scholarly journals On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups

2022 ◽  
Vol 40 ◽  
pp. 1-13
Author(s):  
Mohammed M. Khalaf ◽  
Faisal Yousafzai ◽  
Muhammed Danish Zia
Keyword(s):  
Structural Properties ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Regular Class ◽  
Associative Law ◽  
Generalized Ideals

An ordered AG-groupoid can be referred to as a non-associativeordered semigroup, as the main di¤erence between an ordered semigroup and anordered AG-groupoid is the switching of an associative law. In this paper, wede…ne the smallest left (right) ideals in an ordered AG-groupoid and use them tocharacterize a (2; 2)-regular class of a unitary ordered AG-groupoid along with itssemilattices and (2 ;2 _q)-fuzzy left (right) ideals. We also give the conceptof an ordered A*G**-groupoid and investigate its structural properties by usingthe generated ideals and (2 ;2 _q)-fuzzy left (right) ideals. These concepts willverify the existing characterizations and will help in achieving more generalizedresults in future works.

scholarly journals A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Venus Amjid ◽  
Faisal Yousafzai ◽  
Kostaq Hila
Keyword(s):  
Structural Properties ◽  
Ordered Semigroup ◽  
Regular Class ◽  
Strongly Regular ◽  
Associative Law

An ordered AG-groupoid can be referred to as an ordered left almost semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an ordered AG-groupoid and use them to characterize a strongly regular class of a unitary ordered AG-groupoid along with its semilattices and fuzzy one-sided ideals. We also introduce the concept of an orderedAG⁎⁎⁎-groupoid and investigate its structural properties by using the generated ideals and fuzzy one-sided ideals. These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.

scholarly journals Fuzzy ideals of ordered semigroups with fuzzy orderings

2016 ◽  
Vol 14 (1) ◽  
pp. 841-856
Author(s):  
Xiaokun Huang ◽  
Qingguo Li
Keyword(s):  
Fuzzy Relation ◽  
Lattice Structures ◽  
Ordered Semigroup ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
Fuzzy Orderings

AbstractThe purpose of this paper is to introduce the notions of ∈, ∈ ∨qk-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨qk-fuzzy left (resp. right) ideals and ∈, ∈ ∨qk-fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨qk-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨qk-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of ∈, ∈ ∨qk-fuzzy ideals (resp. ∈, ∈ ∨qk-fuzzy interior ideals) are developed.

scholarly journals A Non-associative Ordered Semigroup Characterizated by Anti fuzzy Interior Ideals

2020 ◽  
Vol 13 (1) ◽  
pp. 113-129
Author(s):  
Nasreen Kausar ◽  
Meshari Alesemi ◽  
Salahuddin .
Keyword(s):  
Ordered Semigroup ◽  
Ordered Semigroups

The purpose of this paper is to investigate, the characterizations of different classes of non-associative ordered semigroups by using anti fuzzy left (resp. right, interior) ideals.

scholarly journals Sums and products of intervals in ordered semigroups

2021 ◽  
Vol 29 (2) ◽  
pp. 187-198
Author(s):  
T. Glavosits ◽  
Zs. Karácsony
Keyword(s):  
Real Line ◽  
Ordered Semigroup ◽  
Translation Invariant ◽  
Famous Theorem ◽  
Ordered Semigroups ◽  
The Real ◽  
Ordered Ring

Abstract We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b. The multiplicative version of the above example is shown too. The product of open intervals in the ordered ring of all integers (denoted by ℤ) is also investigated. Let Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ by g ( x ) : = max { y ∈ ℤ + | I y ⊆ I x ⋅ I x } g\left( x \right): = \max \left\{ {y \in {\mathbb{Z}_ + }|{I_y} \subseteq {I_x} \cdot {I_x}} \right\} for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev. Finally, we formulate some questions concerning the above topics.

scholarly journals CHARACTERIZATION OF ORDERED SEMIGROUPS BASED 0N (|;qk)-QUASI-COINCIDENT WITH RELATION

2021 ◽  
pp. 1157
Author(s):  
Faiz Muhammad Khan ◽  
Nie Yufeng ◽  
Madad Khan ◽  
Weiwei Zhang
Keyword(s):  
Characteristic Functions ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Completely Regular

Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (2;2_(|;qk))fuzzy bi-ideals of an ordered semigroup S: Further, upper/lower parts of (2;2 _(|;qk))-fuzzy bi-ideals of S are determined. Finally, some well known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (2;2_(|;qk))-fuzzy bi-ideals.

