On the Construction of the Properties of t - Norms in the Q-Fuzzy T-Sub algebra and Ideals in the BP-Algebra

M Premkumar; M A Rifayathali; A Prasanna; J Juliet Jeyapackiam; Dhirendra Kumar Shukla; R Parameswari

doi:10.17485/IJST/v17sp1.144

Article

On the Construction of the Properties of t - Norms in the Q-Fuzzy T-Sub algebra and Ideals in the BP-Algebra

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PDF 42

Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17sp1.144

Year: 2024, Volume: 17, Issue: Special Issue 1, Pages: 52-57

Original Article

On the Construction of the Properties of t - Norms in the Q-Fuzzy T-Sub algebra and Ideals in the BP-Algebra

M Premkumar^1*, M A Rifayathali², A Prasanna², J Juliet Jeyapackiam³, Dhirendra Kumar Shukla⁴, R Parameswari¹

¹Department of Mathematics, Sathyabama Institute of Science and Technology (Deemed To Be University), Chennai, Tamil Nadu, 600119, India
²PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli, 620020, Tamil Nadu, India
³Department of Mathematics, Jayaraj Annapackiam CSI College of Engineering Nazareth, Tuticorin, 628617, India
⁴Department of Engineering Mathematics, Technocrats Institute of Technology, Bhopal, 462021, Madhya Pradesh, India

*Corresponding Author
Email: [email protected]

Received Date:29 August 2023, Accepted Date:05 March 2024, Published Date:27 May 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

In the present piece, we propound t- norms of the QFTSA ὦȴȵŦὦȴὦȵ in BP-Algebra and also t- norms of the QFTI ὦὦȴὦȴɉŦŦὦȴȵɉὦȵὦȵ , ȴȵɉĜ of the BP-Algebra and we assay some of their features. Likewise, we define Cartesian products of QFTSAs and QFTI of BP algebras. These, as well as other algebraic features, are bandied in depth. Objective: This article generally aimed at investigating t- norms concepts. It can also be applied to the algebraic properties of Q-Fuzzy T-Ideals, Q-Fuzzy T-Sub algebra and also defined for Cartesian products of QFTSAs and QFTI of BP algebras.Methods: t -norms concepts can apply for the algebraic properties of Q-Fuzzy T-Ideals, and T-Sub algebra related to the theorems, lemma, and examples we find the proof.Findings: In the present study, we propound ȶ- norms of the QFTSA ὦȴȵŦὦȴὦȵ in BP-Algebra and also ȶ- norms of the QFTI ὦὦȴὦȴɉŦŦὦȴȵɉὦȵὦȵ , ȴȵɉĜ of the BP-Algebra and we assay some of their features. Likewise, we define Cartesian products of QFTSAs and QFTI of BP algebras. These, as well as other algebraic features, are bandied in depth. Novelty: This study has defined new concepts of t-norms that apply to Q-fuzzy T-Ideals and Q fuzzy T-sub-algebra in BP algebras.

Keywords: Fuzzy Set (FS), Q-Fuzzy Sets (QFS), Q-Fuzzy Subset (QFSb), Q-Fuzzy T-Ideal (QFTI), Q-Fuzzy T-Subalgebra (QFTSA)

References

YCJ, Chandramouleeswaran M. L - Fuzzy BP – Algebras. IRA-International Journal of Applied Sciences (ISSN 2455-4499). 2016;4(1):68–75. Available from: https://dx.doi.org/10.21013/jas.v4.n1.p8
Jefferson YC, Chandramouleeswaran M. Fuzzy T-ideals in BP-algebras. International Journal of Contemporary Mathematical Sciences. 2016;11:425–436. Available from: https://dx.doi.org/10.12988/ijcms.2016.6845
Gulzar M, Alghazzawi D, Mateen MH, Premkumar M. On some characterization of Q-complex fuzzy sub-rings. Journal of Mathematics and Computer Science. 2022;22(03):295–305. Available from: https://doi.org/10.22436/jmcs.022.03.08
Kaviyarasu M, Indhira K, Chandrasekaran VM. Fuzzy p-ideal in INK-Algebra Journal of Xi'an University of. Architecture & Technology. 2020;12(3). Available from: https://doi.org/10.37896/JXAT12.03/433
Gupta MM, Qi J. Theory of T-norms and fuzzy inference methods. Elsevier BV. 1991. doi: 10.1016/0165-0114(91)90171-l Available from: https://dx.doi.org/10.1016/0165-0114(91)90171-l
Ismail A, Premkumar M, Prasanna A, S, Mohideen I, Shukla DK. On Product of Doubt ψ-Ǭ- Fuzzy Subgroup. 2022. Available from: https://doi.org/10.1007/978-981-19-3575-6_41
Osama Rashad El-Gendy Bipolar Fuzzy α-ideal of BP-algebra. American Journal of Mathematics and Statistics. 2020;10(2):33–37. Available from: https://doi.org/10.5923/j.ajms.20201002.01
Premkumar M, Bai HG, Prasanna A, Parmar KPS, Karuna MS, Rinawa ML. On Algebraic Characteristics of Fuzzy T-Sub algebra in T-Algebra under the Normalization. 2022 International Conference on Computational Modelling, Simulation and Optimization (ICCMSO). 2022;p. 149–151. Available from: https://doi.org/10.1109/ICCMSO58359.2022.00040
Premkumar M, Prasanna A, Shukla DK, Mohideen SI. On Characteristics of κ-Q- Fuzzy Translation and Fuzzy Multiplication in T-Ideals in T-Algebra. Smart Innovation Systems and Technologies (IOT with Intelligent Applications). 2022;1:91–96. Available from: https://doi.org/10.1007/978-981-19-3571-8_11
Premkumar M, Bai HG, Shukla DK, Garg AK, Prasanna A, Mohideen SI. A Doubt ₭-Ǫ-Bipolar Fuzzy BCI-Ideals and Doubt ₭-Ǫ-Bipolar Fuzzy BCI-Implicative Ideals in BCI-Algebra. Journal of Pharmaceutical Negative Results. 2022;13:147–151. Available from: https://doi.org/10.47750/pnr.2022.13.S03.024
Prasanna A, Kumar MP, Mohideen SI, Gulzar M. Algebraic Properties on Fuzzy Translation and Multiplication in BP– Algebras. International Journal of Innovative Technology and Exploring Engineering. 2020;9(3):123–126. Available from: https://doi.org/10.35940/ijitee.b6277.019320
Rasuli R. Fuzzy congruence on product lattices under <i>T</i>-norms. Journal of Information and Optimization Sciences. 2021;42(2):333–343. Available from: https://doi.org/10.1080/02522667.2019.1664383
Rasuli R. Fuzzy d-Algberas under t-norms. Engineering and applied Science Letters. 2022;5:27–36. Available from: https://doi.org/10.30538/psrp-easl2022.0082
Rasuli R, . t-norms over fuzzy ideals (implicative, positive implicative) of BCK-algebras. Ptolemy Scientific Research Press. 2021. Available from: https://doi.org/10.30495/maca.2022.1946498.1040
Solairaju A, Nagarajan R. A new Structure and Construction of Q-fuzzy groups. Advances in Fuzzy mathematics. 2009;4:23–29. Available from: https://www.researchgate.net/publication/228689307_A_New_Structure_and_Construction_of_Q-fuzzy_groups
Zadeh LA. Fuzzy sets. Information and Control. 1965;8(3):338–353. Available from: https://dx.doi.org/10.1016/s0019-9958(65)90241-x

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© 2024 Premkumar et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)