On the algebraic structure of binary lattice-valued fuzzy relations

2012 ◽  
Vol 17 (3) ◽  
pp. 411-420 ◽  
Author(s):  
Xiaodong Pan ◽  
Yang Xu
Keyword(s):  
Algebraic Structure ◽  
Fuzzy Relations ◽  
Binary Lattice

Identifying lake longer-term dynamics via fuzzy relations and non-linear Kalman filters

1999 ◽  
Author(s):  
Tatjana D. Kolemishevska-Gugulovska ◽  
Georgi M. Dimirovski ◽  
A. Talha Dinibutun ◽  
Norman E. Gough
Keyword(s):  
Kalman Filters ◽  
Fuzzy Relations ◽  
Non Linear

scholarly journals Gauged double field theory as an L∞ algebra

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Eric Lescano ◽  
Martín Mayo
Keyword(s):  
Field Theory ◽  
Algebraic Structure ◽  
Classical Field ◽  
Field Theories ◽  
Lie Derivative ◽  
Linear Perturbation ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Symmetry Transformations ◽  
Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

scholarly journals Polymorphic Iterable Sequential Effect Systems

2021 ◽  
Vol 43 (1) ◽  
pp. 1-79
Author(s):  
Colin S. Gordon
Keyword(s):  
Algebraic Structure ◽  
Position Effect ◽  
Type Systems ◽  
Sequential Effect ◽  
Prior Work ◽  
Sequential Effects ◽  
Wide Range ◽  
The Relationship ◽  
Categorical Semantics

Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of effects is irrelevant. Understanding such systems in terms of a semilattice of effects grounds understanding of the essential issues and provides guidance when designing new effect systems. By contrast, sequential effect systems—where the order of effects is important—lack an established algebraic structure on effects. We present an abstract polymorphic effect system parameterized by an effect quantale—an algebraic structure with well-defined properties that can model the effects of a range of existing sequential effect systems. We define effect quantales, derive useful properties, and show how they cleanly model a variety of known sequential effect systems. We show that for most effect quantales, there is an induced notion of iterating a sequential effect; that for systems we consider the derived iteration agrees with the manually designed iteration operators in prior work; and that this induced notion of iteration is as precise as possible when defined. We also position effect quantales with respect to work on categorical semantics for sequential effect systems, clarifying the distinctions between these systems and our own in the course of giving a thorough survey of these frameworks. Our derived iteration construct should generalize to these semantic structures, addressing limitations of that work. Finally, we consider the relationship between sequential effects and Kleene Algebras, where the latter may be used as instances of the former.

scholarly journals Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

MEDUSA: A Fuzzy Expert System for Medical Diagnosis of Acute Abdominal Pain

1994 ◽  
Vol 33 (05) ◽  
pp. 522-529 ◽  
Author(s):  
M. Fathi-Torbaghan ◽  
D. Meyer
Keyword(s):  
Fuzzy Logic ◽  
Abdominal Pain ◽  
Expert System ◽  
Acute Abdominal Pain ◽  
Medical Knowledge ◽  
Clinical Problem ◽  
Fuzzy Relations ◽  
Diagnostic Decision ◽  
Special Cases ◽  
Hybrid Concept

Abstract:Even today, the diagnosis of acute abdominal pain represents a serious clinical problem. The medical knowledge in this field is characterized by uncertainty, imprecision and vagueness. This situation lends itself especially to be solved by the application of fuzzy logic. A fuzzy logic-based expert system for diagnostic decision support is presented (MEDUSA). The representation and application of uncertain and imprecise knowledge is realized by fuzzy sets and fuzzy relations. The hybrid concept of the system enables the integration of rulebased, heuristic and casebased reasoning on the basis of imprecise information. The central idea of the integration is to use casebased reasoning for the management of special cases, and rulebased reasoning for the representation of normal cases. The heuristic principle is ideally suited for making uncertain, hypothetical inferences on the basis of fuzzy data and fuzzy relations.

scholarly journals Two semigroups of continuous relations

1977 ◽  
Vol 23 (1) ◽  
pp. 46-58 ◽  
Author(s):  
A. R. Bednarek ◽  
Eugene M. Norris
Keyword(s):  
Large Class ◽  
Algebraic Structure ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Completely Regular ◽  
Topological Semigroups ◽  
Stone Type

SynopsisIn this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

scholarly journals Equipping weak equivalences with algebraic structure

2019 ◽  
Vol 294 (3-4) ◽  
pp. 995-1019 ◽  
Author(s):  
John Bourke
Keyword(s):  
Algebraic Structure

HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1867-1873 ◽  
Author(s):  
CHENG-MING BAI ◽  
MO-LIN GE ◽  
KANG XUE
Keyword(s):  
Representation Theory ◽  
Algebraic Structure ◽  
Zeeman Effect ◽  
Tensor Space ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
Degenerate States ◽  
Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

On Convexity of Fuzzy Sets and Fuzzy Relations

1992 ◽  
Vol 59 (1-2) ◽  
pp. 91-102
Author(s):  
Xu Chen-Wei
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Relations
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