Iranian Journal of Fuzzy Systems
Year:2012 | Volume:9 | Issue:5|Papers Count:10

In a fuzzy metric space (X, M,*), where * is a continuous t-norm, a locally fuzzy contraction mapping is defined. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satisfies the locally fuzzy contractivity condition then it satisfies the global fuzzy contractivity condition.

In this paper, the notions of (T, S)-composition matrix and (T, S) interval-valued intuitionistic fuzzy equivalence matrix are introduced where (T, S) is a dual pair of triangular module. They are the generalization of composition matrix and interval-valued intuitionistic fuzzy equivalence matrix. Furthermore, their properties and characterizations are presented. Then a new method based on a-matrix for clustering is developed. Finally, an example is given to demonstrate our method.

The fixed point alternative methods are implemented to give Hyers- Ulam stability for the quintic functional equation f(x + 3y) - 5f(x + 2y) + 10f (x +y) -10f(x)+5f(x-y)-f(x-2y) = 120f(y) and the sextic functional equation f(x + 3y) - 6f(x + 2y) + 15f(x + y) - 20f(x) + 15f(x - y) - 6f(x -2y) + f(x - 3y) = 720f(y) in the setting of intuitionistic fuzzy normed spaces (IFN-spaces). This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator. Furthermore, the interdisciplinary relation among the fuzzy set theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the paper.

The aim of this paper is to introduce (L, M)-fuzzy closure structure where L and M are strictly two-sided, commutative quantales. Firstly, we define (L, M)-fuzzy closure spaces and get some relations between (L, M)-double fuzzy topological spaces and (L, M)-fuzzy closure spaces. Then, we introduce initial (L, M)-fuzzy closure structures and we prove that the category (L, M)-FC of (L, M)-fuzzy closure spaces and (L, M)-C-maps is a topological category over the category SET. From this fact, we define products of (L, M)-fuzzy closure spaces. Finally, we show that an initial structure of (L, M)-double fuzzy topological spaces can be obtained by the initial structure of (L, M)-fuzzy closure spaces induced by them.

In this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. Moreover, some basic operations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebra with respect to these operations. Afterwards, the Atanassov's operator is applied to intuitionistic fuzzy mappings and the corresponding properties are examined. Finally, the decomposition and representation theorems of intuitionistic fuzzy mappings are established.

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuitionistic fuzzy metric spaces.

The notion of generalized locally bounded I-topological vector spaces is introduced. Some of their important properties are studied. The relationship between this kind of spaces and the locally bounded I-topological vector spaces introduced by Wu and Fang [Boundedness and locally bounded fuzzy topological vector spaces, Fuzzy Math. 5 (4) (1985) 87-94] is discussed. Moreover, we also use the family of generalized fuzzy quasi-norms to characterize the generalized locally bounded I-topological vector spaces, and give some applications of this characterization.

In this paper, the new notions of "belongingness (Îg)" and "quasi-coincidence (qd)" of a fuzzy point with a fuzzy set are introduced. By means of this new idea, the concept of (a , b)-fuzzy nary subhypergroup of an nary hypergroup is given, where a, b Î {Îg, qd, Îg Ù qd, Îg Ú qd} and it is shown that, in 16 kinds of (a , b)-fuzzy n-ary subhypergroups, the significant ones are the (Îg , Îg Ú qd)-fuzzy n-ary subhypergroups,and the (Îg Ù qd , Îg )-fuzzy n-ary subhypergroups.

In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.

The aim of this paper is to give the set of all t-best approximations on fuzzy n-normed spaces and prove some theorems in the sense of Vaezpour and Karimi [13].