We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the...We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).展开更多
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.展开更多
In general,ordered algebraic structures,particularly ordered semigroups,play an important role in fuzzification in many applied areas,such as computer science,formal languages,coding theory,error correction,etc.Nowada...In general,ordered algebraic structures,particularly ordered semigroups,play an important role in fuzzification in many applied areas,such as computer science,formal languages,coding theory,error correction,etc.Nowadays,the concept of ambiguity is important in dealing with a variety of issues related to engineering modeling problems,network theory,decision-making problems in real-life situations,and so on.Several theories have been developed by various researchers to overcome the difficulties that arise from uncertainty,including fuzzy sets,intuitionistic fuzzy sets,probability,softsets,neutrosophic sets,andmanymore.Inthispaper,we focus solelyonneutrosophic set theory.In ordered semigroups,we define and investigate the properties of neutrosophicκ-ideals and neutrosophicκ-interior ideals.We also use neutrosophicκ-ideals and neutrosophicκ-interior ideals to characterize ordered semigroups.展开更多
In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In...In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.展开更多
Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interi...Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal） by using some binary relations on S.展开更多
This paper obtains a group of necessary and sufficient conditions which guarantee a closed linear operator A to be the complete infinitesimal generator of an analytic semigroup of growth order α.
In this paper, we establish a structure theorem of naturally ordered rpp semigroups with max-idempotents. Results on naturally ordered semigroups with max- idempotents in the literature are extended and amplified. Som...In this paper, we establish a structure theorem of naturally ordered rpp semigroups with max-idempotents. Results on naturally ordered semigroups with max- idempotents in the literature are extended and amplified. Some previous results obtained by Blyth, McFadden, Cuo and Xie on regular and abundant ordered semigroups are ex- tended to ordered roo semigrouos.展开更多
The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen has introduced the concept of the F-semigroups. We can see that any ...The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen has introduced the concept of the F-semigroups. We can see that any semigroup can be considered as a F-semigroup. In this paper, we introduce and characterize the concept of the regular congruences OnE ordered F-semigroups and prove the following statements on an ordered F-semigroup M： （1） Every ordered semilattice congruences is a regular congruence. （2） There exists the least regular order on the F-semigroup M/p with respect to a regular congruence p on M. （3） The regular congruences are not ordered semilattice congruences in general.展开更多
Which subset of an ordered semigroup S can serve as a congruence class of certain order-congruence on S is an important problem. XIE Xiangyun proved that if every ideal C of an ordered semigroup S is a congruence clas...Which subset of an ordered semigroup S can serve as a congruence class of certain order-congruence on S is an important problem. XIE Xiangyun proved that if every ideal C of an ordered semigroup S is a congruence class of one order-congruence on S, then C is convex and when C is strongly convex, the reverse statement is true in 2001. In this paper, we give an alternative constructing order congruence method, and we prove that every ideal B is a congruence class of one order congruence on S if and only if B is convex. Furthermore, we show that the order relation defined by this method is "the least" order congruence containing B as a congruence class.展开更多
文摘We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.
基金The authors are grateful to the anonymous referees for careful checking of the details and for helpful comments that improved this paper.This work was supported by the Taif University Researchers Supporting Project(TURSP-2020/246),Taif University,Taif,Saudi Arabia.
文摘In general,ordered algebraic structures,particularly ordered semigroups,play an important role in fuzzification in many applied areas,such as computer science,formal languages,coding theory,error correction,etc.Nowadays,the concept of ambiguity is important in dealing with a variety of issues related to engineering modeling problems,network theory,decision-making problems in real-life situations,and so on.Several theories have been developed by various researchers to overcome the difficulties that arise from uncertainty,including fuzzy sets,intuitionistic fuzzy sets,probability,softsets,neutrosophic sets,andmanymore.Inthispaper,we focus solelyonneutrosophic set theory.In ordered semigroups,we define and investigate the properties of neutrosophicκ-ideals and neutrosophicκ-interior ideals.We also use neutrosophicκ-ideals and neutrosophicκ-interior ideals to characterize ordered semigroups.
基金The NSF (10961014) of Chinathe NSF (S2011010003681) of Guangdong Province+3 种基金the Science and Technology Projects (2010B010600039) of Guangdong Provincethe Excellent Youth Talent Foundation (2012SQRL115ZD) of Anhui Provincethe University Natural Science Project (KJ2012B133) of Anhui Provincethe NSF (2007LZ01) of Fuyang Normal College
文摘In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.
基金Supported by the National Natural Science Foundation of China (Grant No.10961014)the Natural Science Foundation of Guangdong Province (Grant No.0501332)+1 种基金the Excellent Youth Talent Foundation of Anhui Province(Grant No.2009SQRZ149)the Youth Foundation of Fuyang Normal College (Grant No.2008LQ11)
文摘Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal） by using some binary relations on S.
文摘This paper obtains a group of necessary and sufficient conditions which guarantee a closed linear operator A to be the complete infinitesimal generator of an analytic semigroup of growth order α.
文摘In this paper, we establish a structure theorem of naturally ordered rpp semigroups with max-idempotents. Results on naturally ordered semigroups with max- idempotents in the literature are extended and amplified. Some previous results obtained by Blyth, McFadden, Cuo and Xie on regular and abundant ordered semigroups are ex- tended to ordered roo semigrouos.
文摘The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen has introduced the concept of the F-semigroups. We can see that any semigroup can be considered as a F-semigroup. In this paper, we introduce and characterize the concept of the regular congruences OnE ordered F-semigroups and prove the following statements on an ordered F-semigroup M： （1） Every ordered semilattice congruences is a regular congruence. （2） There exists the least regular order on the F-semigroup M/p with respect to a regular congruence p on M. （3） The regular congruences are not ordered semilattice congruences in general.
基金the National Natural Science Foundation of China (Nos.10626012 103410020)+2 种基金the Jiangsu Planned for Postdoctoral Research Found (No.0502022B)the Natural Science Foundation of Guangdong Province (No.0501332)the Educational Department Natural Science Foundation of Guangdong Province (No.Z03070)
文摘Which subset of an ordered semigroup S can serve as a congruence class of certain order-congruence on S is an important problem. XIE Xiangyun proved that if every ideal C of an ordered semigroup S is a congruence class of one order-congruence on S, then C is convex and when C is strongly convex, the reverse statement is true in 2001. In this paper, we give an alternative constructing order congruence method, and we prove that every ideal B is a congruence class of one order congruence on S if and only if B is convex. Furthermore, we show that the order relation defined by this method is "the least" order congruence containing B as a congruence class.
