scholarly journals The Measure of Fuzzy Filters on BL-Algebras

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiang Zhu ◽  
Md Gapar Md Johar ◽  
Lilysuriazna Binti Raya ◽  
Zu-hua Liao
Keyword(s):  
Direct Products ◽  
Fuzzy Filter ◽  
Fuzzy Subset ◽  
Implication Operator ◽  
Fuzzy Filters ◽  
The Relationship ◽  
Fuzzy Subsets

The new concept of the fuzzy filter degree was given by means of the implication operator, which enables to measure a degree to which a fuzzy subset of a BL-algebra is a fuzzy filter. In this paper, we put forward several equivalent characterizations of the fuzzy filter degree by studying its properties and the relationship with level cut sets. Furthermore, we study the fuzzy filter degrees of the intersection and fuzzy direct products of fuzzy subsets and investigate the fuzzy filter degrees of the image and the preimage of a fuzzy subset under a homomorphism.

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.

scholarly journals Coherency and Constructions for Monoids

2020 ◽  
Vol 71 (4) ◽  
pp. 1461-1488
Author(s):  
Yang Dandan ◽  
Victoria Gould ◽  
Miklós Hartmann ◽  
Nik Ruškuc ◽  
Rida-E Zenab
Keyword(s):  
Finiteness Condition ◽  
Direct Products ◽  
Finitely Generated ◽  
Rees Matrix Semigroups ◽  
The Relationship ◽  
Brandt Semigroups ◽  
Finitely Presented ◽  
Matrix Semigroups

Abstract A monoid S is right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. This is a finiteness condition, and we investigate whether or not it is preserved under some standard algebraic and semigroup theoretic constructions: subsemigroups, homomorphic images, direct products, Rees matrix semigroups, including Brandt semigroups, and Bruck–Reilly extensions. We also investigate the relationship with the property of being weakly right noetherian, which requires all right ideals of S to be finitely generated.

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.

scholarly journals The Interaction between Fuzzy Subsets and Groupoids

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Seung Joon Shin ◽  
Hee Sik Kim ◽  
J. Neggers
Keyword(s):  
Binary System ◽  
Fuzzy Subset ◽  
Linear Combinations ◽  
Real Linear ◽  
Fuzzy Subsets

We discuss properties of a class of real-valued functions on a setX2constructed as finite (real) linear combinations of functions denoted asX,*;μ, whereX,*is a groupoid (binary system) andμis a fuzzy subset ofXand whereX,*;μx,y≔μx*y-minμx,μy. Many properties, for example,μbeing a fuzzy subgroupoid ofX,*, can be restated as some properties ofX,*;μ. Thus, the context provided opens up ways to consider well-known concepts in a new light, with new ways to prove known results as well as to provide new questions and new results. Among these are identifications of many subsemigroups and left ideals ofBinX;□for example.

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 characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets

2017 ◽  
Vol 26 (1) ◽  
pp. 46-56
Author(s):  
Niovi Kehayopulu
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Subset ◽  
Fuzzy Subsets

Abstract We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f ≼ f ο 1 ο f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f ≼1 ο f ο f ο 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f (resp. f ≼ f ο 1 ο f ο 1) and it is semisimple if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f ο 1. The characterization of regular and intra-regular hypersemigroups in terms of fuzzy subsets are very useful for applications.

scholarly journals ANTI SUBGRUP α-FUZZY

2020 ◽  
Vol 14 (1) ◽  
pp. 10
Author(s):  
Fiqriani Noor ◽  
Saman Abdurrahman ◽  
Naimah Hijriati
Keyword(s):  
Normal Subgroup ◽  
Group Structure ◽  
Normal Subgroups ◽  
Fuzzy Subset ◽  
New Concepts ◽  
Fuzzy Algebra ◽  
Sufficient And Necessary Conditions ◽  
Fuzzy Subgroup ◽  
Fuzzy Subgroups ◽  
The Relationship

The concept of fuzzy subgroups is a combination of the group structure with the fuzzy set, which was first introduced by Rosenfeld (1971). This concept became the basic concept in other the fuzzy algebra fields such as fuzzy normal subgroups, anti fuzzy subgroups and anti fuzzy normal subgroups. The development in the area of fuzzy algebra is characterized by the continual emergence of new concepts, one of which is the α-anti fuzzy subgroup concept. The idea of α-anti fuzzy subgroups is a combination between the α-anti fuzzy subset and anti fuzzy subgroups. The α-anti subset fuzzy which is an anti fuzzy subgroup is called as α-anti fuzzy subgroup. The purpose of this study is to prove that the α-anti fuzzy subset is an anti fuzzy subgroup, examine the relationship between α-anti fuzzy subgroups with anti fuzzy subgroups and α-fuzzy normal subgroups with anti fuzzy subgroups. The results of this study are, if A is an anti fuzzy subgroup (an anti fuzzy normal subgroup), then an α-anti subset fuzzy of A is an anti fuzzy subgroup (an anti fuzzy normal subgroup). However, this does not apply otherwise. Furthermore, this study also provides sufficient and necessary conditions for an α-anti fuzzy subset of any group to be an α-anti fuzzy subgroup and the formation of a group of factors that are built from an α-anti fuzzy normal subgroup.Keywords : Anti Fuzzy Subgroup, Anti Fuzzy Normal Subgroup, α-Anti Fuzzy Subgroup and α-Anti Fuzzy Normal Subgroup.

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 Residual quotient fuzzy subset in near-rings

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
P. Dheena ◽  
S. Coumaressane
Keyword(s):  
Fuzzy Subset ◽  
Fuzzy Subsets

For any fuzzy subsetsλandμ, we introduce the notion of residual quotient fuzzy subset (λ:μ) and we have characterized residual quotient fuzzy subset in near-rings.

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