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Interval-valued ideals in BCK-algebras

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In this paper, we introduce the concepts of interval-valued ideals, interval-valued positive implicative ideals, interval-valued positive ideals and commutative ideals, and investigate some of their properties respectively. In particular, we obtain some of their characterizations respectively.

Abstract

In this paper, we introduce the concepts of interval-valued ideals, interval-valued positive implicative ideals, interval-valued positive ideals and commutative ideals, and investigate some of their properties respectively. In particular, we obtain some of their characterizations respectively.

참고문헌 (13)

  1. Y. Yao, "Interval sets and interval set algebras", Proc. 8th IEEE Int. Conf. on Cognitive Intormatics (ICCI'09), pp.307~314 (2009)
  2. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8, pp.199~249 (1975)
  3. 김준희, "Topological structures based on interval-valued sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 20(3), pp.273~295 (2020), 기초자연과학연구소[DOI]
  4. 이정곤, "Topological structures via interval-valued soft sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 22(2), pp.133~169 (2021), 기초자연과학연구소[DOI]
  5. D. Molodtsov, "Soft set theory ^OC ^oFirst results", Comput. Math. Appl, 37(4-5), pp.19~31 (1999)
  6. K. Iseki, "On ideals in BCK-algebras", Math. Seminar Notes, 3, pp.1~12 (1975)
  7. Jie Meng, "BCK-algebras" (1994), Kyung Moon Sa Co
  8. Young Bae Jun, "Interval-valued fuzzy subalgebras", ideals in BCK-algebras, 2000, pp.3(3), 435~444
  9. K. Iseki, "On bounded BCK-algebras", Math. Seminar Notes, 3, pp.23~33 (1975)
  10. S. Tanaka, "A new class of algebras", Math. Seminar Notes, 3, pp.37~43 (1975)
  11. S. Tanaka, "Examples of BCK-algebrasA new class of algebras", Math. Seminar Notes, 3, pp.75~82 (1975)
  12. J. Meng, "Some notes on BCK-algebras", J. Northwest Univ, 16(4), pp.8~11 (1986)
  13. J. Meng, "Commutative ideals in BCK-algebras", Pure Appl. Math. (in P. R. China), 9, pp.49~53 (1991)

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