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Journal articles on the topic 'Fuzzy left (right) zero semigroup'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

A., M. Aminpour, and Seilani M. "Minimal Ideals and Minimal Idempotents in Some Compact Semigroups." Journal of Academic and Applied Studies 3, no. 9 (2013): 64. https://doi.org/10.5281/zenodo.1059032.

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Abstract In this paper we present an important new results for study of fuzzy semigroups (both algebric and topological), in particular, fuzzy compact right topological semigroups. Principal result are that every fuzzy compact Hausdorff right topological semigroup S&tilde; contains at least one minimal idempotent [theorem 4.1] and every fuzzy left (resp. fuzzy right) ideal contains a fuzzy minimal left (resp. right) ideal [corollary 4.2]. Mathematical Society Classification: 2010 MSC.18340.

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2

Khan, Madad, Feng Feng, and M. Nouman Aslam Khan. "On Minimal Fuzzy Ideals of Semigroups." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/475190.

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The present paper contains the sufficient condition of a fuzzy semigroup to be a fuzzy group using fuzzy points. The existence of a fuzzy kernel in semigroup is explored. It has been shown that every fuzzy ideal of a semigroup contains every minimal fuzzy left and every minimal fuzzy right ideal of semigroup. The fuzzy kernel is the class sum of minimal fuzzy left (right) ideals of a semigroup. Every fuzzy left ideal of a fuzzy kernel is also a fuzzy left ideal of a semigroup. It has been shown that the product of minimal fuzzy left ideal and minimal fuzzy right ideal of a semigroup forms a gr

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3

K.V.Naga Lakshmi, N.Srimannarayana, Srinivas Telikepalli, A. Gangadhara Rao,. "Fuzzy Simple Partially Ordered Γ- Semigroups". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, № 5 (2021): 842–45. http://dx.doi.org/10.17762/turcomat.v12i5.1492.

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In this paper, it is shown that and are respectively fuzzy left and fuzzy right ideals of S. S is a fuzzy left(right) simple po- Γ -semigroup ( ) .  It is proved that for any semi group S “TFAE” (1) S is left(right) simple po- Γ -semigroup. (2) S is a fuzzy left(right)simple Γ-semigroup.  The union of all proper fuzzy ideals of S is the only fuzzy maximal ideal of S ,where S is a PO -Γ-Semigroupwith 'e', unity.

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4

Abbasi, Mohammad Y., Aakif F. Talee, Sabahat A. Khan та Kostaq Hila. "A Hesitant Fuzzy Set Approach to Ideal Theory in Γ-Semigroups". Advances in Fuzzy Systems 2018 (2 вересня 2018): 1–6. http://dx.doi.org/10.1155/2018/5738024.

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We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hesitant fuzzy left (right and bi-) ideals. We introduce the hesitant fuzzy left (resp., right and two-sided) ideal, hesitant fuzzy bi-ideal, and hesitant fuzzy interior ideal in Γ-semigroup and study some properties of them. Finally, a characterization of a simple Γ-semigroup by means of a hesitant fuzzy simple Γ-semigroup is obtained.

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5

Rehman, Ubaid Ur, Tahir Mahmood, and Muhammad Naeem. "Bipolar complex fuzzy semigroups." AIMS Mathematics 8, no. 2 (2022): 3997–4021. http://dx.doi.org/10.3934/math.2023200.

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<abstract> <p>The notion of the bipolar complex fuzzy set (BCFS) is a fundamental notion to be considered for tackling tricky and intricate information. Here, in this study, we want to expand the notion of BCFS by giving a general algebraic structure for tackling bipolar complex fuzzy (BCF) data by fusing the conception of BCFS and semigroup. Firstly, we investigate the bipolar complex fuzzy (BCF) sub-semigroups, BCF left ideal (BCFLI), BCF right ideal (BCFRI), BCF two-sided ideal (BCFTSI) over semigroups. We also introduce bipolar complex characteristic function, positive $ \left(

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Asaad, Samah H., and Akram S. Mohammed. "New Properties of Anti Fuzzy Ideals of Regular Semigroups." Ibn AL-Haitham Journal For Pure and Applied Sciences 32, no. 3 (2019): 109–16. http://dx.doi.org/10.30526/32.3.2287.

