A New Generalization of Fuzzy Bi-ideals in Semigroups and Its Applications in Fuzzy Finite State Machines

In this paper, we introduce a generalization of anti fuzzy bi-ideals of semigroups of type (alpha, beta)*-fuzzy bi-ideals, where alpha, beta is an element of {<, gamma(k), < boolean OR gamma(k), < boolean AND gamma(k)) with alpha not equal < boolean AND gamma(k). We prove some basic results of (alpha, beta)*-fuzzy bi-ideals of semigroups. Moreover, we give characterizations of regular semigroups by the properties of (alpha, beta)*-fuzzy bi-ideals. We also prove that a fuzzy set,F in a semigroup g is an (<, < boolean OR gamma(k))*-fuzzy bi-ideal of G if and only if F o(k) F superset of F and F o(k) theta o(k) F superset of F, where theta(x) = 0 for all x is an element of G. We define an anti fuzzy finite state machine and an (<, < boolean OR gamma(k))*-fuzzy transformation semigroup. We describe some, applications of the given concept to an (<, < boolean OR gamma(k))*-fuzzy transformation semigroup and an anti fuzzy finite state machine.