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In this paper we introduce the concepts of pseudo-convexity, invexity and pseudo-invexity for fuzzy mappings of one variable based on the notion of di erentiability proposed by Goetschel and Voxman [4], and investigate the relationship between convex fuzzy mappings, preinvex fuzzy mappings and these classes of fuzzy mappings. We shall prove that(More)
Since almost all practical problems are fuzzy and approximate, fuzzy decision making becomes one of the most important practical approaches. However, the resulting problems are frequently complicated and difficult to solve. One effective way to overcome these difficulties is to explore the concavity or generalized concavity properties of the resulting(More)
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)
Human judgment plays an important role in the rating of enterprise financial conditions. The recently developed fuzzy adaptive network (FAN), which can handle systems whose behaviour is influenced by human judgment, appears to be ideally suited for the modelling of this credit rating problem. In this paper, FAN is used to model the credit rating of small(More)
The concepts of ( 1; 2)-convexity, 1-B-vexity and 1-convexity for fuzzy mappings are introduced through the so-called “fuzzy max” order among fuzzy numbers. We show that the class of ( 1; 2)-convex fuzzy mappings, 1-B-vex fuzzy mappings and 1-convex fuzzy mappings includes many well-known classes of fuzzy mappings such as convex fuzzy mappings and preinvex(More)