XIV.—On Isotone Homomorphic Boolean Images of Ordered Semigroups

1970 ◽  
Vol 68 (3) ◽  
pp. 211-228
Author(s):  
T. S. Blyth
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Necessary And Sufficient

SynopsisNecessary and sufficient conditions for an ordered semigroup to admit an isotone homomorphic Boolean image are given together with a complete description of how all such images are obtained. Also discussed are the situations arising from a strengthening of the notion of a homomorphism.

scholarly journals Characterizations of Regular Ordered Semigroups by (∈,∈∨(k∗,qk))-Fuzzy Quasi-Ideals

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 401 ◽  
Author(s):  
Ahsan Mahboob ◽  
Abdus Salam ◽  
Md. Firoj Ali ◽  
Noor Mohammad Khan
Keyword(s):  
Existence Theorems ◽  
Equivalent Condition ◽  
Ordered Semigroup ◽  
Ordered Semigroups

In this paper, some properties of the ( k ∗ , k ) -lower part of ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideals are obtained. Then, we characterize regular ordered semigroups in terms of its ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideals, ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy generalized bi-ideals, ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy left ideals and ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy right ideals, and an equivalent condition for ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy left (resp. right) ideals is obtained. Finally, the existence theorems for an ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideal as well as for the minimality of an ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideal of an ordered semigroup are provided.

scholarly journals The Archimedean property in an ordered semigroup

1968 ◽  
Vol 8 (3) ◽  
pp. 547-556 ◽  
Author(s):  
Tôru Saitô
Keyword(s):  
Positive Integer ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Simple Order ◽  
Archimedean Property ◽  
Image Position

By an ordered semigroup we mean a semigroup with a simple order which is compatible with the semigroup operation. Several authors, for example Alimov [1], Clifford [2], Conrad [4] and Hion [7], studied the archimedean property in some special kinds of ordered semigroups. For a general ordered semigroup, Fuchs [6] defined the archimedean equivalence as follows: a ~ b if and only if one of the four conditionsholds for some positive integer n.

Some New Concepts on int-soft Ideals in Ordered Semigroups

2021 ◽  
pp. 1-13
Author(s):  
G. Muhiuddina ◽  
Ebtehaj N. Alenzea ◽  
Ahsan Mahboobb ◽  
Anas Al-Masarwahc
Keyword(s):  
Soft Set ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Basic Properties ◽  
New Concepts ◽  
Soft Point

In the present paper, we introduce some new notions on ordered semigroup. In fact, notion of a convex soft set in an ordered semigroup is introduced, and its basic properties are investigated. Moreover, we consider a characterization of a convex soft set. Furthermore, relations between a convex soft set and an int-soft [Formula: see text]-ideal (or, int-soft [Formula: see text]-ideal) are studied. Finally, int-soft [Formula: see text]-ideals (or, int-soft [Formula: see text]-ideals) generated by an ordered soft point are established.

scholarly journals Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Faiz Muhammad Khan ◽  
Nie Yufeng ◽  
Hidayat Ullah Khan ◽  
Bakht Muhammad Khan
Keyword(s):  
Applied Sciences ◽  
Characteristic Function ◽  
Ideal Theory ◽  
Ordered Semigroup ◽  
Algebraic Structures ◽  
Ordered Semigroups ◽  
Central Focus ◽  
Fuzzy Ideal ◽  
New Type

A new trend of using fuzzy algebraic structures in various applied sciences is becoming a central focus due to the accuracy and nondecoding nature. The aim of the present paper is to develop a new type of fuzzy subsystem of an ordered semigroup S. This new type of fuzzy subsystem will overcome the difficulties faced in fuzzy ideal theory of an ordered semigroup up to some extent. More precisely, we introduce ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals of S. These concepts are elaborated through appropriate examples. Further, we are bridging ordinary ideals and ∈,∈∨qkδ-fuzzy ideals of an ordered semigroup S through level subset and characteristic function. Finally, we characterize regular ordered semigroups in terms of ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals.

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