Int-soft ideals over the soft sets in ordered semigroups

G. Muhiuddin; Ahsan Mahboob; G. Muhiuddin; Ahsan Mahboob

doi:10.3934/math.2020159

AIMS Mathematics

2020, Volume 5, Issue 3: 2412-2423. doi: 10.3934/math.2020159

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Research article

Int-soft ideals over the soft sets in ordered semigroups

G. Muhiuddin ^{1
,
,},
Ahsan Mahboob ²

1.
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
2.
Department of Mathematics, Madanapalle Institute of Technology & Science, Angallu, Madanapalle-517325, India

Received: 30 November 2019 Accepted: 14 February 2020 Published: 05 March 2020
MSC : 06F05, 06D72, 20M12

In this paper, the notions of int-soft left (right) ideals, int-soft interior ideals and int-soft bi-ideals over the soft sets are introduced and several related properties of these notions are investigated. Characterizations of int-soft ideals over the soft sets are considered. Moreover, for any soft set $(\eta, U)$ over $S$, the notion of a soft set over the soft sets $(\chi_{\eta(u)}, V)$ is introduced. It is prove that a soft set $(\eta, S)$ is a soft left ideal (resp. right ideal, interior ideal, bi-ideal) over $S$ if and only if $(\chi_{\eta(x)}, S)$ is an int-soft left ideal (resp. right ideal, interior ideal, bi-ideal) over the soft sets.
- ordered semigroups,
- soft sets,
- soft ideals over the soft sets,
- int-soft left (right) ideals,
- int-soft interior ideals,
- int-soft bi-ideals
Citation: G. Muhiuddin, Ahsan Mahboob. Int-soft ideals over the soft sets in ordered semigroups[J]. AIMS Mathematics, 2020, 5(3): 2412-2423. doi: 10.3934/math.2020159

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Abstract

In this paper, the notions of int-soft left (right) ideals, int-soft interior ideals and int-soft bi-ideals over the soft sets are introduced and several related properties of these notions are investigated. Characterizations of int-soft ideals over the soft sets are considered. Moreover, for any soft set $(\eta, U)$ over $S$, the notion of a soft set over the soft sets $(\chi_{\eta(u)}, V)$ is introduced. It is prove that a soft set $(\eta, S)$ is a soft left ideal (resp. right ideal, interior ideal, bi-ideal) over $S$ if and only if $(\chi_{\eta(x)}, S)$ is an int-soft left ideal (resp. right ideal, interior ideal, bi-ideal) over the soft sets.

