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Generalization of preinvex and B-vex fuzzy mappings

机译：Preinvex和B-vex模糊映射的一般化

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摘要

A class of fuzzy mappings, called B-preinvex, and strictly B-preinvex fuzzy mappings, is introduced by relaxing the definition of preinvexity of a fuzzy mapping. Similarly, based on a notion of differentability of fuzzy mappings different from the usual one, the class of pseudo-B-vex, B-invex, and pseudo-B-invex fuzzy mappings is defined as a generalization of pseudo-convex, invex, and pseudo-invex fuzzy mappings. We prove that a strictly B-vex, or B-preinvex fuzzy mapping has at most one global minimum point, and that the class of B-vex fuzzy mappings forms a subset of the class of quasi- convex fuzzy mappings. B-vex (resp. B-preinvex) fuzzy mappings satisfy most of the basic properties of convex (resp. Preinvex) fuzzy mappings. In addition characterizations and sufficient optimality conditions are obtained for B-vex and B-preinvex fuzzy mappings.
机译：通过放宽模糊映射的前凸性的定义，引入了一类模糊映射，称为B-前凸模糊映射，严格地称为B-preinvex模糊映射。同样，基于模糊映射的可区别性不同于通常的概念，将伪B-vex，B-invex和伪B-invex模糊映射的类别定义为伪凸，凸，和伪整数模糊映射。我们证明严格的B-vex或B-preinvex模糊映射最多具有一个全局最小点，并且B-vex模糊映射的类构成了拟凸模糊映射的类的子集。 B-vex（分别为B-preinvex）模糊映射满足凸（分别为Preinvex）模糊映射的大多数基本属性。此外，获得了B-vex和B-preinvex模糊映射的特征和足够的最优条件。

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