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In this article, we study some properties of anti-fuzzy sub-semigroup, anti fuzzy left (right, two sided) ideal, anti fuzzy ideal, anti fuzzy generalized bi-ideal, anti fuzzy interior ideals and anti fuzzy two sided ideal of regular semigroup. Also, we characterized regular LA-semigroup in terms of their anti fuzzy ideal.

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7

MALTCEV, VICTOR. "CAYLEY AUTOMATON SEMIGROUPS." International Journal of Algebra and Computation 19, no. 01 (2009): 79–95. http://dx.doi.org/10.1142/s021819670900497x.

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In this paper we characterize when a Cayley automaton semigroup is finite, is free, is a left zero semigroup, is a right zero semigroup, is a group, or is trivial. We also introduce dual Cayley automaton semigroups and discuss when they are finite.

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8

Khan, Faiz Muhammad, Nie Yufeng, Hidayat Ullah Khan та Bakht Muhammad Khan. "Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals". Advances in Fuzzy Systems 2018 (10 червня 2018): 1–10. http://dx.doi.org/10.1155/2018/5304514.

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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 o

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9

Habib, Sana, Harish Garg, Yufeng Nie, and Faiz Muhammad Khan. "An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application." Mathematics 7, no. 12 (2019): 1183. http://dx.doi.org/10.3390/math7121183.

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The objective of this paper is put forward the novel concept of possibility fuzzy soft ideals and the possibility of fuzzy soft interior ideals. The various results in the form of the theorems with these notions are presented and further validated by suitable examples. In modern life decision-making problems, there is a wide applicability of the possibility fuzzy soft ordered semigroup which has also been constructed in the paper to solve the decision-making process. Elementary and fundamental concepts including regular, intra-regular and simple ordered semigroups in terms of possibility fuzzy

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10

Sanpan, Hataikhan, Pakorn Palakawong na Ayutthaya, and Somsak Lekkoksung. "On (m, n)-Fuzzy Sets and Their Application in Ordered Semigroups." International Journal of Analysis and Applications 23 (April 14, 2025): 90. https://doi.org/10.28924/2291-8639-23-2025-90.

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In this paper, we introduce the concepts of (m, n)-fuzzy subsemigroups, (m, n)-fuzzy left (right, two-sided, bi-, (1, 2)-) ideals of an ordered semigroup and some their algebraic properties are studied, thereafter the relationship among their (m, n)-fuzzy ideals was investigated. Moreover, we characterize left (resp., right, two-sided, bi-) ideals by using (m, n)-fuzzy left (resp., right, two-sided, bi-) ideals. Finally, we characterize regular ordered semigroups and intra-regular ordered semigroups in terms of (m, n)-fuzzy left ideals, (m, n)-fuzzy right ideals, and (m, n)-fuzzy bi-ideals.

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11

Et. al., Dr D. Mrudula Devi. "A characterization of Commutative Semigroups." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 5150–55. http://dx.doi.org/10.17762/turcomat.v12i3.2065.

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This paper deals with some results on commutative semigroups. We consider (s,.) is externally commutative right zero semigroup is regular if it is intra regular and (s,.) is externally commutative semigroup then every inverse semigroup is u – inverse semigroup. We will also prove that if (S,.) is a H - semigroup then weakly cancellative laws hold in H - semigroup. In one case we will take (S,.) is commutative left regular semi group and we will prove that (S,.) is ∏ - inverse semigroup. We will also consider (S,.) is commutative weakly balanced semigroup and then prove every left (right) regul

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12

Khalaf, Mohammed M., Faisal Yousafzai, and Muhammed Danish Zia. "On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups." Boletim da Sociedade Paranaense de Matemática 40 (January 1, 2022): 1–13. http://dx.doi.org/10.5269/bspm.42419.

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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. The

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13

Huang, Xiaokun, and Qingguo Li. "Fuzzy ideals of ordered semigroups with fuzzy orderings." Open Mathematics 14, no. 1 (2016): 841–56. http://dx.doi.org/10.1515/math-2016-0076.

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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

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14

Fındık, Şehmus, and Osman Kelekci̇. "Hausdorff series in a semigroup ring." International Journal of Algebra and Computation 30, no. 04 (2020): 853–59. http://dx.doi.org/10.1142/s0218196720500228.

