title: A novel approach toward fuzzy generalized bi-ideals in ordered semigroups.
abstract: In several advanced fields like control engineering, computer science, fuzzy automata, finite state machine, and error correcting codes, the use of fuzzified algebraic structures especially ordered semigroups plays a central role. In this paper, we introduced a new and advanced generalization of fuzzy generalized bi-ideals of ordered semigroups. These new concepts are supported by suitable examples. These new notions are the generalizations of ordinary fuzzy generalized bi-ideals of ordered semigroups. Several fundamental theorems of ordered semigroups are investigated by the properties of these newly defined fuzzy generalized bi-ideals. Further, using level sets, ordinary fuzzy generalized bi-ideals are linked with these newly defined ideals which is the most significant part of this paper.
authors.affiliation: Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtunkhwa 19130, Pakistan.
authors.forename: Faiz Muhammad
authors.initials: FM
authors.lastname: Khan
authors.affiliation: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, UTM, 81310 Johor Bahru, Johor, Malaysia.
authors.forename: Nor Haniza
authors.initials: NH
authors.lastname: Sarmin
authors.affiliation: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, UTM, 81310 Johor Bahru, Johor, Malaysia.
authors.forename: Hidayat Ullah
authors.initials: HU
authors.lastname: Khan
mesh_terms: D017143:Fuzzy Logic; D008433:Mathematics / Q000379:methods*; D008962:Models, Theoretical