[PDF] Top 20 A Study on Rough, Fuzzy and Rough Fuzzy Bi-ideals of Ternary Semigroups

... Kar and Maity [8] studied congruences on ternary semi- groups. Congruence is a special type of equivalence relation which plays a vital role in the quotient structure of algebraic structures. Let T be a ... See full document

... our study to the application of rough set theory in fuzzy ideals with respect to ...of rough fuzzy ideals, rough fuzzy bi- ideals and ... See full document

... Ordered semigroups have many applications in the theory of sequential machines, formal languages, computer arithmetics, and error-correcting ...a fuzzy set, introduced by ...the study of fuzzy ... See full document

... of ternary semigroup [6]. The algebraic structures of ternary semigroups were also studied by some authors, for example, Sioson studied ideals in ternary semigroups ...and ... See full document

... of fuzzy sets was first studied by Zadeh [17] in 1965. Many papers on fuzzy sets appeared showing the importance of the concept and its applications to logic, set theory, group theory, ring theory, real ... See full document

... of fuzzy setting. The notion of fuzzy subgroup was made by Rosenfeld [16] in ...1971. Fuzzy ideals in rings were introduced by ...studied fuzzy ideals in semirings. The theory of ... See full document

... and fuzzy automata, fuzzification of algebraic structures have now become synonymous with other useful branches of contemporary mathematics ...1965, fuzzy sets have had a long, study history in the ... See full document

... intuitionistic fuzzy sets[1,2] are intuitively straightforward extension of Zadeh’s[12] fuzzy sets; while a fuzzy set gives the degree of membership of an element in a given set, an Atanassov’s ... See full document

... in ternary semgroups. He also introduced the notion of regular ternary semigroups and characterized them by using the notion of quasi ...of ideals in ternary semigroups. The ... See full document

... a ternary semigroup and the notion of Γ-semigroup was introduced by Sen and Saha [11] in ...and ternary semigroup, Akram et ...biΓ- ternary semigroup just ...biΓ- ternary semigroup and ... See full document

... investigated rough semigroups and rough fuzzy semigroups based on fuzzy ...a fuzzy ideal and showed that U(µ, t) is a congruence relation on rings, and the author ... See full document

... Ordered semigroups have many applications in the theory of sequential machines, formal languages, computer arithmetics, design of fast adders and error-correcting ...a fuzzy filter in ordered ... See full document

... ( µ 1 ∪ µ 2 x = µ 1 x µ 2 x = µ 1 x ∨ µ 2 x and ( µ 1 ∩ µ 2 ) ( x ) = min { µ 1 ( x ), µ 2 ( x ) } = µ 1 ( x ) ∧ µ 2 ( x ) for all x ∈ T . Where ∨ denotes maximum or supremum and ∧ denotes minimum or infimum. Definition ... See full document

... of fuzzy set was initiated by L. Zadeh [1]. The study of fuzzy algebraic structures started with the introduction of the concepts of fuzzy groups in the pioneering paper of Rosenfeld ...a ... See full document

... the fuzzy rough theory. Taking a decision system with fuzzy rough coefficients ...with fuzzy rough coefficients), the objective functions as well as some constraints involving ... See full document

... It was shown that both R d S i (x) or R d T i (x) depends on the nearest miss of x, i.e., the nearest sample from different classes of x. As we know, the statistics of minimum and maximum are very sensitive to noisy ... See full document

... The rough set theory and fuzzy set theory are extensions of classical set theory, and they are related but distinct and complementary ...The rough set theory[1,2] is mainly focused on crisp ... See full document

... introduced fuzzy soft groups in 2009.Thereafter many reaserchers are applying fuzzy soft tools to other algebraic structures ...modules, semigroups ([7, 8, ... See full document

... )-fuzzy rough approximation operators with respect to a T L-fuzzy ideal of the ...-upper fuzzy rough approximations with respect to T -congruence L-fuzzy relation on a ... See full document

... interior ideals in a semigroup S, and investigate some properties of such ...intuitionistic fuzzy interior ideal of T , then the preimage f −1 (B) = (f −1 (µ B ), f −1 (γ B )) of B under f is an ... See full document