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On Multipliers of Lattice Implication Algebras for Hierarchical Convergence Models

계층적 융합모델을 위한 격자함의 대수의 멀티플라이어

  • Kim, Kyoum-Sun (Department of Mathematics, Chungbuk National University) ;
  • Jeong, Yoon-Su (Division of Information and Communication Convergence Engineering, Mokwon University) ;
  • Yon, Yong-Ho (College of Liberal Education, Mokwon University)
  • 김겸순 (충북대학교 수학과) ;
  • 정윤수 (목원대학교 정보통신융합공학부) ;
  • 연용호 (목원대학교 교양교육원)
  • Received : 2019.03.06
  • Accepted : 2019.05.20
  • Published : 2019.05.28

Abstract

Role-based access or attribute-based access control in cloud environment or big data environment need requires a suitable mathematical structure to represent a hierarchical model. This paper define the notion of multipliers and simple multipliers of lattice implication algebras that can implement a hierarchical model of role-based or attribute-based access control, and prove every multiplier is simple multiplier. Also we research the relationship between multipliers and homomorphisms of a lattice implication algebra L, and prove that the lattice [0, u] is isomorphic to a lattice $[u^{\prime},1]$ for each $u{\in}L$ and that L is isomorphic to $[u,1]{\times}[u^{\prime},1]$ as lattice implication algebras for each $u{\in}L$ satisfying $u{\vee}u^{\prime}=1$.

JKOHBZ_2019_v9n5_7_f0001.png 이미지

Fig. 1. Hasse diagram of (A, •)

Table 1. Cayley table of binary operation • on L  

JKOHBZ_2019_v9n5_7_t0001.png 이미지

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