The theory of fuzzy measures and fuzzy integrals was introduced by S u g e n o [16] and intensively studied. Monographs [15] and [18] are dedicated to this topic. Recently, several classical inequalities were generalized to fuzzy integral. F l o r e sF r a n u l i č and R o m á n-F l o r e s [11] provided a Chebyshev type inequality for fuzzy integral of continuous and strictly monotone functio...

After the introduction of fuzzy sets by Zadeh [15] in 1965 and fuzzy topology by chang [4] in 1967. Several researches were conducted on the generalizations of the notions of fuzzy sets and fuzzy topology. The concept of intuitionistic fuzzy sets was introduced by Atanassov [1] as a generalization of fuzzy sets . In the last 20 years various concepts of fuzzy mathematics have been extended for ...

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of Gfuzzy congruences on semigroups.

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal element...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

The concept of fuzzy magic labeling is introduced.Fuzzy magic labeling for some graphs like path, cycle and star graph are defined. It is proved that, every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. And we show that the removal of a fuzzy bridge from a fuzzy magic graph G, such that G* is a cycle with odd number of nodes is a fuzzy magic graph.And also some prop...

In this paper, we introduced two types of fuzzy stabilizers St R (F) and St ⊕ R (F) of a fuzzy set F and the stabilizer St ∨(F, G) of F with respect to G in IMTL-algebras. We proved that St R (F), St ⊕ R (F) and St ∨(F, G) are fuzzy filters of M. We investigated some properties of the stabilizers. By introducing the ⊗̃ operation of two fuzzy filters, we prove that ⊗̃ and St∨(·, ·) form an adjoint...

In this paper, we count the number of fuzzy subgroups of cyclic group G = Zp × Zq × Zr × Zs with p, q, r, s are distinct prime numbers. We define an equivalence relation on the fuzzy subgroups of any groups G and determine all of its subgroups. Then we draw the diagram of lattice subgroups of G. The number of fuzzy subgroups of G by observing the diagram then will be counted. Mathematics Subjec...

Let G be an intuitionistic fuzzy graph. Let u and v be two vertices of G. A subset D of V is called a fuzzy equitable dominating set if every v ∈ V − Dthere exist a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| = 1 where deg(u) denotes the degree of vertex u and deg(v) denotes the degree of vertex v and μ2(vi, vj ) = μ1(vi) ∧ μ1(vj ), γ2(vi, vj ) = γ1(vi) ∨ γ1(vj ). The minimum cardina...

Any complete hypergroup H may be represented as the union g g G H A ∈ =  , where G is a group and the subsets Ag of H satisfy certain properties. With any hypergroupoid 〈H, o〉 we may associate a particular fuzzy set μ . In this paper we determine sufficient and necessary conditions for a finite complete hypergroup 〈H, o〉, where p G (Z , ) ≅ + or 2p G (Z , ) ≅ + , p a prime number, such that t...