Extension Error Set Based on Extension Set

This paper gives the concepts of extension error set and fuzzy extension error set, discusses diverse extension error set and fuzzy extension error set based on extension set and error set, and puts forward the relevant propositions and operations. Finally, it provides proofs of the soundness and completeness for the propositions and operations.


Introduction
In the field of fuzzy mathematics, the research of set mainly concentrates on the static form of fuzzy set and its effective forms of reasoning and rule.However, the dynamic changes of the fuzzy set are important parts of set research.In this paper, firstly, we study extension error set and fuzzy extension error set's dynamic concept based on the theory of error eliminating and extenics.Then, we research diverse extension error set and fuzzy extension error set, and put forward the relevant propositions and operations.Finally, we provide proofs of the soundness and completeness for the propositions and operations.In one word, because of the study of extension error set, this paper has very important theoretical and practical significance in different fields.As the fundamental element for matter description, it's referred to as 1-dimensional matter-element, and m , vm are referred to as the three key elements of matterelement M, within which, the two-tuples composed of cm and is referred to as the characteristic-element of matter .A matter with multiple characteristics, similar to 1dimensional matter-element, can be defined as a multidimensional matter-element:

Affair-Element
Interaction between matters is referred to as affair, described by affair-element.

Relation-Element
In the boundless universe, there is a network of relations among any matter, affair, person, information, knowledge and other matter, affair, person, information and knowledge.Because of interaction and interplay among these relations, the matter-element, affair-element and relation-element describing them also have various relations with other matter-elements, affair-elements and relation-elements, and the changes of theses relations will also be interacting and interplaying.Relation-element is a formalized tool to describe this kind of phenomena.

The Research of Extension Error Set
We research extension error set based on the theory of Extenics, and explore classical extension error set, fuzzy extension error set, multivariate extension error set.Moreover, we put forward the relevant propositions and operations.According to thses propositions and operations, we provide some proofs.

The Definition of Extension Error Set
Suppose is an object set, is a set of association rules, if , , , we call that "E" is an extension error set for association rule in domain .In detail, is a domain, ) is a set of association rules, M refers to the matter-element, A representative affairelement, R represents the relationship between relationelement; represents the correlation functions of extension error set, R is the real number field, T refers to the time.In this paper we take extension error set as a complex system, its' elements as subsystems. So, are called extension error set's extension of the domain, negative extension field, extension, stable domain and negative stable region, critical region respectively.In the definition ´, , This contradiction with 1 E E  2 .so, 1 2 f f . The end.


We according to the features of the elements can be di vided: 1) Classic extension error set 3) Have critical point extension error set , ,

The Research of Fuzzy Extension Error Set
eration of extension error set.
This section mainly research the definition, relation, op

The Definition of Fuzzy Extension Error
, we call that E is a fuzzy extensio  n error set for S in U .

Error Set
Defi uppose

The Relation between Fuzzy Extension s 4.2.1. Equation nition
for association rule S, is the subset , or Proposition 3.1.2.4 Suppose are subsets for associatio

The Operations of between Fuz Extension
Error Sets   attracted the atten cially in the fields of management and decision-making.So we study the extension error set and fuzzy extension error set.But, what we have done is not enough.It's in administrative before our theory is perfect.So, we call for more scholars from all over the world to do research about extenics and error eliminating theory.Only in this way, can they have wider value of applications in more fields.

he Inte Fuzzy Extension
An ordered triple composed of the measure v m of O m about c m , with matter O m as object, and cm as characteristic

m
For convenience, the whole matter-element is ex-pressed as   £ M , the whole matter is expressed as the domain of measure of c m .
there are clearly tablished the following proposition: