Abstract
AbstractThe notions of doubt Atanassov's intuitionistic fuzzy sub-implicative ideals and doubt Atanassov's intuitionistic fuzzy P-ideals of BCI-algebras are introduced. We show that an Atanassov's intuitionistic fuzzy subset of BCI-algebras is an Atanassov's intuitionistic fuzzy sub-implicative ideal if and only if the complement of this Atanassov's intuitionistic fuzzy subset is a doubt Atanassov's intuitionistic fuzzy sub-implicative-ideal. We prove that any doubt Atanassov's intuitionistic fuzzy P-ideal is always a doubt Atanassov's intuitionistic fuzzy sub-implicative ideal. Moreover, some other properties about doubt Atanassov's intuitionistic fuzzy sub-implicative ideals and doubt Atanassov's intuitionistic fuzzy P-ideals of BCI-algebras are given.
Highlights
After the introduction of fuzzy sets by Zadeh 1, there has been a number of generalisation of this fundamental concept
In 1966, Imai and Iseki 4,5,6 introduced the notion of BCI-algebras
Liu and Meng 9 introduced the notion of sub-implicative ideals in BCI-algebras
Summary
After the introduction of fuzzy sets by Zadeh 1, there has been a number of generalisation of this fundamental concept. Xi 7 applied the concept of fuzzy set to BCI-algebras and gave some properties of it. After that Jun and Meng investigated the properties of fuzzy BCI-algebras and fuzzy ideals 8. Liu and Meng 9 introduced the notion of sub-implicative ideals in BCI-algebras. In 2002, Jun introduced fuzzy sub-implicative ideals in BCI-algebras. In 2012, Palaniappan et al introduced the notions of Atanassov’s intuitionistic fuzzy sub-implicative ideals and Atanassov’s intuitionistic fuzzy sub-commutative ideals of BCI-algebras. Solairaju introduced the notion of Atanassov’s intuitionistic fuzzy P-ideal of BCI-algebra and investigated some related properties. In 20, the authors have studied doubt Atanassov’s intuitionistic fuzzy H-ideals in BCK/BCI-algebras. We give conditions for a doubt Atanassov’s intuitionistic fuzzy ideal to be a doubt Atanassov’s intuitionistic fuzzy sub-implicative ideals in BCI-algebras. Relations among doubt Atanassov’s intuitionistic fuzzy p-ideals and doubt Atanassov’s intuitionistic fuzzy sub-implicative ideals are investigated
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