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New Kinds of Fuzzy Ideals in BCI-algebras*

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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.

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Authors and Affiliations

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

    Zhang Guangji, Zhang Cheng, Liu Zixin & Gang Jiatai

Authors
  1. Zhang Guangji
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  2. Zhang Cheng
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  3. Liu Zixin
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  4. Gang Jiatai
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Correspondence to Zhang Guangji.

Additional information

*Foundation Item:Supported by NNSF of China(60274016). Biography:Zhang Guang-ji(1947-),male,Professor

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Guangji, Z., Cheng, Z., Zixin, L. et al. New Kinds of Fuzzy Ideals in BCI-algebras*. Fuzzy Optim Decis Making 5, 177–186 (2006). https://doi.org/10.1007/s10700-006-7335-9

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  • DOI: https://doi.org/10.1007/s10700-006-7335-9

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