Fuzzy filters of Sheffer stroke Hilbert algebras

2021 ◽  
Vol 40 (1) ◽  
pp. 759-772
Author(s):  
Tahsin Oner ◽  
Tugce Katican ◽  
Arsham Borumand Saeid
Keyword(s):  
Cartesian Product ◽  
Hilbert Algebra ◽  
Fuzzy Filter ◽  
Hilbert Algebras ◽  
Sheffer Stroke ◽  
Fuzzy Filters

The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. Some fuzzy filters of a Sheffer stroke Hilbert algebra are defined by a homomorphism. Normal and maximal fuzzy filters of a Sheffer stroke Hilbert algebra and the relation between them are presented. By giving the Cartesian product of fuzzy filters of a Sheffer stroke Hilbert algebra, various properties are examined.

scholarly journals Square-integrable representations of non-unimodular groups

1976 ◽  
Vol 15 (1) ◽  
pp. 1-12 ◽  
Author(s):  
A.L. Carey
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Hilbert Algebra ◽  
Technical Tool ◽  
Integrable Representation ◽  
Hilbert Algebras ◽  
Orthogonality Relations ◽  
Square Integrable Representation ◽  
Main Technical Tool

In the last three years a number of people have investigated the orthogonality relations for square integrable representations of non-unimodular groups, extending the known results for the unimodular case. The results are stated in the language of left (or generalized) Hilbert algebras. This paper is devoted to proving the orthogonality relations without recourse to left Hilbert algebra techniques. Our main technical tool is to realise the square integrable representation in question in a reproducing kernel Hilbert space.

scholarly journals Generalizations of(∈,∈∨q)-Fuzzy Filters inR0-Algebras

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Young Bae Jun ◽  
Seok Zun Song ◽  
Jianming Zhan
Keyword(s):  
Fuzzy Filter ◽  
Fuzzy Filters

Generalizations of a part of the paper (Ma et al., 2009) are considered. As a generalization of an(∈,∈∨q)-fuzzy filter, the notion of an(∈,∈∨qk)-fuzzy filter is introduced, and its characterizations are provided. The implication-based fuzzy filters of anR0-algebra are discussed.

Fuzzy filters of BE-algebras

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Grzegorz Dymek ◽  
Andrzej Walendziak
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Filter ◽  
Fuzzy Filters

AbstractCharacterizations of fuzzy filters in a BE-algebra are established. Conditions for a fuzzy set to be a fuzzy filter are given. For a fuzzy set µ the least fuzzy filter containing µ is constructed. The homomorphic properties of fuzzy filters of a BE-algebra are provided. Finally, characterizations of Noetherian BE-algebras and Artinian BE-algebras via fuzzy filters are obtained.

Implicational formulas in intuitionistic logic

1974 ◽  
Vol 39 (4) ◽  
pp. 661-664 ◽  
Author(s):  
Alasdair Urquhart
Keyword(s):  
Propositional Calculus ◽  
Modus Ponens ◽  
Equivalence Classes ◽  
Alternative Proof ◽  
Hilbert Algebra ◽  
Hilbert Algebras ◽  
Free Generators ◽  
Finite Set ◽  
Image Position ◽  
The Right

In [1] Diego showed that there are only finitely many nonequivalent formulas in n variables in the positive implicational propositional calculus P. He also gave a recursive construction of the corresponding algebra of formulas, the free Hilbert algebra In on n free generators. In the present paper we give an alternative proof of the finiteness of In, and another construction of free Hilbert algebras, yielding a normal form for implicational formulas. The main new result is that In is built up from n copies of a finite Boolean algebra. The proofs use Kripke models [2] rather than the algebraic techniques of [1].Let V be a finite set of propositional variables, and let F(V) be the set of all formulas built up from V ⋃ {t} using → alone. The algebra defined on the equivalence classes , by settingis a free Hilbert algebra I(V) on the free generators . A set T ⊆ F(V) is a theory if ⊦pA implies A ∈ T, and T is closed under modus ponens. For T a theory, T[A] is the theory {B ∣ A → B ∈ T}. A theory T is p-prime, where p ∈ V, if p ∉ T and, for any A ∈ F(V), A ∈ T or A → p ∈ T. A theory is prime if it is p-prime for some p. Pp(V) denotes the set of p-prime theories in F(V), P(V) the set of prime theories. T ∈ P(V) is minimal if there is no theory in P(V) strictly contained in T. Where X = {A1, …, An} is a finite set of formulas, let X → B be A1 →····→·An → B (ϕ → B is B). A formula A is a p-formula if p is the right-most variable occurring in A, i.e. if A is of the form X → p.

