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 Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 992
Author(s):  
Hanan Alolaiyan ◽  
Halimah A. Alshehri ◽  
Muhammad Haris Mateen ◽  
Dragan Pamucar ◽  
Muhammad Gulzar
Keyword(s):  
Normal Subgroup ◽  
Fuzzy Sets ◽  
Classical Group ◽  
Machine Learning Algorithms ◽  
Normal Subgroups ◽  
Specific Complex ◽  
Alternative Conceptualization ◽  
Fuzzy Subgroup ◽  
Fuzzy Subgroups ◽  
Bipolar Fuzzy Sets

A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction of (α,β)-complex fuzzy sets and then define α,β-complex fuzzy subgroups. Furthermore, we prove that every complex fuzzy subgroup is an (α,β)-complex fuzzy subgroup and define (α,β)-complex fuzzy normal subgroups of given group. We extend this ideology to define (α,β)-complex fuzzy cosets and analyze some of their algebraic characteristics. Furthermore, we prove that (α,β)-complex fuzzy normal subgroup is constant in the conjugate classes of group. We present an alternative conceptualization of (α,β)-complex fuzzy normal subgroup in the sense of the commutator of groups. We establish the (α,β)-complex fuzzy subgroup of the classical quotient group and show that the set of all (α,β)-complex fuzzy cosets of this specific complex fuzzy normal subgroup form a group. Additionally, we expound the index of α,β-complex fuzzy subgroups and investigate the (α,β)-complex fuzzification of Lagrange’s theorem analog to Lagrange’ theorem of classical group theory.

scholarly journals On Structural Properties of ξ -Complex Fuzzy Sets and Their Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Aneeza Imtiaz ◽  
Umer Shuaib ◽  
Hanan Alolaiyan ◽  
Abdul Razaq ◽  
Muhammad Gulistan
Keyword(s):  
Normal Subgroup ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Quotient Group ◽  
Physical Situation ◽  
The Novel ◽  
Complex Fuzzy Set ◽  
Fuzzy Subgroup ◽  
Fuzzy Subgroups ◽  
Necessary And Sufficient

Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α , δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an ξ -complex fuzzy set is ξ -complex fuzzy subgroup. Furthermore, we extend the idea of ξ -complex fuzzy normal subgroup to define the quotient group of a group G by this particular ξ -complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of G by a specific normal subgroup G A ξ .

scholarly journals Complex Fuzzy Groups Based on Rosenfeld’s Approach

2021 ◽  
Vol 20 ◽  
pp. 368-377
Author(s):  
Eman A. Abuhijleh ◽  
Mourad Massa’deh ◽  
Amani Sheimat ◽  
Abdulazeez Alkouri
Keyword(s):  
Group Theory ◽  
Normal Subgroup ◽  
Fuzzy Sets ◽  
Unit Disk ◽  
Mathematical Tool ◽  
Membership Functions ◽  
Fuzzy Group ◽  
Fuzzy Subgroup ◽  
Fuzzy Subgroups

Complex fuzzy sets (CFS) generalize traditional fuzzy sets (FS) since the membership functions of CFS reduces to the membership functions of FS. FS values are always at [0, 1], unlike CFS which has values in the unit disk of C. This paper merges notion and concept in group theory and presents the notion of a complex fuzzy subgroup of a group. This proposed idea represents a more general and better optional mathematical tool as one of the approaches in the fuzzy group. However, this research defines the notion of complex fuzzy subgroupiod, complex fuzzy normal subgroup, and complex fuzzy left(right) ideal. Therefore, the lattice, homomorphic preimage, and image of complex fuzzy subgroupiod and ideal are introduced and studied its properties. Finally, complex fuzzy subgroups and their properties are presented and investigated

Product of Implication-Based Intuitionistic Fuzzy Semiautomatons over Finite Groups

2019 ◽  
Vol 15 (03) ◽  
pp. 503-515 ◽  
Author(s):  
M. Selvarathi
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Direct Product ◽  
Finite Groups ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Subgroup ◽  
Fuzzy Subgroups ◽  
A Finite Group

In this paper, Implication-based intuitionistic fuzzy semiautomaton (IB-IFSA) of a finite group is defined and investigated. The theory of an implication-based intuitionistic fuzzy kernel and implication-based intuitionistic fuzzy subsemiautomaton of an IB-IFSA over a finite group are formulated using the approach of implication-based intuitionistic fuzzy subgroup and implication-based intuitionistic fuzzy normal subgroup. The product of implication-based intuitionistic fuzzy subgroups is postulated and investigated. Further, direct product of implication-based intuitionistic fuzzy semiautomatons over the finite groups is elaborately studied. Fundamental properties concerning them are also dealt with.

scholarly journals SUBGRUP FUZZY ATAS SUATU GRUP

2014 ◽  
Vol 6 (1) ◽  
pp. 33
Author(s):  
Fatkhur Rozi ◽  
Ari Wardayani ◽  
Suroto Suroto
Keyword(s):  
Classical Group ◽  
Necessary Conditions ◽  
Fuzzy Subset ◽  
Sufficient And Necessary Conditions ◽  
Fuzzy Subgroup ◽  
Fuzzy Subsets

This paper discusses a fuzzy subgroup of a classical group. It’s constructed by defining fuzzy subsets and employing products and inverse notions on classical group. The result obtained is sufficient and necessary conditions for the fuzzy subset to be fuzzy subgroup.

