5,545 research outputs found
Join and Meet Operations for Type-2 Fuzzy Sets With Nonconvex Secondary Memberships
In this paper, we will present two theorems for the join and meet operations for general type-2 fuzzy sets with arbitrary secondary memberships, which can be nonconvex and/or nonnormal type-1 fuzzy sets. These results will be used to derive the join and meet operations of the more general descriptions of interval type-2 fuzzy sets presented in a paper by Bustince Sola et al. ('Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: Towards a wider view on their relationship,' IEEE Trans. Fuzzy Syst., vol. 23, pp. 1876-1882, 2015), where the secondary grades can be nonconvex. Hence, this study will help to explore the potential of type-2 fuzzy logic systems which use the general forms of interval type-2 fuzzy sets which are not equivalent to interval-valued fuzzy sets. Several examples for both general type-2 and the more general forms of interval type-2 fuzzy sets are presented
Towards a generalisation of formal concept analysis for data mining purposes
In this paper we justify the need for a generalisation of Formal
Concept Analysis for the purpose of data mining and begin the
synthesis of such theory. For that purpose, we first review semirings and
semimodules over semirings as the appropriate objects to use in abstracting
the Boolean algebra and the notion of extents and intents, respectively.
We later bring to bear powerful theorems developed in the field
of linear algebra over idempotent semimodules to try to build a Fundamental
Theorem for K-Formal Concept Analysis, where K is a type of
idempotent semiring. Finally, we try to put Formal Concept Analysis in
new perspective by considering it as a concrete instance of the theory
developed
Bell-type inequalities for bivariate maps on orthomodular lattices
Bell-type inequalities on orthomodular lattices, in which conjunctions of
propositions are not modeled by meets but by maps for simultaneous measurements
(s-maps), are studied. It is shown that the most simple of these inequalities,
that involves only two propositions, is always satisfied, contrary to what
happens in the case of traditional version of this inequality in which
conjunctions of propositions are modeled by meets. Equivalence of various
Bell-type inequalities formulated with the aid of bivariate maps on
orthomodular lattices is studied. Our invesigations shed new light on the
interpretation of various multivariate maps defined on orthomodular lattices
already studied in the literature. The paper is concluded by showing the
possibility of using s-maps and j-maps to represent counterfactual conjunctions
and disjunctions of non-compatible propositions about quantum systems.Comment: 14 pages, no figure
Semiclassical Quantum Gravity: Statistics of Combinatorial Riemannian Geometries
This paper is a contribution to the development of a framework, to be used in
the context of semiclassical canonical quantum gravity, in which to frame
questions about the correspondence between discrete spacetime structures at
"quantum scales" and continuum, classical geometries at large scales. Such a
correspondence can be meaningfully established when one has a "semiclassical"
state in the underlying quantum gravity theory, and the uncertainties in the
correspondence arise both from quantum fluctuations in this state and from the
kinematical procedure of matching a smooth geometry to a discrete one. We focus
on the latter type of uncertainty, and suggest the use of statistical geometry
as a way to quantify it. With a cell complex as an example of discrete
structure, we discuss how to construct quantities that define a smooth
geometry, and how to estimate the associated uncertainties. We also comment
briefly on how to combine our results with uncertainties in the underlying
quantum state, and on their use when considering phenomenological aspects of
quantum gravity.Comment: 26 pages, 2 figure
Gauge Theories on Deformed Spaces
The aim of this review is to present an overview over available models and
approaches to non-commutative gauge theory. Our main focus thereby is on gauge
models formulated on flat Groenewold-Moyal spaces and renormalizability, but we
will also review other deformations and try to point out common features. This
review will by no means be complete and cover all approaches, it rather
reflects a highly biased selection.Comment: v2 references added; v3 published versio
Integration of decision support systems to improve decision support performance
Decision support system (DSS) is a well-established research and development area. Traditional isolated, stand-alone DSS has been recently facing new challenges. In order to improve the performance of DSS to meet the challenges, research has been actively carried out to develop integrated decision support systems (IDSS). This paper reviews the current research efforts with regard to the development of IDSS. The focus of the paper is on the integration aspect for IDSS through multiple perspectives, and the technologies that support this integration. More than 100 papers and software systems are discussed. Current research efforts and the development status of IDSS are explained, compared and classified. In addition, future trends and challenges in integration are outlined. The paper concludes that by addressing integration, better support will be provided to decision makers, with the expectation of both better decisions and improved decision making processes
Operations on Concavoconvex Type-2 Fuzzy Sets
Concavoconvex fuzzy set is the result of the com-bination of the concepts of convex and concave fuzzy sets. This paper investigates concavoconvex type-2 fuzzy sets. Basic operations, union, intersection and complement on concavoconvex type-2 fuzzy sets us-ing min and product t-norm and max t-conorm are studied and some of their algebraic properties are explored
Integrating Fuzzy Decisioning Models With Relational Database Constructs
Human learning and classification is a nebulous area in computer science. Classic decisioning problems can be solved given enough time and computational power, but discrete algorithms cannot easily solve fuzzy problems. Fuzzy decisioning can resolve more real-world fuzzy problems, but existing algorithms are often slow, cumbersome and unable to give responses within a reasonable timeframe to anything other than predetermined, small dataset problems. We have developed a database-integrated highly scalable solution to training and using fuzzy decision models on large datasets. The Fuzzy Decision Tree algorithm is the integration of the Quinlan ID3 decision-tree algorithm together with fuzzy set theory and fuzzy logic. In existing research, when applied to the microRNA prediction problem, Fuzzy Decision Tree outperformed other machine learning algorithms including Random Forest, C4.5, SVM and Knn. In this research, we propose that the effectiveness with which large dataset fuzzy decisions can be resolved via the Fuzzy Decision Tree algorithm is significantly improved when using a relational database as the storage unit for the fuzzy ID3 objects, versus traditional storage objects. Furthermore, it is demonstrated that pre-processing certain pieces of the decisioning within the database layer can lead to much swifter membership determinations, especially on Big Data datasets. The proposed algorithm uses the concepts inherent to databases: separated schemas, indexing, partitioning, pipe-and-filter transformations, preprocessing data, materialized and regular views, etc., to present a model with a potential to learn from itself. Further, this work presents a general application model to re-architect Big Data applications in order to efficiently present decisioned results: lowering the volume of data being handled by the application itself, and significantly decreasing response wait times while allowing the flexibility and permanence of a standard relational SQL database, supplying optimal user satisfaction in today\u27s Data Analytics world. We experimentally demonstrate the effectiveness of our approach
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