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Let [Formula: see text] and [Formula: see text] be the semigroup rings spanned on the right zero semigroup [Formula: see text], and on the left zero semigroup [Formula: see text], respectively, together with the identity element [Formula: see text]. We suggest a closed formula solving the equation [Formula: see text] which is the evolution of the Campbell–Baker–Hausdorff formula given by the Hausdorff series [Formula: see text] where [Formula: see text], in the algebras [Formula: see text] and [Formula: see text].

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15

AUINGER, K., and T. E. HALL. "REPRESENTATIONS OF SEMIGROUPS BY TRANSFORMATIONS AND THE CONGRUENCE LATTICE OF AN EVENTUALLY REGULAR SEMIGROUP." International Journal of Algebra and Computation 06, no. 06 (1996): 655–85. http://dx.doi.org/10.1142/s0218196796000386.

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On any eventually regular semigroup S, congruences ν, μL, μR, μ, K, KL, KR, ζ are introduced which are the greatest congruences over: nil-extensions (n.e.) of completely simple semigroups, n.e. of left groups, n.e. of right groups, n.e. of groups, n.e. of rectangular bands, n.e. of left zero semigroups, n.e. of right zero semigroups, nil-semigroups, respectively. Each of these congruences is induced by a certain representation of S which is defined on an arbitrary semigroup. These congruences play an important role in the study of lattices of varieties, pseudovarieties and existence varieties.

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16

Sun, Yan. "On Semilattices of R-Ample Semigroups with Left Central Idempotents." Applied Mechanics and Materials 530-531 (February 2014): 617–20. http://dx.doi.org/10.4028/www.scientific.net/amm.530-531.617.

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In this article, the semilattice decomposition of r-ample semigroups with left central idempotents is given. By using this decomposition, we show that a semigroup is a r-ample semigroup with left central idempotents if and only if it is a strong semilattice of , where is a monoid and is a right zero band. As a corollary, the characterization theorem of Clifford semigroups is also extended from a strong semilattice of groups to a strong semilattice of right groups. These theories are the basis that the structure theorem of r-ample semigroups with left central idempotents can be established.

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17

Mahboob, Ahsan, Abdus Salam, Md Firoj Ali, and Noor Mohammad Khan. "Characterizations of Regular Ordered Semigroups by (∈,∈∨(k∗,qk))-Fuzzy Quasi-Ideals." Mathematics 7, no. 5 (2019): 401. http://dx.doi.org/10.3390/math7050401.

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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 mini

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18

Fleischer, Lukas, and Trevor Jack. "The complexity of properties of transformation semigroups." International Journal of Algebra and Computation 30, no. 03 (2019): 585–606. http://dx.doi.org/10.1142/s0218196720500125.

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We investigate the computational complexity for determining various properties of a finite transformation semigroup given by generators. We introduce a simple framework to describe transformation semigroup properties that are decidable in [Formula: see text]. This framework is then used to show that the problems of deciding whether a transformation semigroup is a group, commutative or a semilattice are in [Formula: see text]. Deciding whether a semigroup has a left (respectively, right) zero is shown to be [Formula: see text]-complete, as are the problems of testing whether a transformation se

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19

Nupo, Nuttawoot, and Sayan Panma. "Independent domination number in Cayley digraphs of rectangular groups." Discrete Mathematics, Algorithms and Applications 10, no. 02 (2018): 1850024. http://dx.doi.org/10.1142/s1793830918500246.

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Let [Formula: see text] denote the Cayley digraph of the rectangular group [Formula: see text] with respect to the connection set [Formula: see text] in which the rectangular group [Formula: see text] is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. An independent dominating set of [Formula: see text] is the independent set of elements in [Formula: see text] that can dominate the whole elements. In this paper, we investigate the independent domination number of [Formula: see text] and give more results on Cayley digraphs of left groups and righ

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20

Guo, Junying, and Xiaojiang Guo. "Algebras of right ample semigroups." Open Mathematics 16, no. 1 (2018): 842–61. http://dx.doi.org/10.1515/math-2018-0075.

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AbstractStrict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an alge

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21

Gutik, O. V., and K. M. Maksymyk. "On semitopological simple inverse $\omega$-semigroups with compact maximal subgroups." Carpathian Mathematical Publications 17, no. 1 (2025): 110–27. https://doi.org/10.15330/cmp.17.1.110-127.

