Akram, Muhammad (2010) *On Bifuzzy K-algebras.* PhD thesis, University of Arid Agriculture, Rawalpindi.

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## Abstract

In this thesis we introduce a new class of logical algebras: K-algebras on a group G with identity element e by adjoining the induced binary operations on a group G, if G is not an elementary abelian 2-group. A K-algebra is non-commutative and non-associative with right identity element e. We characterize K-algebras by using their left and right mappings. Homomorphism of K-algebras is studied. Isomorphism theorems are given. We introduce the notion of fuzzy K-ideals of K-algebras and give connection between fuzzy ideals and fuzzy K-ideals of K-algebras. Fuzzy isomorphism theorems are given. We discuss a new kind of fuzzy ideal of a K-algebra called, an (ε,ε Vq)- fuzzy ideal. We introduce the notion of interval-valued fuzzy ideals of K-algebras and investigate some of their properties. Using interval-valued fuzzy ideals, characterizations of Noetherian K-algebras are established. A new generalized fuzzy K-subalgebra is introduced. We introduce the notion of bifuzzy ideals of K-algebras and investigate some interesting properties. We also introduce the notion of bifuzzy topological K-algebras and investigate some of their properties.

Item Type: | Thesis (PhD) |
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Uncontrolled Keywords: | Bifuzzy, K-algebras, logical, left, right, mappings, topological |

Subjects: | Physical Sciences (f) > Mathematics(f5) |

ID Code: | 3029 |

Deposited By: | Mr. Javed Memon |

Deposited On: | 01 Jun 2010 12:35 |

Last Modified: | 26 May 2011 15:00 |

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