References

[1]	D. Molodtsov, Soft set theory-First results, Comput. Math. Appl., 37 (1999), 19-31.
[2]	P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077-1083. doi: 10.1016/S0898-1221(02)00216-X
[3]	P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562. doi: 10.1016/S0898-1221(03)00016-6
[4]	H. Aktaş, N. Çağman, Soft sets and soft groups, Inf. Sci., 177 (2007), 2726-2735. doi: 10.1016/j.ins.2006.12.008
[5]	F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl., 56 (2008), 2621-2628. doi: 10.1016/j.camwa.2008.05.011
[6]	S. Naz, M. Shabir, On soft semihypergroups, J. Intell. Fuzzy Syst., 26 (2014), 2203-2213. doi: 10.3233/IFS-130894
[7]	S. Naz, M. Shabir, On prime soft bi-hyperideals of semihypergroups, J. Intell. Fuzzy Syst., 26 (2014), 1539-1546. doi: 10.3233/IFS-130837
[8]	S. Z. Song, H. S. Kim, Y. B. Jun, Ideal theory in semigroups based on intersectional soft sets, Sci. World J., 2014, Article ID 136424 (2014), 7.
[9]	W. A. Dudek, Y. B. Jun, Int-soft interior ideals of semigroups, Quasigroups Relat. Syst., 22 (2014), 201-208.
[10]	Y. B. Jun, S. Z. Song, G. Muhiuddin, Concave soft sets, critical soft points, and Union-Soft ideals of ordered semigroups, Sci. World J., Article ID 467968, 2014 (2014), 11.
[11]	Y. B. Jun, M. A. Ozturk, G. Muhiuddin, A novel generalization of fuzzy subsemigroups, Annals Fuzzy Math. Inf., 14 (2017), 359-370.
[12]	Y. B. Jun, S. Z. Song, G. Muhiuddin, Hesitant fuzzy semigroups with a frontier, J. Intell. Fuzzy Syst., 30 (2016), 1613-1618. doi: 10.3233/IFS-151869
[13]	G. Muhiuddin, Cubic interior ideals in semigroups, Appl. Appl. Math., 14 (2019), 463-474.
[14]	G. Muhiuddin, Ahsan Mahboob, Noor Mohammad Khan, A new type of fuzzy semiprime subsets in ordered semigroups, J. Intell. Fuzzy Syst., 37 (2019), 4195-4204. doi: 10.3233/JIFS-190293
[15]	G. Muhiuddin, Neutrosophic subsemigroups, Ann. Commun. Math., 1 (2018), 1-10.
[16]	G. Muhiuddin, N. Rehman, Y. B. Jun, A generalization of (∈, ∈ ∨q)-fuzzy ideals in ternary semigroups, Annals Commun. Math., 1 (2019), 73-83.
[17]	G. Muhiuddin, A. M. Al-roqi, S. Aldhafeeri, Filter theory in MTL-algebras based on Uni-soft property, Bulletin Iranian Math. Soc., 43 (2017), 2293-2306.
[18]	G. Muhiuddin, A. M. Al-roqi, Unisoft filters in R0-algebras, J. Comp. Analy. Appl., 19 (2015), 133-143.
[19]	G. Muhiuddin, F. Feng, Y. B. Jun, Subalgebras of BCK/BCI-Algebras based on cubic soft sets, Sci. World J., 2014, Article ID 458638 (2014), 9.
[20]	G. Muhiuddin, A. M. Al-roqi, Cubic soft sets with applications in BCK/BCI-algebras, Annals Fuzzy Math. Inf., 8 (2014), 291-304.
[21]	G. Muhiuddin, S. J. Kim, Y. B. Jun, Implicative N-ideals of BCK-algebras based on neutrosophic N-structures, Discrete Math. Algorithms Appl., 11 (2019), 17.
[22]	G. Muhiuddin, S. Aldhafeeri, N-Soft p-ideal of BCI-algebras, Eur. J. Pure Appl. Math., 12 (2019), 79-87. doi: 10.29020/nybg.ejpam.v12i1.3343
[23]	G. Muhiuddin, H. S. Kim, S. Z. Song, et al., Hesitant fuzzy translations and extensions of subalgebras and ideals in BCK/BCI-algebras, J. Intell. Fuzzy Syst., 32 (2017), 43-48. doi: 10.3233/JIFS-151031
[24]	A. Al-roqi, G. Muhiuddin, S. Aldhafeeri, Normal unisoft filters in R0-algebras, Cogent Math., 1 (2017), 1-9.
[25]	Y. B. Jun, G. Muhiuddin, M. A. Ozturk, et al., Cubic soft ideals in BCK/BCI-algebras, J. Comput. Analy. Appl., 22 (2017), 929-940.
[26]	T. Senapati, Y. B. Jun, G. Muhiuddin, et al., Cubic intuitionistic structures applied to ideals of BCI-algebras, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 27 (2019), 213-232. doi: 10.2478/auom-2019-0028
[27]	Y. B. Jun, K. J. Lee, A. Khan, Soft ordered semigroups, Math. Logic Q., 56 (2010), 42-50. doi: 10.1002/malq.200810030
[28]	A. Khan, Y. B. Jun, S. I. A. Shah, et al., Applications of soft union sets in ordered semigroups via uni-soft quasi-ideals, J. Intell. Fuzzy Syst., 30 (2016), 97-107.
[29]	M. Ali, Soft ideals and soft fiters of soft ordered semigroups, Comput. Math. Appl., 62 (2011), 3396-3403. doi: 10.1016/j.camwa.2011.08.054
[30]	C. F. Yang, Fuzzy soft semigroups and fuzzy soft ideals, Comput. Math. Appl., 61 (2011), 255-261. doi: 10.1016/j.camwa.2010.10.047
[31]	A. Khan, N. H. Sarmin, F. M. Khan, et al., A study of fuzzy soft interior ideals of ordered semigroups, Iran J. Sci. Technol. A., 37A3 (2013), 237-249.
[32]	J. Chvalina, S. Hoskova-Mayerova, On certain proximities and preorderings on the transposition hypergroups of linear first-order paerential operators, An. Stiint. Univ. Ovidius Constanta Ser. Mat., 22 (2014), 85-103.
[33]	M. Izhar, A. Khan, M. Farooq, et al., (M, N)-Double framed soft ideals of Abel Grassmanns groupoids, J. Intell. Fuzzy Syst., 35 (2018), 1-15.
[34]	M. Izhar, A. Khan, M. Farooq, et al., Double-framed soft generalized bi-ideals of intra-regular AG-groupoids, J. Intell. Fuzzy Syst., 35 (2018), 1-15.
[35]	M. Khalaf, A. Khan, T. Izhar, Double-framed soft LA-semigroups, J. Intell. Fuzzy Syst., 33 (2017), 3339-3353. doi: 10.3233/JIFS-162058
[36]	A. Khan, M. Farooq, H. Khan, Uni-soft hyperideals of ordered semihypergroups, J. Intell. Fuzzy Syst., 35 (2018), 1-15.
[37]	F. Yousafzai, A. Ali, S. Haq, et al., Non-associative semigroups in terms of semilattices via soft ideals, J. Intell. Fuzzy Syst., 35 (2018), 4837-4847. doi: 10.3233/JIFS-18873

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