Study On The Continuity Problems Of Fuzzy N-Cell Number Valued Functions

In classical analytical mathematics,numbers and functions and the mathematical theories formed by them are the basis for studying analytical mathematics and its applications.Similarly,fuzzy numbers and fuzzy number valued function and their developing theories have also become important research topics in fuzzy analysis and its applications.With the efforts of many scholars,the research on the continuity of fuzzy number valued function(1-dimensional fuzzy number valued function)and their applications has made good progress and achieved a lot of research results.However,due to the complexity of the structure of n-dimensional fuzzy numbers,there are few research results on the continuity of n-dimensional fuzzy number valued functions.With the research and development of fuzzy analysis and its applications,it is necessary to further study the continuity of n-dimensional fuzzy number valued functions(n≥2).Therefore,this paper further studies the continuous problem of a special kind of n-dimensional fuzzy number valued functions—fuzzy n-cell number valued functions.The specific work done is as follows:1.The concept of semi-continuity of fuzzy number valued function is generalized and developed,and the concept and related properties of semi-continuity of fuzzy n-cell number valued functions are given,and the necessary and sufficient conditions of semi-continuity of fuzzy n-cell number valued functions are given.On this basis,the convexity of fuzzy n-cell number valued functions is studied,and several necessary and sufficient conditions for semi-continuous fuzzy n-cell number valued functions to be convex are given.2.The boundedness of the continuous fuzzy n-cell number valued functions is discussed,the existence of the upper and lower bounds of the continuous fuzzy n-cell number valued functions on the closed interval are proved,and the continuous fuzzy n-cell number valued functions on the closed interval is illustrated with an example.The function is not necessarily able to reach the supremum;and the necessary and sufficient conditions for it to reach the supremum are given.3.The square fuzzy Bernstein polynomials and related properties of the fuzzy n-cell number valued functions are given,and the square fuzzy Bernstein polynomials are proved to be continuous fuzzy n-cell number valued functions.On this basis,the approximation problem of continuous fuzzy n-cell number valued functions is discussed using square fuzzy Bernstein polynomials,and its corresponding Weierstrass approximation theorem is given.4.By discussing the addition and multiplication of continuous fuzzy n-cell number valued functions,it is proved that the space of continuous fuzzy n-cell number valued functions becomes a cone.At the same time,the corresponding supremum metric is established on the continuous fuzzy n-cell number valued functions space,and it is proved that the space of continuous fuzzy n-cell number valued functions becomes a complete metric space under this supremum metric.