Generalized fuzzy K-algebras

A new kind of logical algebra, known as K-algebra, was introduced by the authors in 2003 and published in 2005. A K-algebra was built on a group G by adjoining the induced binary operation on G. The group G is particularly of the type in which each non-identity element is not of order 2. This algebraic structure is, in general, non-commutative and non-associative with right identity element. In 2005, the authors introduced fuzzy K-algebras. They then developed fuzzy K-algebras with other researchers worldwide. In this monograph, theory of K-algebras, K-homomorphisms and subclasses of K- algebras have been presented. Then the concepts and results of K-algebras have been broadened to the fuzzy setting frames by applying Zadeh's fuzzy set theory and its generalizations, namely, interval- valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, bipolar fuzzy sets and vague sets. Finally, some open-ended problems and applications of K-algebras are stated.

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M Akram has MSc degrees in Mathematics and Computer Science, MPhil in (Computational) Mathematics and PhD in Mathematics. His research interest is in Fuzzy Algebraic Structures and Numerical Algorithms. He has published numerous research articles in these areas and has received several incentive awards on his research publications from PU.