scholarly journals Semigroup Structures and Commutative Ideals of BCK-Algebras Based on Crossing Cubic Set Structures

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 25
Author(s):  
Mehmet Ali Öztürk ◽  
Damla Yılmaz ◽  
Young Bae Jun
Keyword(s):  
Level Set ◽  
Extension Property ◽  
Binary Operations ◽  
Commutative Ideal ◽  
The Relationship

First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra, and several properties are investigated. The relationship between crossing cubic ideal and commutative crossing cubic ideal is discussed. An example to show that crossing cubic ideal is not commutative crossing cubic ideal is given, and then the conditions in which crossing cubic ideal can be commutative crossing cubic ideal are explored. Characterizations of commutative crossing cubic ideal are discussed, and the relationship between commutative crossing cubic ideal and crossing cubic level set is considered. An extension property of commutative crossing cubic ideal is established, and the translation of commutative crossing cubic ideal is studied. Conditions for the translation of crossing cubic set structure to be commutative crossing cubic ideal are provided, and its characterization is processed.

On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability

2021 ◽  
pp. 1-19
Author(s):  
M. Miri Karbasaki ◽  
M. R. Balooch Shahriari ◽  
O. Sedaghatfar
Keyword(s):  
Linear Function ◽  
Level Set ◽  
Fuzzy Numbers ◽  
Sufficient Condition ◽  
Continuous Linear ◽  
Generalized Differentiability ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of ◽  
Dimensional Mapping

This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fréchet and Gâteaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fréchet and Gâteaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fréchet and Gâteaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fréchet and Gâteaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.

scholarly journals On the Relationship between Variational Level Set-Based and SOM-Based Active Contours

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Mohammed M. Abdelsamea ◽  
Giorgio Gnecco ◽  
Mohamed Medhat Gaber ◽  
Eyad Elyan
Keyword(s):  
Level Set ◽  
Active Contour ◽  
Active Contours ◽  
Level Set Methods ◽  
Energy Functional ◽  
Self Organizing Maps ◽  
Complex Shapes ◽  
Variational Level Set ◽  
Preservation Property ◽  
The Relationship

Most Active Contour Models (ACMs) deal with the image segmentation problem as a functional optimization problem, as they work on dividing an image into several regions by optimizing a suitable functional. Among ACMs, variational level set methods have been used to build an active contour with the aim of modeling arbitrarily complex shapes. Moreover, they can handle also topological changes of the contours. Self-Organizing Maps (SOMs) have attracted the attention of many computer vision scientists, particularly in modeling an active contour based on the idea of utilizing the prototypes (weights) of a SOM to control the evolution of the contour. SOM-based models have been proposed in general with the aim of exploiting the specific ability of SOMs to learn the edge-map information via their topology preservation property and overcoming some drawbacks of other ACMs, such as trapping into local minima of the image energy functional to be minimized in such models. In this survey, we illustrate the main concepts of variational level set-based ACMs, SOM-based ACMs, and their relationship and review in a comprehensive fashion the development of their state-of-the-art models from a machine learning perspective, with a focus on their strengths and weaknesses.

scholarly journals Property $(w)$ of upper triangular operator Matrices

2020 ◽  
Vol 51 (2) ◽  
pp. 81-99
Author(s):  
Mohammad M.H Rashid
Keyword(s):  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Extension Property ◽  
Operator Matrices ◽  
Single Valued Extension Property ◽  
Triangular Operator ◽  
Upper Triangular Operator Matrices ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Number Of Authors

Let $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}\in\LB(\x,\y)$ be be an upper triangulate Banach spaceoperator. The relationship between the spectra of $M_C$ and $M_0,$ and theirvarious distinguished parts, has been studied by a large number of authors inthe recent past. This paper brings forth the important role played by SVEP,the {\it single-valued extension property,} in the study of some of these relations. In this work, we prove necessary and sufficient conditions of implication of the type $M_0$ satisfies property $(w)$ $\Leftrightarrow$ $M_C$ satisfies property $(w)$ to hold. Moreover, we explore certain conditions on $T\in\LB(\hh)$ and $S\in\LB(\K)$ so that the direct sum $T\oplus S$ obeys property $(w)$, where $\hh$ and $\K$ are Hilbert spaces.

scholarly journals Onn-fold fuzzy implicative/commutative ideals of BCK-algebras

2001 ◽  
Vol 27 (7) ◽  
pp. 419-424 ◽  
Author(s):  
Young Bae Jun
Keyword(s):  
Extension Property ◽  
Commutative Ideal

We consider the fuzzification of the notion of ann-fold implicative ideal, ann-fold (weak) commutative ideal. We give characterizations of ann-fold fuzzy implicative ideal. We establish an extension property forn-fold fuzzy commutative ideals.

Folding Theory for Fantastic Filters in BL-Algebras

2011 ◽  
Vol 2 (4) ◽  
pp. 32-42 ◽  
Author(s):  
Celestin Lele
Keyword(s):  
Level Set ◽  
Fuzzy Set ◽  
Extension Property ◽  
Fuzzy Filter ◽  
Fantastic Filter

In this paper, the author examines the notion of n-fold fantastic and fuzzy n-fold fantastic filters in BL-algebras. Several characterizations of fuzzy n-fold fantastic filters are given. The author shows that every n-fold (fuzzy n-fold) fantastic filter is a filter (fuzzy filter), but the converse is not true. Using a level set of a fuzzy set in a BL-algebra, the author gives a characterization of fuzzy n-fold fantastic filters. Finally, the author establishes the extension property for n-fold and fuzzy n-fold fantastic filters in BL-algebras. The author also constructs some algorithms for folding theory applied to fantastic filters in BL-algebras.

