scholarly journals Hierarchies and Uncertainty Measures on Pythagorean Fuzzy Approximation Spaces

2020 ◽  
Author(s):  
Xiaojing Luo ◽  
Jingjing Song ◽  
Huili Dou ◽  
Xibei Yang ◽  
Taihua Xu
Keyword(s):  
Lattice Structure ◽  
Order Relation ◽  
Fuzzy Information ◽  
Information Granularity ◽  
Approximation Spaces ◽  
Information Granules ◽  
First Order ◽  
Fuzzy Approximation ◽  
Uncertainty Measures ◽  
The Relationship

In Granular Computing, the hierarchies and uncertainty measures are two important concepts to investigate the granular structures and uncertainty of approximation spaces. In this paper, hierarchies and uncertainty measures on pythagorean fuzzy approximation spaces will be researched. Firstly, the introduction and operations of pythagorean fuzzy granular structures are given, and three hierarchies and a lattice structure on pythagorean fuzzy approximation spaces are examined. The hierarchies are characterized by three order relations, the first order relation is defined on the inclusion relation of pythagorean fuzzy information granules, the second one is defined on the cardinality of pythagorean fuzzy information granules, and the third one is defined on the sum of the cardinality of pythagorean fuzzy information granules. The lattice structure is constructed on the first order relation on pythagorean fuzzy approximation spaces. Fuzzy information granularity and fuzzy information entropy are extended to describe the uncertainty of pythagorean fuzzy granular structures, and the relationship between the uncertainty measures and hierarchies are discussed. The examples show that hierarchies are effective to analyze the relationships among all granular structures on pythagorean fuzzy approximation spaces.

On Bijective Correspondence between Fuzzy Reflexive Approximation Spaces and Fuzzy Transformation Systems

2020 ◽  
Vol 16 (02) ◽  
pp. 291-304
Author(s):  
Sutapa Mahato ◽  
S. P. Tiwari
Keyword(s):  
Lattice Structure ◽  
Approximation Space ◽  
Double Negation ◽  
Approximation Spaces ◽  
Bijective Correspondence ◽  
Fuzzy Approximation ◽  
Fuzzy Transformation ◽  
Double Negation Law ◽  
Transformation Systems ◽  
The Relationship

The objective of this paper is to establish the relationship between fuzzy approximation operators and fuzzy transformation systems. We show that for each upper fuzzy transformation system there exists a fuzzy reflexive approximation space and vice-versa. We further establish such relationship between lower fuzzy transformation systems and fuzzy reflexive approximation spaces under the condition that the underline lattice structure satisfies double negation law.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

scholarly journals On the correspondence between nested calculi and semantic systems for intuitionistic logics

2020 ◽  
Author(s):  
Tim Lyon
Keyword(s):  
Intuitionistic Logic ◽  
Structural Rules ◽  
First Order ◽  
Constant Domains ◽  
The Relationship ◽  
Intuitionistic Logics

Abstract This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

scholarly journals A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard

2007 ◽  
Vol 72 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Ehud Hrushovski ◽  
Ya'acov Peterzil
Keyword(s):  
Real Numbers ◽  
The Real ◽  
First Order ◽  
Real Closed Fields ◽  
Minimal Structure ◽  
Closed Fields ◽  
New Construction ◽  
The Relationship

AbstractWe use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

scholarly journals Photocatalytic degradation of indigo carmine by ZnO photocatalyst under visible light irradiation

2017 ◽  
Vol 14 (3) ◽  
pp. 582-587
Author(s):  
Baghdad Science Journal
Keyword(s):  
Zinc Oxide ◽  
Photocatalytic Degradation ◽  
Indigo Carmine ◽  
Catalyst Loading ◽  
Order Kinetic ◽  
Kinetic Reaction ◽  
First Order ◽  
Pseudo First Order ◽  
The Relationship ◽  
Influential Parameters

In this work, the photocatalytic degradation of indigo carmine (IC) using zinc oxide suspension was studied. The effect of influential parameters such as initial indigo carmine concentration and catalyst loading were studied with the effect of Vis irradiation in the presence of reused ZnO was also investigated. The increased in initial dye concentration decreased the photodegradation and the increased catalyst loading increased the degradation percentage and the reused-ZnO exhibits lower photocatalytic activity than the ZnO catalyst. It has been found that the photocatalytic degradation of indigo carmine obeyed the pseudo-first-order kinetic reaction in presence of zinc oxide. This was found from plotting the relationship between ln (C0/Ct) and irradiation the rate constant of the process.UV- spectrophotometer was used to study the indigo carmine photodegradation.

scholarly journals On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

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