n维模糊集的扩展原理及其性质

Extension principle on n-dimensional fuzzy sets and properties

扩展原理是模糊数学理论最基本原理之一,具有重要的理论意义与实际应用价值,而对n维模糊集扩展原理的研究不仅可以进一步丰富模糊数学的基本理论,而且还对n维模糊集的应用提供理论支撑.根据n维模糊集的截集、分解定理和表现定理,利用模糊集的扩展原理,建立n维模糊集的扩展原理.首先对应不同截集下得到的n维模糊集的3个分解定理和3个表现定理,给出相应的n维模糊集的3个扩展原理;其次,结合n维模糊集运算的定义及模糊集扩展原理的性质,讨论了n维模糊集扩展原理的有关性质;最后,给出复合函数的n维模糊集扩展原理,并利用复合函数的模糊集扩展原理的性质,讨论了复合函数的n维模糊集扩展原理的性质.

The extension principle of fuzzy set,with the important theoretical significance and application value,is a fundamental principle.So,the research about the extension principle of n-dimensional fuzzy set will not only further enrich the basic theory of fuzzy mathematics but also provide theoretic basis for the application of n-dimensional fuzzy set.According to the cut sets,decomposition theorem and representation theorem of n-dimensional fuzzy set,using the extension principle of fuzzy set,the extension principle of n-dimensional fuzzy set is established.Firstly,in accordance with three kinds of decomposition theorem and three kinds of representation theorem of n-dimensional fuzzy set,three kinds of extension principle of n-dimensional fuzzy set are given.Secondly,under the operations of n-dimensional fuzzy set and the properties of fuzzy set ’ s extension principle,the properties of extension principle of n-dimensional fuzzy set are discussed.Finally,the n-dimensional fuzzy set ’ s extension principle of the composite functions and their properties are acquired.