Missouri Journal of Mathematical Sciences

Int-soft Implicative hyper $BCK$-ideals in hyper $BCK$-algebras

Rajab Ali Borzooei, Xiao Long Xin, Eun Hwan Roh, and Young Bae Jun

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Abstract

The notion of an int-soft (weak) implicative hyper BCK-ideal is introduced, and related properties are investigated. Relations between an int-soft weak implicative hyper BCK-ideal, an int-soft implicative hyper BCK-ideal, an int-soft hyper BCK-ideal, and an int-soft strong hyper BCK-ideal are considered, and characterizations of an int-soft weak implicative hyper BCK-ideal are discussed. Conditions for an int-soft hyper BCK-ideal to be an int-soft weak implicative hyper BCK-ideal are provided. Using an int-soft weak implicative hyper BCK-ideal, a new int-soft weak implicative hyper BCK-ideal is established. Finally, we show the hyper homomorphic preimage of an int-soft implicative hyper BCK-ideal is also an int-soft implicative hyper BCK-ideal.

Article information

Source
Missouri J. Math. Sci., Volume 31, Issue 2 (2019), 152-163.

Dates
First available in Project Euclid: 16 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1573873231

Digital Object Identifier
doi:10.35834/2019/3102152

Subjects
Primary: 06F35: BCK-algebras, BCI-algebras [See also 03G25]
Secondary: 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35] 06D72: Fuzzy lattices (soft algebras) and related topics

Keywords
int-soft (weak, strong, $s$-weak) hyper BCK-ideal int-soft weak implicative hyper BCK-ideal int-soft implicative hyper BCK-ideal

Citation

Borzooei, Rajab Ali; Xin, Xiao Long; Roh, Eun Hwan; Jun, Young Bae. Int-soft Implicative hyper $BCK$-ideals in hyper $BCK$-algebras. Missouri J. Math. Sci. 31 (2019), no. 2, 152--163. doi:10.35834/2019/3102152. https://projecteuclid.org/euclid.mjms/1573873231


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