Tazid Ali

Fuzzy Algebra: Some Advances Tazid Ali

A classical subset of a universal set X is identified by its corresponding characteristic function which is a function from X to {0,1}. This can be generalized by considering a function from X to [0,1]. The corresponding subset is called a fuzzy subset and the function is called a membership function. This generalization helps in fuzzifying different theories involving sets. Algebra is an important field in which fuzzification is done. In this book an attempt has been made to deal with the study of some types of algebraic structures in different fuzzy setting. Homomorphism of different types in fuzzy setting are dealt with in group structures. A fuzzy set called translational invariant fuzzy set is introduced and with respect to it different algebraic structures are constructed. Lattice structure in fuzzy setting is considered and product of different fuzzy structures are studied. No previous knowledge of fuzzy set is assumed and so all basics of fuzzy set theory is discussed here. It is expected that post graduate students and researchers in fuzzy algebra will be benefited from this monograph.