Innovative types of fuzzy gamma ideals in ordered gamma semigroups

The fuzzification of algebraic structures plays an important role in handling many areas of multi-disciplinary research, such as computer science, control theory, information science, topological spaces and fuzzy automata to handle many real world problems. For instance, algebraic structures are particularly useful in detecting permanent faults on sequential machine behaviour. However, the idea of ordered T-semigroup as a generalization of ordered semigroup in algebraic structures has rarely been studied. In this research, a new form of fuzzy subsystem in ordered T-semigroup is defined. Specifically, a developmental platform of further characterizations on ordered T-semigroups using fuzzy subsystems properties and new fuzzified ideal structures of ordered semigroups is developed based on a detailed study of ordered T-semigroups in terms of the idea of belongs to (E) and quasicoincidence with (q) relation. This idea of quasi-coincidence of a fuzzy point with a fuzzy set played a remarkable role in obtaining several types of fuzzy subgroups and subsystems based on three contributions. One, a new form of generalization of fuzzy generalized bi T-ideal is developed, and the notion of fuzzy bi T-ideal of the form (E,E Vqk) in an ordered T-semigroup is also introduced. In addition, a necessary and sufficient condition for an ordered T-semigroup to be simple T-ideals in terms of this new form is stated. Two, the concept of (E,E Vqk)-fuzzy quasi T-ideals, fuzzy semiprime T-ideals, and other characterization in terms of regular (left, right, completely, intra) in ordered T-semigroup are developed. Three, a new fuzzified T-ideal in terms of interior T-ideal of ordered T-semigroups in many classes are determined. Thus, this thesis provides the characterizations of innovative types of fuzzy T-ideals in ordered T-semigroups with classifications in terms of completely regular, intra-regular, for fuzzy generalized bi T-ideals, fuzzy bi T-ideals, fuzzy quasi and fuzzy semiprime T-ideals, and fuzzy interior T-ideals. These findings constitute a platform for further advancement of ordered T-semigroups and their applications to other concepts and branches of algebra

Bi-ideals of ordered semigroups based on the interval-valued fuzzy point

Interval-valued fuzzy set theory (advanced generalization of Zadeh’s fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, we introduce the notion of generalized quasi-coincident with (q(Formula Presented)) relation of an interval-valued fuzzy point with an interval-valued fuzzy set. In fact, this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. Applying this newly defined idea, the notion of an interval-valued (∈,∈vq(Formula Presented)) -fuzzy bi-ideal is introduced. Moreover, some characterizations of interval-valued (∈,∈vq(Formula Presented)) -fuzzy bi-ideals are described. It is shown that an interval-valued (∈,∈vq(Formula Presented)) -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. Finally, the concept of implication-based interval-valued fuzzy bi-ideals, characterizations of an interval-valued fuzzy bi-ideal and an interval-valued (∈,∈vq(Formula Presented)) - fuzzy bi-ideal are considered

Characterizations of non associative ordered semigroups by the properties of their fuzzy ideals with thresholds (α, β]

In this paper, we give the characterizations of regular (intra-regular, both regular and intra-regular) ordered AG-groupoids by the properties of fuzzy (left, right, quasi-, bi-, generalized bi-) ideals with thresholds (а, β]

CHARACTERIZATION OF ORDERED SEMIGROUPS BASED 0N (|;qk)-QUASI-COINCIDENT WITH RELATION

Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (2;2_(|;qk))fuzzy bi-ideals of an ordered semigroup S: Further, upper/lower parts of (2;2 _(|;qk))-fuzzy bi-ideals of S are determined. Finally, some well known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (2;2_(|;qk))-fuzzy bi-ideals

Regular ag-groupoids characterized by (∈, ∈ ∨ q k)-fuzzy ideals

In this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in AG -groupoids. Generalizing the concepts of (∈, ∈ ∨q) -fuzzy bi-ideals (interior ideal), we define (∈, ∈ ∨ q k) -fuzzy bi-ideals, (∈, ∈ ∨ q k )-fuzzy left (right)-ideals and ( , ) k ? ? ?q -fuzzy interior ideals in AG -groupoids and discuss some fundamental aspects of these ideals in AG -groupoids. We further define ( ∈, ∈ ∨ q k) -fuzzy bi-ideals and (∈, ∈ ∨ q k)-fuzzy interior ideals and give some of their basic properties in AG -groupoids. In the last section, we define lower/upper parts of (∈, ∈ ∨ q k ) -fuzzy left (resp. right) ideals and investigate some characterizations of regular and intera-regular AG -groupoids in terms of the lower parts of ( ∈, ∈ ∨ q k ) -fuzzy left (resp. right) ideals and ( ∈, ∈ ∨ q k )-fuzzy bi-ideal of AG -groupoids

A new characterization of fuzzy ideals of semigroups and its applications

In this paper, we develop a new technique for constructing fuzzy ideals of a semigroup. By using generalized Green\u27s relations, fuzzy star ideals are constructed. It is shown that the new fuzzy ideal of a semigroup can be used to investigate the relationship between fuzzy sets and abundance and regularity for an arbitrary semigroup. Appropriate examples of such fuzzy ideals are given in order to illustrate the technique. Finally, we explain when a semigroup satisfies conditions of regularity

On Ordered (p; q)-Lateral Ideals in Ordered Ternary Semigroups

In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary semigroups. Also, some properties of (p; q)-lateral simple ordered ternary semigroup have been examined. Further, we characterize the relationship between minimal (resp., maximal) ordered (p; q)- lateral ideals and (p; q)-lateral simple ordered ternary semigroups

Effects of oil palm (elais guineensis) fruit extracts on glucose uptake activity of muscle, adipose and liver cells

The effect of oil palm (Elaeis guineensis) fruit aqueous extract (OPF) on glucose uptake activity of three different cell lines was investigated. The cell lines were incubated with different concentrations of OPF to evaluate the stimulatory effect of OPF towards glucose uptake activity of L6 myotubes, 3T3F442A adipocytes and Chang liver cell line. The glucose uptake activities of all tested cells were enhanced in the presence of OPF extract (basal condition). Nevertheless in combination of OPF extract and 100 nM insulin, the glucose uptake activity was only significantly enhanced in L6 myotubes and 3T3F442A adipocytes cell lines. The extracts enhanced the glucose uptake into cells through either insulin-mimetic or insulin-sensitizing property or combination of these two properties. It can be suggested that the OPF extract exerts its antihyperglycemic action partly by mediated glucose uptake into the glucose-responsive disposal cells, muscle, adipose and liver