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We describe the structure of ($0$-)simple inverse Hausdorff semitopological $\omega$-semigroups with compact maximal subgroups. In particular, we show that if $S$ is a simple inverse Hausdorff semitopological $\omega$-semigroup with compact maximal subgroups, then $S$ is topologically isomorphic to the Bruck-Reilly extension $\left(\mathbf{BR}(T,\theta),\tau_{\mathbf{BR}}^{\oplus}\right)$ of a finite semilattice $T=\left[E;G_\alpha,\varphi_{\alpha,\beta}\right]$ of compact groups $G_\alpha$ in the class of topological inverse semigroups, where $\tau_{\mathbf{BR}}^{\oplus}$ is the sum direct to

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22

Khan, Hidayat Ullah, Asghar Khan, Faiz Muhammad Khan, Amir Khan, and Muhammad Taj. "A NEW VIEW OF FUZZY ORDERED SEMIGROUPS." Open Journal of Science and Technology 1, no. 1 (2018): 9–17. http://dx.doi.org/10.31580/ojst.v1i1.150.

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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 so

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23

T. Muthuraji. "Semigroups on some new operations over intuitionistic fuzzy matrices." Malaya Journal of Matematik 8, no. 04 (2020): 2273–76. http://dx.doi.org/10.26637/mjm0804/0162.

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In this article, different kinds of component wise max-max operations are introduced on intuitionistic fuzzy matrix and some algebraic properties are studied together with the component wise \(\min -\min\left(\wedge_m\right)\) operation. Also some semigroup algebraic structures are constructed using these new operations on intuitionistic fuzzy matrices.

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Wendt, Gerhard. "Primitive Near-rings — Some Structure Theorems." Algebra Colloquium 14, no. 03 (2007): 417–24. http://dx.doi.org/10.1142/s1005386707000387.

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We show that any zero symmetric 1-primitive near-ring with descending chain condition on left ideals can be described as a centralizer near-ring in which the multiplication is not the function composition but sandwich multiplication. This result follows from a more general structure theorem on 1-primitive near-rings with multiplicative right identity, not necessarily having a chain condition on left ideals. We then use our results to investigate more closely the multiplicative semigroup of a 1-primitive near-ring. In particular, we show that the set of regular elements forms a right ideal of t

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KOLOGANI, MONA AALY, MOHAMMAD MOHSENI TAKALLO, RAJAB ALI BORZOOEI, and YOUNG BAE JUN. "Right and Left Mappings in Equality Algebras." Kragujevac Journal of Mathematics 46, no. 5 (2022): 815. http://dx.doi.org/10.46793/kgjmat2205.815k.

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The notion of (right) left mapping on equality algebras is introduced, and related properties are investigated. In order for the kernel of (right) left mapping to be ﬁlter, we investigate what conditions are required. Relations between left mapping and →-endomorphism are investigated. Using left mapping and →-endomorphism, a characterization of positive implicative equality algebra is established. By using the notion of left mapping, we deﬁne →-endomorphism and prove that the set of all →-endomorphisms on equality algebra is a commutative semigroup with zero element. Also, we show that the set

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26

KELEKCI, OSMAN. "Hausdorff series in semigroup rings of rectangular bands." Creative Mathematics and Informatics 32, no. 1 (2022): 49–54. http://dx.doi.org/10.37193/cmi.2023.01.06.

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"The Hausdorff series provides a solution to the equation $w=\log(e^ue^v)$ given by a recursive formula which can be expressed as nested commutators of $u$ and $v$. Evolutions of the Haussdorff series in various algebras and rings has been considered in obtaining a closed form of this formula. We consider the rectangular band $L_m\times R_n$ determined by the left zero semigroup $L_m$ and the right zero semigroup $R_n$ of order $m$ and $n$, respectively. Let $\mathbb R\langle L_m\times R_n\rangle$ be the semigroup ring spanned on $L_m\times R_n$ together with the identity element $1$. We provi

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27

Kausar, Nasreen, Meshari Alesemi, and Salahuddin . "A Non-associative Ordered Semigroup Characterizated by Anti fuzzy Interior Ideals." European Journal of Pure and Applied Mathematics 13, no. 1 (2020): 113–29. http://dx.doi.org/10.29020/nybg.ejpam.v13i1.3576.

