New Kinds of Fuzzy Ideals in BCI-algebras*

  • Authors:

  • Zhang Guangji;Zhang Cheng;Liu Zixin;Gang Jiatai

  • Affiliations:

  • University Key Lab. of Information Science and Engineering of Dalian University, College of information engineering, Dalian University, Dalian, China 116622;University Key Lab. of Information Science and Engineering of Dalian University, College of information engineering, Dalian University, Dalian, China 116622;University Key Lab. of Information Science and Engineering of Dalian University, College of information engineering, Dalian University, Dalian, China 116622;University Key Lab. of Information Science and Engineering of Dalian University, College of information engineering, Dalian University, Dalian, China 116622

  • Venue:
  • Fuzzy Optimization and Decision Making
  • Year:
  • 2006

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Abstract

Following the seminal work of Xi on the definition of fuzzy ideal in BCI-algebras, three new kinds of definitions of fuzzy ideal of BCI-algebras are proposed. First, by the use of the relations between fuzzy points and fuzzy sets, the definition of a (s,t]-fuzzy ideals of BCI-algebras is introduced. The acceptable nontrivial concepts obtained in this manner are the $$(\in, \in \vee q)$$- fuzzy ideals and$$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy ideals. Second, based on the concept of falling shadow, a theoretical approach of fuzzy ideal is established and the fuzzy ideal based on t-norm is proposed. Finally, by the use of the implication operators of fuzzy logic, an R-fuzzy ideals is proposed and relations between the (s,t]-fuzzy ideals and R-fuzzy ideals are discussed.