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In this paper, based on the ELECTRE method and new ranking for the interval-valued intuitionistic fuzzy set (IVIFS), the IVIF ELECTRE method to solve multi-attribute group decision-making problems with interval-valued intuitionistic fuzzy input data is proposed, it is extending the intuitionistic fuzzy set (IF) ELECTRE method. This method firstly use AHP (Analytic hierarchy process) to find the weights of attribute, and use new ranking method for IVIFS and similarity measure between IVIFS to determine the weights of decision makers (DMs), then give the concordance set, midrange concordance set, weak concordance set and cosponging discordance set, midrange discordance set, weak discordance set. From this, the concordance matrix, discordance index, concordance dominance matrix and discordance dominance matrix are proposed. Finally, the ranking order of all the alternatives Ai(i = 1, 2, ..., n) and the best alternative are obtained. A numerical example is taken to illustrate the feasibility and practicability of the proposed method. [ABSTRACT FROM AUTHOR]

With respect to the Alexandrov fuzzy topologies induced by the generalized fuzzy approximation spaces, Wang defined interior of fuzzy set. In this paper, we give the closure of fuzzy set and discuss some properties of the interior and closure. [ABSTRACT FROM AUTHOR]

Based on the concepts of semigroup and Chang's fuzzy topological space, this paper gives the defines of the γ-fuzzy topological semigroups, γ-fuzzy topological left ideals (γ-fuzzy topological right ideals, γ-fuzzy topological intrinsic ideals and γ-fuzzy topological double ideals) and discusses the fuzzy continuous homomorphic image and the fuzzy continuous homomorphic inverse image of them. [ABSTRACT FROM AUTHOR]

Based on the concepts of semigroup and Chang's fuzzy topological space, this paper gives the defines of the γ-fuzzy topological semigroups, γ-fuzzy topological left ideals (γ-fuzzy topological right ideals, γ-fuzzy topological intrinsic ideals and γ-fuzzy topological double ideals) and discusses the fuzzy continuous homomorphic image and the fuzzy continuous homomorphic inverse image of them. [ABSTRACT FROM AUTHOR]

Based on the concepts of semigroup and Chang's fuzzy topological space, this paper gives the defines of the γ-fuzzy topological semigroups, γ-fuzzy topological left ideals (γ-fuzzy topological right ideals, γ-fuzzy topological intrinsic ideals and γ-fuzzy topological double ideals) and discusses the fuzzy continuous homomorphic image and the fuzzy continuous homomorphic inverse image of them. [ABSTRACT FROM AUTHOR]

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the soft rough set theory is proposed. Soft rough set theory is a combination of a rough theory and a soft set theory. The complement, relative complement, union, restricted union, intersection, restricted intersection, "and" and "or" operations are defined on the soft rough sets. The basic properties of the soft rough sets are also presented and discussed. [ABSTRACT FROM AUTHOR]

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the soft rough set theory is proposed. Soft rough set theory is a combination of a rough theory and a soft set theory. The complement, relative complement, union, restricted union, intersection, restricted intersection, "and" and "or" operations are defined on the soft rough sets. The basic properties of the soft rough sets are also presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper, the notions of intuitionistic fuzzy soft ring and intuitionistic fuzzy soft (left, right) ideal are given. The properties of their union, intersection and (α, δ)-level set are studied for each α, δ ∈ [0, 1]. Finally, homomorphic image and homomorphic inverse image of them are discussed. [ABSTRACT FROM AUTHOR]

In this paper, the trapezoidal method is proposed to solve the "fuzzy initial value problem". The method is obtained by combining the Euler method and a trapezoidal rule calculating integration. Convergence of the proposed methods are also presented in detail. These methods are illustrated by solving some examples. [ABSTRACT FROM AUTHOR]

In this paper, the trapezoidal method is proposed to solve the "fuzzy initial value problem". The method is obtained by combining the Euler method and a trapezoidal rule calculating integration. Convergence of the proposed methods are also presented in detail. These methods are illustrated by solving some examples. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid predictor-corrector method is proposed to solve the "fuzzy initial value problem". The method is obtained by combining an explicit three-step method and an implicit trapezoidal rule calculating integration. Convergence of the proposed methods are also presented in detail. These methods are illustrated by solving some examples. [ABSTRACT FROM AUTHOR]