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Kausar, Nasreen, Meshari Alesemi, and Salahuddin . "A Non-associative Ordered Semigroup Characterizated by Anti fuzzy Interior Ideals." European Journal of Pure and Applied Mathematics 13, no. 1 (2020): 113–29. http://dx.doi.org/10.29020/nybg.ejpam.v1i1.3576.

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Saleem, Kholoud W., Abir K. Salib, and Abrahim A. A.Tentush. "SEMIGROUPS IN TERMS OF INTUITIONISTIC FUZZY BI-IDEALS." EPH - International Journal of Applied Science 7, no. 1 (2021): 23–30. http://dx.doi.org/10.53555/eijas.v7i1.73.

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Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory. The concept of 'intuitionistic fuzzy set' (IFS) was introduced by Atanassov as a generalization of the concept fuzzy set by gives both a degree of membership and the degree of non-membership. As for fuzzy sets, the degree of membership is a real number between 0 and 1. This is also the case for the degree of non-membership, and further the sum of these two degrees is not greater than 1. Since fuzzy bi-ideal play a

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Linesawat, Krittika, and Somsak Lekkoksung. "A Study on Multi-Intuitionistic Fuzzy Sets and Their Application in Ordered Semigroups." International Journal of Analysis and Applications 23 (March 7, 2025): 63. https://doi.org/10.28924/2291-8639-23-2025-63.

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In this paper, we introduce the notion of multi-intuitionistic fuzzy sets in ordered semigroups. The concepts of multi-intuitionistic fuzzy subsemigroups, multi-intuitionistic fuzzy left (right, two-sided, interior) ideals of an ordered semigroup are introduced and some algebraic properties of multi-intuitionistic fuzzy subsemigroups and such their multi-intuitionistic fuzzy ideals are studied. Moreover, the relationships among their multi-intuitionistic fuzzy ideals are investigated. We prove that in regular, intra-regular, and semisimple ordered semigroups, the concepts of multi-intuitionist

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Zelenyuk, Yevhen. "Local Homomorphisms of Topological Groups." Journal of the Australian Mathematical Society 83, no. 1 (2007): 135–48. http://dx.doi.org/10.1017/s1446788700036430.

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AbstractA mapping f : G → s from a left topological group G into a semigroup S is a local homomorphism if for every x є G \ {e}, there is a neighborhood Ux of e such that f (xy) = f (x)f (y) for all y є Ux \ {e}. A local homomorphism f : G → S is onto if for every neighborhood U of e, f(U \ {e}) = S. We show that(1) every countable regular left topological group containing a discrete subset with exactly one accumulation point admits a local homomorphism onto N,(2) it is consistent that every countable topological group containing a discrete subset with exactly one accumulation point admits a l

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Pongpipat, Denpong, and Nuttawoot Nupo. "The Vertex Distance on Cayley Digraphs of Rectangular Groups with respect to the Cartesian Product Connection Sets." International Journal of Mathematics and Computer Science 20, no. 1 (2024): 123–30. http://dx.doi.org/10.69793/ijmcs/01.2025/nupo.

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A rectangular group S is a semigroup isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. The Cayley digraph Cay(S,A) of a finite rectangular group S with respect to a nonempty subset A of S is defined as a digraph with vertex set S and arc set consisting of ordered pairs (u,ua) in SxS for some a in A. The set A is called a connection set of Cay(S,A). Let u and v be in S. The distance from u to v in Cay(S,A), denoted by d(u,v), is the number of arcs in the shortest directed u-v path if one exists and is infinity otherwise. In this paper, we characteri

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Khan, Faiz Muhammad, Violeta Leoreanu-Fotea, Saifullah, and Amanullah. "A Benchmark Generalization of Fuzzy Soft Ideals in Ordered Semigroups." Analele Universitatii "Ovidius" Constanta - Seria Matematica 29, no. 2 (2021): 155–71. http://dx.doi.org/10.2478/auom-2021-0023.

