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On (⋶, ⋶ ∨ q)-fuzzy ideals of BCI-algebras

# On (⋶, ⋶ ∨ q)-fuzzy ideals of BCI-algebras,10.1007/s00521-010-0376-6,Neural Computing and Applications,Jianming ZhanYoung,Young Bae Jun

On (⋶, ⋶ ∨ q)-fuzzy ideals of BCI-algebras
The concepts of $$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy (p-, q- and a-) ideals of BCI-algebras are introduced and some related properties are investigated. In particular, we describe the relationships among ordinary fuzzy (p-, q- and a-) ideals, (∈, ∈ ∨ q)-fuzzy (p-, q- and a-) ideals and $$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy (p-,q- and a-) ideals of BCI-algebras. Moreover, we prove that a fuzzy set μ of a BCI-algebra X is an $$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy a-ideal of X if and only if it is both an $$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy p-ideal and an $$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy q-ideal. Finally, we give some characterizations of three particular cases of BCI-algebras by these generalized fuzzy ideals.
Journal: Neural Computing and Applications - NCA , vol. 20, no. 3, pp. 319-328, 2011
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## Citation Context (3)

• ...In [20], we introduced the concepts of ([, [ _ q)-fuzzy (p-,q- and a-) ideals of BCI-algebras and investigated some of their related properties...
• ...Theorem 2.10 [9, 20] A fuzzy set l of X is an ([, [ _ q)fuzzy (p-, q- and a-) ideal of X if and only if each nonempty level subset lt is a (p-, q- and a-) ideal of X for all 0 \ t B 0.5, respectively...
• ...Consider J = {t| t [ (0, 1] and lt is an empty set or a p-ideal of X}. In [20], we obtained the following results:...
• ...Lemma 3.2.3 [20] A fuzzy set l of X is an ð2; 2_ qÞfuzzy p-ideal of X if and only if it satisfies (GF5) and (F3’)...
• ...Definition 3.2.7 [20] Let a, b [ [0, 1] and a \b. Then a fuzzy set l of X is called a fuzzy p-ideal with thresholds (a, b ]o fX if it satisfies (F1 00 ) and...
• ...Theorem 3.2.8 [20] A fuzzy set l of X is a fuzzy p-ideal with thresholds (a, b ]o fX if and only if lt(= ; )i s a p-ideal of X for all a \ t B b...
• ...In [20], we introduced the concepts of ([, [ _ q)-fuzzy (p-, q- and a-) ideals of BCI-algebras and investigated some of their related properties...
• ...As a continuation of [20], we further discuss this topic in the present paper...

### Jianming ZhanYoung, et al. On (⋶, ⋶ ∨ q)-fuzzy ideals of BCI-algebras

• ...33 A fuzzy set μ in a BCI-algebra X is called an
Young Bae Junet al. Soft ideals of BCK/BCI-algebras based on fuzzy set theory
• ...It is well known that BCK and BCI-algebras are two classes of logical algebras; they were introduced by Iséki 8 and have been extensively investigated by many researchers 4 5 10 11 12 13 14 15 16 17 18 24 25 26...

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