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http://dx.doi.org/10.5831/HMJ.2019.41.3.581

PERMEABLE VALUES AND ENERGETIC SETS IN BCK/BCI-ALGEBRAS BASED ON FUZZY POINTS

Song, Seok Zun (Department of Mathematics, Jeju National University)
Kim, Hee Sik (Department of Mathematics, Hanyang University)
Roh, Eun Hwan (Department of Mathematics Education, Chinju National University of Education)
Jun, Young Bae (Department of Mathematics Education, Gyeongsang National University)

Publication Information

Honam Mathematical Journal / v.41, no.3, 2019 , pp. 581-593 More about this Journal

Abstract

The notions of ( ${\in}$ , ${\in}{\vee}q$ )-permeable S-value and ( ${\in}$ , ${\in}{\vee}q$ )-permeable I-value are introduced, and related properties are investigated. Relations among ( ${\in}$ , ${\in}{\vee}q$ )-fuzzy subalgebra, ( ${\in}$ , ${\in}{\vee}q$ )-fuzzy ideal, (strong) lower and (strong) upper level sets, ( ${\in}$ , ${\in}{\vee}q$ )-permeable S-value, ( ${\in}$ , ${\in}{\vee}q$ )-permeable I-value, S-energetic set, I-energetic set, right stable set and right vanished set are discussed.

Keywords

( ${\in}$ , ${\in}{\vee}q$ )-permeable S-value; ( ${\in}$ , ${\in}{\vee}q$ )-permeable I-value; S-energetic set; I-energetic set;

Citations & Related Records

Reference

1	S. M. Hong and Y. B. Jun, Anti fuzzy ideals in BCK-algebras, Kyungpook Math. J. 38 (1998), 145-150.
2	Y. Huang, BCI-algebra, Science Press, Beijing, 2006.
3	Y. B. Jun, On ( ${\alpha},{\beta}$ )-fuzzy ideals of BCK/BCI-algebras, Sci. Math. Jpn. 60 (2004), 613-617.
4	Y. B. Jun, On ( ${\alpha},{\beta}$ )-fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc. 42 (2005), 703-711. DOI
5	Y. B. Jun, Fuzzy subalgebras of type ( ${\alpha},{\beta}$ ) in BCK/BCI-algebras, Kyungpook Math. J. 47 (2007), 403-410.
6	Y. B. Jun, S. S. Ahn and E. H. Roh, Energetic subsets and permeable values with applications in BCK/BCI-algebras, Appl. Math. Sci. 7(89) (2013), 4425-4438.
7	J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa Co. Seoul, 1994.
8	V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004) 277-288. DOI
9	P. M. Pu and Y. M. Liu, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), 571-599. DOI
10	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965) 338-353. DOI