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Abstract In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨qk )-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk )-fuzzy soft left(right) ideals. Some binary operations like ◦ λ , intersection ∩ λ and union of fuzzy soft sets ∪ λ are given and various fundamental results of ideal theory are developed throu

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Gambo, Ibrahim, Nor Haniza Sarmin, Hidayat Ullah Khan, and Muhammad Faiz Khan. "The characterization of regular ordered Gamma semigroups in terms of (E,EVq_k)-fuzzy Gamma ideals." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4 (2017): 576–80. http://dx.doi.org/10.11113/mjfas.v0n0.608.

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The advancement in the fascinating area of fuzzy set theory has become area of much interest, generalization of the existing fuzzy subsystems of other algebraic structures is very important to tackle more current real life problems. In this paper, we give more generalized form of regular ordered gamma semigroups in terms of (E,EVq_k)-fuzzy gamma ideals. Particularly, we characterized left regular, right regular, simple and completely regular ordered gamma semigroups in terms of this new notion. Some necessary and sufficient conditions for ordered gamma semigroup to be completely regular are pr

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Abdurrahman, Saman. "CROSS PRODUCT OF IDEAL FUZZY SEMIRING." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 2 (2023): 1131–38. http://dx.doi.org/10.30598/barekengvol17iss2pp1131-1138.

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If one of the axioms in the ring, namely the inverse axiom in the addition operation, is omitted, it will produce another algebraic structure, namely a semiring. Analogous to a ring, there are zero elements, ideal (left/right) in a semiring, and the cross product of the semiring ideal. The analog of the fuzzy semiring has zero elements, ideal (left/right), and the cross product of the semiring fuzzy ideal associated with the membership value. This paper will discuss the cross-product of two (more) fuzzy ideals from a semiring. Furthermore, the cross-product of two (more) fuzzy ideals from a se

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Bashir, Shahida, Medhit Fatima, and Muhammad Shabir. "Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals." Mathematics 7, no. 3 (2019): 233. http://dx.doi.org/10.3390/math7030233.

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Our main objective is to introduce the innovative concept of (α,ß)-bipolar fuzzy ideals and (α,ß)-bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set h = (S; hn, hp) in an ordered ternary semigroup S is the (∈,∈ ∨ q)-bipolar fuzzy generalized bi-ideal of S, it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the (

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Bashir, Shahida, Ahmad N. Al-Kenani, Maria Arif, and Rabia Mazhar. "A new method to evaluate regular ternary semigroups in multi-polar fuzzy environment." AIMS Mathematics 7, no. 7 (2022): 12241–63. http://dx.doi.org/10.3934/math.2022680.

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<abstract> <p>Theory of $m$-polar fuzzy set deals with multi-polar information. It is used when data comes from $m$ factors $\left({m \ge 2} \right)$. The primary objective of this work is to explore a generalized form of $m$-polar fuzzy subsemigroups, which is $m$-polar fuzzy ternary subsemigroups. There are many algebraic structures which are not closed under binary multiplication that is a reason to study ternary operation of multiplication such as the set of negative integer is closed under the operation of ternary multiplication but not closed for the binary multiplication. Th

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Mitsch, Heinz. "Quasiresiduals in Semigroups with Natural Partial Order." Algebra Colloquium 24, no. 03 (2017): 361–80. http://dx.doi.org/10.1142/s1005386717000220.

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A semigroup (S, ·) is called right (left) quasiresiduated if for any a, b in S there exists x in S such that ax ≤S b (xa ≤S b) with respect to the natural partial order ≤S of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right (left) simplicity of semigroups. It is first studied for totally-, resp., trivially-ordered semigroups, and then for semigroups with idempotents. In particular, the cases when (S, ≤S) is directed downwards and when S contains a zero (with respect to a more restrictive definition) are dealt with. Thr

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Azeef Muhammed, P. A., and A. R. Rajan. "Cross-connections of completely simple semigroups." Asian-European Journal of Mathematics 09, no. 03 (2016): 1650053. http://dx.doi.org/10.1142/s1793557116500534.

