The Convex Fuzzy Subsets Based On Interval-valued Fuzzy Points

The concept of the common convex fuzzy subsets is described as the relations between fuzzy points and fuzzy sets. In this paper, the concept of convex fuzzy subsets is generalized, by the use of interval-valued fuzzy points, three new kinds of convex fuzzy subsets are researched based on the neighborhood relations between interval-valued fuzzy points and Zadeh’s fuzzy sets, interval-valued fuzzy points and interval-valued fuzzy sets, interval-valued fuzzy points and intuitionistic fuzzy sets, respectively, i.e.(α,β)-Zadeh’s convex fuzzy subsets,(α,β)-interval-valued convex fuzzy subsets and(α,β)-intuitionistic convex fuzzy subsets. And the relations between three new kinds of convex fuzzy subsets and triple valued convex fuzzy subsets are established, respectively. The main contents of the paper are as follows:First of all, the current research states of the theories of convex fuzzy subsets are introduced, the theories of interval-valued fuzzy subsets and intuitionistic fuzzy subsets are outlined, and the pre-knowledge of interval-valued fuzzy points and convex fuzzy subsets are proposed.Secondly, by the use of the concept of interval-valued level cut sets on Zadeh’s fuzzy sets, the neighborhood relations between interval-valued fuzzy points and Zadeh’s fuzzy sets are defined, by the use of the neighborhood relations, the theories of(α,β)-convex fuzzy subsets are given. Then the properties of sixteen kinds of (α,β)-convex fuzzy subsets are researched and discussed.Thirdly, by the use of the neighborhood relations between interval-valued fuzzy points and interval-valued fuzzy sets, the concepts of (α,β)-interval-valued convex fuzzy subsets are proposed. The properties of sixteen kinds of (α,β)-interval-valued convex fuzzy subsets are discussed. Then the relations between interval-valued convex fuzzy subsets and triple valued convex fuzzy subsets are given.Finally, by the use of the neighborhood relations between interval-valued fuzzy points and intuitionistic fuzzy subsets,(α,β)-intuitionistic convex fuzzy subsets are defined. And sixteen kinds of (α,β)-intuitionistic convex fuzzy subsets are researched. Then the relations between intuitionistic convex fuzzy subsets and triple valued convex fuzzy subsets are given.