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.

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.

BI-IDEALS OF ORDERED SEMIGROUPS BASED ON THE INTERVAL-VALUED FUZZY POINT

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Hidayat Ullah Khan ◽  
Nor Haniza Sarmin ◽  
Asghar Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Fuzzy Set Theory ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
Interval Valued ◽  
Real World Problems

Interval-valued fuzzy set theory (advanced generalization of Zadeh's fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, we introduce the notion of generalized quasi-coincident with () relation of an interval-valued fuzzy point with an interval-valued fuzzy set. In fact, this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. Applying this newly defined idea, the notion of an interval-valued -fuzzy bi-ideal is introduced. Moreover, some characterizations of interval-valued -fuzzy bi-ideals are described. It is shown that an interval-valued -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. Finally, the concept of implication-based interval-valued fuzzy bi-ideals, characterizations of an interval-valued fuzzy bi-ideal and an interval-valued -fuzzy bi-ideal are considered. 

scholarly journals New fuzzy generalized bi Γ-ideals of the type (∈,∈∨qk) in ordered Γ-semigroups

2017 ◽  
Vol 13 (4) ◽  
pp. 6666-670
Author(s):  
Ibrahim Gambo ◽  
Nor Haniza Sarmin ◽  
Hidayat Ullah Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Characteristic Function ◽  
Real Number ◽  
Fuzzy Set ◽  
Unit Interval ◽  
Membership Functions ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
The Past ◽  
Fuzzy Point

A fuzzy subset A defined on a set X is represented as A = {(x, A (x), where x ∈ X}. It is not always possible for membership functions of type λA : X → [0,1] to associate with each point x in a set X a real number in the closed unit interval [0,1] without the loss of some useful information. The importance of the ideas of “belongs to” (∈) and “quasi coincident with” (q) relations between a fuzzy point and fuzzy set is evident from the research conducted during the past two decades. Ordered Γ-semigroup (generalization of ordered semigroups) play an important role in the broad study of ordered semigroups. In this paper, we provide an extension of fuzzy generalized bi Γ-ideals and introduce (∈,∈∨qk)-fuzzy generalized bi Γ-ideals of ordered Γ-semigroup. The purpose of this paper is to link this new concept with ordinary generalized bi Γ-ideals by using level subset and characteristic function.

Novel Approaches to Low-Voltage Scanning Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 366-367
Author(s):  
Arthur V. Jones
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Low Voltage ◽  
Electron Optics ◽  
Current Interest ◽  
New Concepts ◽  
Opportune Time ◽  
Novel Approaches ◽  
Voltage Scanning ◽  
Scanning Electron

In comparison with the developers of other forms of instrumentation, scanning electron microscope manufacturers are among the most conservative of people. New concepts usually must wait many years before being exploited commercially. The field emission gun, developed by Albert Crewe and his coworkers in 1968 is only now becoming widely available in commercial instruments, while the innovative lens designs of Mulvey are still waiting to be commercially exploited. The associated electronics is still in general based on operating procedures which have changed little since the original microscopes of Oatley and his co-workers.The current interest in low-voltage scanning electron microscopy will, if sub-nanometer resolution is to be obtained in a useable instrument, lead to fundamental changes in the design of the electron optics. Perhaps this is an opportune time to consider other fundamental changes in scanning electron microscopy instrumentation.

New Concepts in Congenital Deafness

1971 ◽  
Vol 4 (2) ◽  
pp. 431-443
Author(s):  
LaVonne Bergstrom ◽  
Janet Stewart
Keyword(s):  
Congenital Deafness ◽  
New Concepts

The Black Swan: Yeats and the Science of the Unknown

2017 ◽  
Vol 47 (2) ◽  
pp. 350-359
Author(s):  
Aoife Lynch
Keyword(s):  
Twentieth Century ◽  
Scientific Theory ◽  
Black Swan ◽  
Max Planck ◽  
Universal History ◽  
New Concepts ◽  
Wave Particle Duality ◽  
Paradigmatic Change

This essay views science as a creative mask for the poetry and philosophy of W.B. Yeats. It explores the changing worldview which occurred at the beginning of the twentieth century with the discovery of wave-particle duality by Max Planck in 1900. It considers the new concepts of reality which arose at this time in relation to modernism and Yeats's response to the paradigmatic change of era he was a part of. Accordingly, the poet's understanding of universal history in A Vision (1925, 1937) is used alongside close readings of his poetry to evince an argument which unites that poetry with philosophy, scientific theory, and modernism as aspects of one universe of knowledge which refracts different aspects of itself through the prism of time.

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