Volume 19 • Issue 1 • PP: 363-374 • 2022
Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras
Abstract
Interval-valued neutrosophic sets (IVNSs) are a notion that was initially developed by Wang et al.19 The idea
of IVNSs to deductive systems (DSs) in Hilbert algebras is presented in this study. It is shown how intervalvalued
neutrosophic deductive systems (IVNDSs) relate to their level cuts. In addition, certain related features
are examined as well as the homomorphic inverse image of IVNDSs in Hilbert algebras.
Keywords
References
[1] B. Ahmad, A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst., vol. 2009, Article ID 586507, 6 pages, 2009.
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., vol. 20, no. 1, pp. 87–96, 1986.
[3] M. Atef, M. I. Ali, T. Al-shami, Fuzzy soft covering based multi-granulation fuzzy rough sets and their
applications, Comput. Appl. Math., vol. 40, no. 4, pp. 115, 2021.
[4] D. Busneag, A note on deductive systems of a Hilbert algebra, Kobe J. Math., vol. 2, pp. 29–35, 1985.
[5] D. Busneag, Hilbert algebras of fractions and maximal Hilbert algebras of quotients, Kobe J. Math., vol.
5, pp. 161–172, 1988.
[6] N. Caˇgman, S. Enginoˇglu, F. Citak, Fuzzy soft set theory and its application, Iran. J. Fuzzy Syst., vol. 8,
no. 3, pp. 137–147, 2011.
[7] A. Diego, Sur les alg´ebres de Hilbert, Collection de Logique Math. Ser. A (Ed. Hermann, Paris), vol. 21,
pp. 1–52, 1966.
[8] W. A. Dudek, On fuzzification in Hilbert algebras, Contrib. Gen. Algebra, vol. 11, pp. 77–83, 1999.
[9] W. A. Dudek, On ideals in Hilbert algebras, Acta Universitatis Palackianae Olomuciensis Fac. rer. nat.
ser. Math., vol. 38, pp. 31–34, 1999.
[10] H. Garg, K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on
the set pair analysis theory and their application in decision making, Soft Comput., vol. 22, no. 15, pp.
4959–4970, 2018.
[11] H. Garg, K. Kumar, Distance measures for connection number sets based on set pair analysis and its
applications to decision-making process, Appl. Intell., vol. 48, no. 10, pp. 3346–3359, 2018.
[12] H. Garg, S. Singh, A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation operators,
Iran. J. Fuzzy Syst., vol. 15, no. 5, pp. 69–93, 2018.
[13] Y. B. Jun, Deductive systems of Hilbert algebras, Math. Japon., vol. 43, pp. 51–54, 1996.
[14] Y. B. Jun, R. Bandaru, Deductive systems of GE-algebras, Algebr. Struct. Appl., vol. 9, no. 1, pp. 53–67,
2022.
[15] Y. B. Jun, F. Smarandache, C. S. Kim, Neutrosophic cubic sets, New Math. Nat. Comput., vol. 13, no. 1,
pp. 41–54, 2017.
[16] F. Smarandache, A unifying field in logics: Neutrosophic logic, neutrosophy, neutrosophic set, neutrosophic
probability, American Research Press, 1999.
[17] F. Smarandache, Neutrosophic set, a generalization of intuitionistic fuzzy sets, Int. J. Pure Appl. Math.,
vol. 24, no. 5, pp. 287–297, 2005.
[18] K. Taboon, P. Butsri, A. Iampan, A cubic set theory approach to UP-algebras, J. Interdiscip. Math., vol.
23, no. 8, pp. 1449–1486, 2020.
[19] H. Wang, F. Smarandache, Y. Q. Zhang, R. Sunderraman, Interval neutrosophic sets and logic: Theory
and applications in computing, Hexis, Phoenix, Ariz, USA, 2005.
[20] L. A. Zadeh, Fuzzy sets, Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
[21] J. Zhan, Z. Tan, Intuitionistic fuzzy deductive systems in Hibert algebra, Southeast Asian Bull. Math.,
vol. 29, no. 4, pp. 813–826, 2005.
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