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—The keynote contains two parts, one is the formal theory, the other is the current state. Though we have used the full title, this paper contains only the formal theory. Neighborhood system generalizes topological neighborhood system by simply dropping the axioms of topology. In this paper, we use it to define Zadeh's Granular Mathematics (GrM). The main… (More)

Neural-fuzzy systems have been proved to be very useful and have been applied to modeling many humanistic problems. But these systems also have problems such as those of generalization, dimensionality, and convergence. Support vector machines, which are based on statistical learning theory and kernel transformation, are powerful modeling tools. However,… (More)

In this paper, based on the more restrictive definition of fuzzy convexity due to Ammar and Metz [1], several useful composition rules are developed. The advantages in using the more restrictive definition of fuzzy convexity are that local optimality implies global optimality, and that any convex combination of such convex fuzzy sets is also a convex fuzzy… (More)