Complex Fuzzy Structured Element and Its Properties

The first part of this paper gives the definition about complex fuzzy structured element on the basis of one-dimensional fuzzy structured element and some of its property. The following part introduces its limit and continuity. All of this has opened up a vision for the research of fuzzy structured element, and also played an important role in promoting its progress. (2) ~ ~ E F  modulus, continuity of complex fuzzy structured element


Introduction
Many scholars have further studied the fuzzy structured element, and they also have given out a lot of properties about the fuzzy structured element.But the study of complex fuzzy structured element is at its beginning stage.In this paper, we study the complex fuzzy structured element, which breaking the blank situation of researching the complex fuzzy structured element, and laying a foundation for the further research of complex fuzzy structured element.It also breaks the blank field of researching area in complex fuzzy number, and brings motivations for people to study the calculus in the field of the fuzzy structured element.Meanwhile, it also enriches the knowledge of fuzzy mathematics and widens the vision for the research of the fuzzy control, fuzzy decision-making, etc.It also broadens a new area for its study.Of course, the study of this paper is a qualitative leap from the real area to the complex area, and brings great convenience for the information classification and management.In order to give a clear introduction for the following part, we give the following illustrations as the starting point, for a coordinate point ( , ) f a b a ib   ( , of two-dimensional space, every coordinate point ) f x y  x iy  its degree of near ( , ) f a b can be expressed by the fuzzy sets in fuzzy numbers, Recorded as (2) ~( , ) A x y (hear we add (2) in the upper right corner of the two-dimensional space of symbols, which is different from one-dimensional space of symbols).In one-dimensional space we have membership function 2 ( ) ( )

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(of course there are others).As to the membership function of two-dimensional space, we take the membership func- , according we defined the membership function of two-dimensional space as

The
， meet the following nature, we say the two-dimensional fuzzy set is complex fuzzy structuring element of .
(2) , ) y .Here we state is all the fuzzy numbers generated by the linear and (2) ) is all the fuzzy numbers generated by the linear ， F (2) , let .There exist limited real numbers , , , is the modulus of the complex fuzzy number . Recorded .
Recorded as .

The Limit of the Complex Fuzzy Structuring Element Definition 3.1 Let , ~(
) is true, we say  con- verge to n Li according to fuzzy distance .

Recorded as .
( In the following we give a theorem about the convergence of complex fuzzy numbers with the help of converge to Proof.Only serves to prove (3), It is easy to get the result when .In t clusion is correct when Theorem 3.3 (The uniqueness of the limit) Let ~~, (2) ~( , As  is arbitrary we 0 obtain: (2) ~( , )

2) (2) ~Ẽ -F Modulus of the Complex Fuzzy Structured Element and Its Related Concept 2.1. The Complex Fuzzy Structured Element
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