scholarly journals Tuning of Fuzzy Sharpening Filters for Biomedical Image Enhancement

MENDEL ◽  
2019 ◽  
Vol 24 (1) ◽  
pp. 121-128
Author(s):  
Jaromir Kukal ◽  
Abduljalil Sireis ◽  
Zuzana Krbcova
Keyword(s):  
Signal To Noise Ratio ◽  
Fuzzy Filter ◽  
Image Smoothing ◽  
Signal To Noise ◽  
Tomographic Images ◽  
Biomedical Image ◽  
Linear Behavior ◽  
Ratio Criterion ◽  
Low Pass ◽  
Fuzzy Filters

Various approaches are used for image smoothing and sharpening. The class of fuzzy filters is widely used in the case of spiky noise due to their non–linear behavior. A lot of popular fuzzy filters are realizable in Lukasiewicz algebra with square root. Frequently applied low-pass fuzzy filters were selected from literature and used for the image sharpening with dyadic weights. The first aim of the paper is to find the optimum sharpening with the best Signal–to–Noise Ratio criterion for various noise types and offer general suggestions for fuzzy filter selection. Our results are directly applicable to tomographic images from MRI, PET and SPECT scanners.

scholarly journals A NEW VIEW OF FUZZY ORDERED SEMIGROUPS

2018 ◽  
Vol 1 (1) ◽  
pp. 9-17
Author(s):  
Hidayat Ullah Khan ◽  
Asghar Khan ◽  
Faiz Muhammad Khan ◽  
Amir Khan ◽  
Muhammad Taj
Keyword(s):  
Coding Theory ◽  
State Machines ◽  
Ordered Semigroup ◽  
Fuzzy Filter ◽  
Fuzzy Coding ◽  
Finite State ◽  
Fuzzy Subgroup ◽  
Characterization Theorems ◽  
Fuzzy Filters ◽  
Interval Valued

fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an interval-valued -fuzzy filter of an ordered semigroup, where with. Since the concept of an interval-valued -fuzzy filter is an important and useful generalization of the ordinary interval-valued fuzzy filter, we discuss some fundamental aspects of an interval-valued -fuzzy filters. An interval-valued -fuzzy filter is a generalization of the existing concept of an interval-valued fuzzy filter. We discuss the concept of an interval-valued -fuzzy left (right)-filters and provide some characterization theorems. Finally, we extend the concept of an interval-valued fuzzy subgroup with thresholds to the concept of an interval-valued fuzzy left (right)-filter with thresholds of s.

scholarly journals μ -Fuzzy Filters in Distributive Lattices

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wondwosen Zemene Norahun
Keyword(s):  
Distributive Lattice ◽  
Special Class ◽  
Distributive Lattices ◽  
Fuzzy Filter ◽  
One To One ◽  
Fuzzy Filters

In this paper, we introduce the concept of μ -fuzzy filters in distributive lattices. We study the special class of fuzzy filters called μ -fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators. We observe that every μ -fuzzy filter is the intersection of all prime μ -fuzzy filters containing it. We also topologize the set of all prime μ -fuzzy filters of a distributive lattice. Properties of the space are also studied. We show that there is a one-to-one correspondence between the class of μ -fuzzy filters and the lattice of all open sets in X μ . It is proved that the space X μ is a T 0 space.

scholarly journals On GE-Algebras

2020 ◽  
Author(s):  
Ravikumar Bandaru ◽  
Arsham Borumand Saeid ◽  
Young Bae Jun
Keyword(s):  
Intuitionistic Logic ◽  
Algebraic Structure ◽  
Classical Logic ◽  
Hilbert Algebra ◽  
Hilbert Algebras ◽  
Exchange Algebra ◽  
Generalized Exchange

Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.

scholarly journals On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Rajesh K. Thumbakara
Keyword(s):  
Frame Theory ◽  
Fuzzy Filter ◽  
Intuitionistic Fuzzy ◽  
Open Set ◽  
Fuzzy Filters ◽  
The Given

Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes.

scholarly journals Fuzzy Filters of Hoops Based on Fuzzy Points

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 430 ◽  
Author(s):  
Mona Aaly Kologani ◽  
Mohammad Mohseni Takallo ◽  
Hee Sik Kim
Keyword(s):  
Congruence Relation ◽  
Fuzzy Filter ◽  
Fuzzy Filters

In this paper, we define the concepts of ( ∈ , ∈ ) and ( ∈ , ∈ ∨ q ) -fuzzy filters of hoops, discuss some properties, and find some equivalent definitions of them. We define a congruence relation on hoops by an ( ∈ , ∈ ) -fuzzy filter and show that the quotient structure of this relation is a hoop.

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