New concepts on the structure of the neuronal networks: The miniaturization and hierarchical organization of the central nervous system*

1984 ◽  
Vol 4 (2) ◽  
pp. 93-98 ◽  
Author(s):  
Luigi F. Agnati ◽  
Kjell Fuxe
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Neuronal Networks ◽  
Hierarchical Organization ◽  
Memory Storage ◽  
Information Handling ◽  
New Concepts ◽  
The Central Nervous System ◽  
Local Circuits ◽  
The Relationship

The hypothesis is introduced that miniaturization of neuronal circuits in the central nervous system and the hierarchical organization of the various levels, where information handling can take place, may be the key to understand the enormous capability of the human brain to store engrams as well as its astonishing capacity to reconstruct and organize engrams and thus to perform highly sophisticated integrations. The concept is also proposed that in order to understand the relationship between the structural and functional plasticity of the central nervous system it is necessary to postulate the existence of memory storage at the network level, at the local circuit level, at the synaptic level, at the membrane level, and finally at the molecular level. Thus, memory organization is similar to the hierarchical organization of the various levels, where information handling takes place in the nervous system. In addition, each higher level plays a role in the reconstruction and organization of the engrams stored at lower levels. Thus, the trace of the functionally stored memory (i.e. its reconstruction and organization at various levels of storage) will depend not only on the chemicophysical changes in the membranes of the local circuits but also on the organization of the local circuits themselves and their associated neuronal networks.

scholarly journals Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1781
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Soft Sets ◽  
New Concepts ◽  
Bitopological Spaces ◽  
The Relationship ◽  
Soft Topological Space

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

scholarly journals Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

2011 ◽  
Vol 31 (6) ◽  
pp. 1835-1847 ◽  
Author(s):  
PAUL A. SCHWEITZER, S. J.
Keyword(s):  
Normal Subgroup ◽  
Compact Manifold ◽  
Normal Subgroups ◽  
Open Manifold ◽  
Open Manifolds ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

Fear, history, stigma, and bias in the COVID-19 pandemic

2020 ◽  
Vol 18 (7) ◽  
pp. 177-182
Author(s):  
Kevin Kupietz, PhD ◽  
Lesley Gray, MPH
Keyword(s):  
Emergency Management ◽  
Disease Outbreaks ◽  
Social Effects ◽  
Evidence Based ◽  
Stigma And Discrimination ◽  
Emergency Managers ◽  
Global Pandemic ◽  
New Concepts ◽  
History Of ◽  
The Relationship

Introduction: The greatest enemy of a global pandemic is not the virus itself, but the fear, rumor, and stigma that envelopes people. This article explores the context and history of fear and stigma relating to pandemic, summarizing key actions to mitigate the harms during an active pandemic.Method: Our article draws from accounts in literature and journalist accounts documenting the relationship between infectious diseases and major disease outbreaks that have garnered fear and stigmatization. Results: Fear, stigma, and discrimination are not new concepts for pandemics. These social effects run the risk of diverting attention from the presenting disease and government responses. Reactions to fear, stigma, and discrimination risk sabotaging effective efforts to contain, manage, and eradicate the disease.Conclusion: Emergency managers have an important role in dispelling myths, disseminating appropriate and evidence-based information without exacerbating fears. Knowledge about the roots of fear and bias along with a good understanding of historical plagues and pandemics is vital to ensure those in the field of emergency management can effectively manage irrational fears.

scholarly journals Generalized Fuzzy Interior Ideals in Abel Grassmann's Groupoids

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Asghar Khan ◽  
Young Bae Jun ◽  
Tahir Mahmood
Keyword(s):  
Fuzzy Subset ◽  
Fuzzy Point ◽  
New Concepts

Using the notion of a fuzzy point and its belongness to and quasicoincidence with a fuzzy subset, some new concepts of a fuzzy interior ideal in Abel Grassmann's groupoidsSare introduced and their interrelations and related properties are invesitigated. We also introduce the notion of a strongly belongness and strongly quasicoincidence of a fuzzy point with a fuzzy subset and characterize fuzzy interior ideals ofSin terms of these relations.

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