Folding Theory for Fantastic Filters in BL-Algebras

2013 ◽  
pp. 261-271
Author(s):  
Celestin Lele
Keyword(s):  
Level Set ◽  
Fuzzy Set ◽  
Extension Property ◽  
Fuzzy Filter ◽  
Fantastic Filter

In this paper, the author examines the notion of n-fold fantastic and fuzzy n-fold fantastic filters in BL-algebras. Several characterizations of fuzzy n-fold fantastic filters are given. The author shows that every n-fold (fuzzy n-fold) fantastic filter is a filter (fuzzy filter), but the converse is not true. Using a level set of a fuzzy set in a BL-algebra, the author gives a characterization of fuzzy n-fold fantastic filters. Finally, the author establishes the extension property for n-fold and fuzzy n-fold fantastic filters in BL-algebras. The author also constructs some algorithms for folding theory applied to fantastic filters in BL-algebras.

scholarly journals Whether Loyalty to a Football Club Can Translate into a Political Support for the Club Owner: An Empirical Evidence from Thai League

2018 ◽  
Vol 11 (3) ◽  
pp. 47
Author(s):  
Thanaporn Sriyakul ◽  
Anurak Fangmanee ◽  
Kittisak Jermsittiparsert
Keyword(s):  
Empirical Evidence ◽  
Level Set ◽  
Educational Level ◽  
Political Support ◽  
The Political ◽  
Significance Level ◽  
Football Club ◽  
The Past ◽  
Football Clubs ◽  
The Relationship

The participation of politicians and their kin in the sport of football, as presidents of football clubs, in the past many years has been widely criticized as a use of the football clubs as tools to gain popularity and, possibly, a political base or a voting bloc for these politicians. This research is conducted in order to (1) study the loyalty level towards football clubs and the corresponding political supports expressed towards the football club executives and (2) examine the relationship between such demographic factors as gender, age, educational level, occupation, income, duration of being a fan, as well as loyalty to the football club and the aforementioned political supports, by collecting data from fans of five football clubs competing in the Thai League during the 2016 season. Including 385 fans, the data are collected using questionnaire, and then analyzed in terms of frequency, percentage, mean, standard variation, and Pearson’s correlation coefficient analysis with the significance level set at five percent. The research finds that overall the fans of all five clubs are highly loyal to the club and express a moderate political support for the club executives. It also finds that gender, age, and education have no relationship to the political support, while occupation, income, duration of being a fan, and especially loyalty to the football club are correlated with the political support. This result confirms the hypothesis that loyalty to a football club can, in fact, potentially translate into a political support for the politicians who are also the owners of the football clubs.

scholarly journals Imploring GE-Filters of GE-Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Seok-Zun Song ◽  
Ravikumar Bandaru ◽  
Young Bae Jun
Keyword(s):  
Extension Property ◽  
The Relationship ◽  
Provided Examples

Relations between a transitive GE-algebra, a belligerent GE-algebra, an antisymmetric GE-algebra, and a left exchangeable GE-algebra are displayed. A new substructure, so called imploring GE-filter, is introduced, and its properties are investigated. The relationship between a GE-filter, an imploring GE-filter, a belligerent GE-filter, and a prominent GE-filter are considered. Conditions for an imploring GE-filter to be a belligerent GE-filter are given, and the conditions necessary for a (belligerent) GE-filter to be an imploring GE-filter are found. Relations between a prominent GE-filter and an imploring GE-filter are discussed, and a condition for an imploring GE-filter to be a prominent GE-filter is provided. Examples to show that a belligerent GE-filter and a prominent GE-filer are independent concepts are given. The extension property of the imploring GE-filter is established.

scholarly journals M-hypercyclicity of C 0-semigroup and Svep of its generator

2021 ◽  
Vol 8 (1) ◽  
pp. 187-191
Author(s):  
A. Toukmati
Keyword(s):  
Banach Space ◽  
Closed Subspace ◽  
Extension Property ◽  
Single Valued Extension Property ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
The Relationship

Abstract Let 𝒯 = (Tt ) t ≥0 be a C 0-semigroup on a separable infinite dimensional Banach space X, with generator A. In this paper, we study the relationship between the single valued extension property of generator A, and the M-hypercyclicity of the C 0-semigroup. Specifically, we prove that if A does not have the single valued extension property at λ ∈ iℝ, then there exists a closed subspace M of X, such that the C 0-semigroup 𝒯 is M-hypercyclic. As a corollary, we get certain conditions of the generator A, for the C 0-semigroup to be M-hypercyclic.

Uni-Hesitant Fuzzy Set Approach to the Ideal Theory of BCK-Algebras

2020 ◽  
pp. 128-139
Author(s):  
G. Muhiuddin
Keyword(s):  
Level Set ◽  
Fuzzy Set ◽  
Theoretical Approach ◽  
Ideal Theory ◽  
Hesitant Fuzzy Set ◽  
Commutative Ideal ◽  
Fuzzy Ideal ◽  
The Ideal

In this chapter, the author studies the uni-hesitant fuzzy set-theoretical approach to the ideals of BCK-algebras. For a hesitant fuzzy set H on S and a subset of [0,1], the set L(H;ʎ):={x∈S|xH⊆ʎ}, is called the uni-hesitant level set of H. Moreover, the author discusses the relations between uni-hesitant fuzzy commutative ideals and uni-hesitant fuzzy ideals. Further, he considered the characterizations of uni-hesitant fuzzy commutative ideals in BCK-algebras. Finally, he proved some conditions for a uni-hesitant fuzzy ideal to be a uni-hesitant fuzzy commutative ideal.

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