In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce...In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.展开更多
In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.
Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued fu...Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued functions are discussed by means of the characteristic the- orems of nonabsolute fuzzy integrals and the embedding theorem,i.e.,the fuzzy number space can be embedded into a concrete Banach space.Several necessary and sufficient conditions and examples are given.展开更多
Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly mon...Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.展开更多
文摘In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.
文摘In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.
基金the National Natural Science Foundation of China （No. 10771171） the Scientific Research Item of Gansu Education Department （No. 0601-20）.
文摘Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued functions are discussed by means of the characteristic the- orems of nonabsolute fuzzy integrals and the embedding theorem,i.e.,the fuzzy number space can be embedded into a concrete Banach space.Several necessary and sufficient conditions and examples are given.
基金Supported by Natural Science Foundation of Gansu Province of China (Grant No.18JR3RM238)Research Foundation of Higher Education of Gansu Province of China (Grant No. 2018A-101)Innovation Ability promotion Project of Higher Education of Gansu Province of China (Grant No. 2019A-117)。
文摘Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.
