clearer intuition is
provided, and several typos correcte
A General Framework for Representing, Reasoning and Querying with Annotated Semantic Web Data
We describe a generic framework for representing and reasoning with annotated
Semantic Web data, a task becoming more important with the recent increased
amount of inconsistent and non-reliable meta-data on the web. We formalise the
annotated language, the corresponding deductive system and address the query
answering problem. Previous contributions on specific RDF annotation domains
are encompassed by our unified reasoning formalism as we show by instantiating
it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we
provide a generic method for combining multiple annotation domains allowing to
represent, e.g. temporally-annotated fuzzy RDF. Furthermore, we address the
development of a query language -- AnQL -- that is inspired by SPARQL,
including several features of SPARQL 1.1 (subqueries, aggregates, assignment,
solution modifiers) along with the formal definitions of their semantics
Quantale Modules and their Operators, with Applications
The central topic of this work is the categories of modules over unital
quantales. The main categorical properties are established and a special class
of operators, called Q-module transforms, is defined. Such operators - that
turn out to be precisely the homomorphisms between free objects in those
categories - find concrete applications in two different branches of image
processing, namely fuzzy image compression and mathematical morphology
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