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A completely simple semigroup [Formula: see text] is a semigroup without zero which has no proper ideals and contains a primitive idempotent. It is known that [Formula: see text] is a regular semigroup and any completely simple semigroup is isomorphic to the Rees matrix semigroup [Formula: see text] (cf. D. Rees, On semigroups, Proc. Cambridge Philos. Soc. 36 (1940) 387–400). In the study of structure theory of regular semigroups, Nambooripad introduced the concept of normal categories to construct the semigroup from its principal left (right) ideals using cross-connections. A normal category

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Ebadi, M. J., M. Suleiman, Fudziah Bt Ismail, A. Ahmadian, M. R. Balooch Shahryari, and S. Salahshour. "A New Distance Measure for Trapezoidal Fuzzy Numbers." Mathematical Problems in Engineering 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/424186.

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We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and left/right spread of trapezoidal fuzzy numbers. Moreover, the metric properties of suggested distance measure are investigated. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right spreads go to zero, then two given fuzzy numbers are equal. Consequently, we complete discussion about the relation between fuzzy number and its centroid which is the firstly discussed by Hadi-Vencheh and All

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S., Subramanaian, and Nalini D. "CHARACTERIZATION OF COMPLEX BI FUZZY SOFT SET ON REGULAR SEMI GROUP." International Journal of Advanced Trends in Engineering and Technology 3, no. 1 (2018): 159–63. https://doi.org/10.5281/zenodo.1285145.

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In this article, we define a new structure of complex bi fuzzy soft left ideals (resp., right) of a semi group S, Union and Intersection of ideals is again ideals. Also, we prove the set of all idempotent elements of S from a right zero semi group of S, then C(x) = C(y) for all idempotents elements of x and y of S. If C<sub>1</sub> and C<sub>2 </sub>be a complex bi fuzzy soft left and right ideals of a semi group S, respectively, then C<sub>1</sub> * C<sub>2</sub>  C<sub>1</sub><sup> </sup>C<sub>2</sub><strong>.</strong> For every Complex bi fuzzy soft right ideal C<strong><sub>1</sub></s

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Kar, S., and I. Dutta. "Globally determined ternary semigroups." Asian-European Journal of Mathematics 10, no. 03 (2017): 1750038. http://dx.doi.org/10.1142/s1793557117500383.

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Let [Formula: see text] be the set of all nonempty subsets of a ternary semigroup [Formula: see text]. Then [Formula: see text] is a ternary semigroup with respect to the ternary multiplication defined by [Formula: see text] for all [Formula: see text]. If [Formula: see text] and [Formula: see text] are isomorphic ternary semigroups, then the corresponding power ternary semigroups [Formula: see text] and [Formula: see text] are obviously isomorphic. It is quite natural to ask whether the converse is true, i.e. is it true that for any ternary semigroups [Formula: see text] and [Formula: see tex

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V., Chinnadurai, та Bharathivelan K. "CUBIC IDEALS OF PO-Γ-SEMIGROUPS". International Journal of Applied and Advanced Scientific Research 1, № 1 (2016): 127–35. https://doi.org/10.5281/zenodo.163762.

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In this paper, we introduce the concept of cubic ideals of po-Γ-semigroups, which is generalized concept of fuzzy ideals of po-Γ-semigroups in order to obtain some characterization theorems. Operator po-semigroups of a po-Γ-semigroup have been made to work by obtaining various relationships between cubic ideals of a po-Γ-semigroup and that of its operator semigroups. We also investigated some of its properties with examples.

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El-Morsy, Salwa, Junaid Ahmad, and Reny George. "On employing pythagorean fuzzy processing time to minimize machine rental cost." AIMS Mathematics 8, no. 7 (2023): 17259–71. http://dx.doi.org/10.3934/math.2023882.

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<abstract> <p>The aim of this paper is to obtain the minimal rental cost of the three-phases flow shop scheduling problems. A novel strategy to tackle this issue using Pythagorean fuzzy processing time is introduced. It depends on converting the three stages machine into two stages when the minimum value of processing time of the first machine is greater than the maximum value of processing time of the second machine. The vague processing time does not convert to its crisp form. The jobs sequencing in machines is obtained using Johnson procedure. The zero element of the Pythagorean

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PETRICH, MARIO. "ON WEAKLY AMPLE SEMIGROUPS." Journal of the Australian Mathematical Society 97, no. 3 (2014): 404–17. http://dx.doi.org/10.1017/s1446788714000202.

