On characterizations of generalized fuzzy ideals of BCI-algebras

Abstract

The aim of this study is to introduce the notions of (∈,∈∨ q)-FSI-ideals and (∈,∈∨ q)-FSC-ideals of BCI-algebras and to investigate some of their related properties. Some characterization theorems of these generalized fuzzy ideals are derived. The relationship among these generalized fuzzy ideals of BCI-algebras is considered. We show that a fuzzy set of a BCI-algebra is an (∈,∈∨ q)-FSI-ideal if and only if it is both an (∈,∈∨ q)-FSC-ideal and an (∈,∈∨ q)-FPI-ideal. Finally, we consider the concepts of implication-based FSI (resp., FSC)-ideals of BCI-algebras.

Keywords:

• BCI-algebra
• sub-implicative(resp., sub-commutative and positive implicative)-ideal
• (∈,∈∨ q)-FSI (FSC and FPI)-ideal
• fuzzy logic
• implication operator

2000 AMS Subject Classifications :

• 06F35
• 03G10
• 03B52

Acknowledgements

The authors would like to express their sincere thanks to the referees for their valuable comments and suggestions that helped a lot for improving the presentation of this paper.

This work was supported by a grant of the National Natural Science Foundation of China (60875034); a grant of the Natural Science Foundation of Education Committee of Hubei Province, China (D20092901; Q20092907; D20082903; B200529001) and also the support of the Natural Science Foundation of Hubei Province, China (2008CDB341).