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AbstractLet$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}S$be a semigroup. Elements$a,b$of$S$are$\widetilde{\mathscr{R}}$-related if they have the same idempotent left identities. Then$S$is weakly left ample if (1) idempotents of$S$commute, (2) $\widetilde{\mathscr{R}}$is a left congruence, (3) for any$a \in S$,$a$is$\widetilde{\mathscr{R}}$-related to a (unique) idempotent, say$a^+$, and (4) for any element$a$and idempotent$e$o

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Alouache, Ali, and Qinghe Wu. "Fuzzy logic PD controller for trajectory tracking of an autonomous differential drive mobile robot (i.e. Quanser Qbot)." Industrial Robot: An International Journal 45, no. 1 (2018): 23–33. http://dx.doi.org/10.1108/ir-07-2017-0128.

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Purpose The aim of this paper is to propose a robust robot fuzzy logic proportional-derivative (PD) controller for trajectory tracking of autonomous nonholonomic differential drive wheeled mobile robot (WMR) of the type Quanser Qbot. Design/methodology/approach Fuzzy robot control approach is used for developing a robust fuzzy PD controller for trajectory tracking of a nonholonomic differential drive WMR. The linear/angular velocity of the differential drive mobile robot are formulated such that the tracking errors between the robot’s trajectory and the reference path converge asymptotically t

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Adhitya, Ryan Yudha. "Sistem Pengendalian Robot KRSRI Menggunakan Logika Fuzzy Sugeno Orde Nol." Jurnal Elektronika dan Otomasi Industri 11, no. 1 (2024): 159–68. http://dx.doi.org/10.33795/elkolind.v11i1.4057.

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Robots are one of the technological developments that unite several aspects, such as mechanical, electrical, and programs that are interrelated to one another. Currently, the robot has also been competed in a competition with various categories. One of them is the SAR (Search and Rescue) robot competition which is accommodated in the KRSRI (Indonesian SAR Robot Contest). This SAR robot has a mission to save and bring victims to a safe zone. To develop the robot so that it is more optimal, several studies have been carried out using various methods. In this study, the SAR robot was optimized wi

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Ahmad, Nisar, Syed Aleem Shah, Wali Khan Mashwani, and Nasim Ullah. "Corrections and Extensions in Left and Right Almost Semigroups." Punjab University Journal of Mathematics, July 27, 2021, 475–96. http://dx.doi.org/10.52280/pujm.2021.530703.

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In this paper we elaborated the concept that on what conditions left almost semigroup (LA-Semigroup), right almost semigroup (RA-Semigroup) and a groupoid become commutative and further extended these results on medial, LA-Group and RA-Group. We proved that the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacement semigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup and semigroup [17, 1, 18] and proved that example discussed in [18] is semigroup

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ZAMAN, Baddi Ul. "On non-regular semigroups: $\lambda$-semidirect products, Zappa-Szép products and representations." Hacettepe Journal of Mathematics and Statistics, January 10, 2024, 1–21. http://dx.doi.org/10.15672/hujms.1189391.

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This article encompasses the study of non-regular semigroups. First, we show that the $\lambda$-semidirect product $M \rtimes^{\lambda} W$ of a left $P$-Ehresmann semigroup $M$ and a left restriction semigroup $W$ is a left $P$-Ehresmann semigroup. We explore the behavior of generalized Green's relations on $M \rtimes^{\lambda} W$, and investigate some properties of $M \rtimes^{\lambda} W$. Second, the Zappa-Szép product of a right Ehresmann semigroup and its distinguished semilattice is studied. Lastly, the theory of representations of left Ehresmann semigroups with zero via homomorphisms of

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Ravi, Srivastava, and Yadav Arvind. "Regular Semigroups and Metatheorem." December 30, 2024. https://doi.org/10.5281/zenodo.14768947.

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Regularity of a semigroup in terms of fuzzy left ideals, fuzzy right ideals, fuzzy ideals, fuzzy bi-ideals, fuzzy interior ideals, fuzzy semiprime ideals and fuzzy quasi-ideals of a semigroup is studied in the light of Tom Head's metatheorem. The classes of different types of fuzzy ideals are shown to be closed under projection. Tom Head's metatheorem is also used to provide proofs of several results pertaining to these fuzzy ideals which doesn't involve calculations. The proofs obtained by metatheorem are simple and shorter. Characterization of a semigroup that is regular, intra-regular, left

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