差异属性值下的尺度VIKOR要领代码实现
Standard VIKOR method code implementation under different attribute values
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MATLAB学习——三角模糊数，
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MATLAB learning - triangular fuzzy numbers,
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模糊数是模糊数学中最基础的看法之一。设X是给定的一个论域，则X上的一个模糊子集为A={x,μ(x)|xϵX}。其中，μ(x):Xϵ[0,1]代表了A的隶属度函数，若是 两个模糊子集A与B相等，记作A=B，当且仅当它们具有相同的隶属度函数，即μA(x)= μB(x)。
Fuzzy numbers are one of the most basic concepts in fuzzy mathematics. Let X be a given domain of discourse, then a fuzzy subset on X is A={x,μ(x)|xϵX}. Among them, μ(x):Xϵ[0,1] represents the membership function of A, if two fuzzy subsets A and B are equal, denoted as A=B, if and only if they have the same membership function, That is μA(x) = μB(x).
界说
模糊数是界说在实数集R上的凸模糊集，若对于某一模糊数ŕ，其隶属度函数知足 ：
A fuzzy number is a convex fuzzy set defined on the set of real numbers R. For a certain fuzzy number R, its membership function satisfies:
则称ŕ=(r1,rm,ru)为三角模糊数，其隶属度函数为，F(x):R[0,1]其中， XϵR，R为实数域。
三角模糊数作为基础的模糊集，因其浅易性和适用 性受到了学术界的普遍 关注，是决议 理论研究者在学术蹊径 上定要掌握的一环。
Then ŕ=(r1,rm,ru) is called a triangular fuzzy number, and its membership function is, F(x):R[0,1] where XϵR, R is the real number field.
The triangular fuzzy number as the basis of the fuzzy set, because of its simplicity and practicability, has received extensive attention in the academic circles, and it is a link that decision theory researchers must master on the academic road.
运算规则
令A=(a1,am,an)与B=(b1,bm,bn)为恣意 两个三角模糊数，则它们的运算规则如下：
Let A=(a1,am,an) and B=(b1,bm,bn) be any two triangular fuzzy numbers, then their algorithms are as follows:
数据尺度化
令Ã为尺度化后的效果 ，则：
若A为效益型指标：
若为成本型指标：
距离测度
VIKOR要领需要对指标与理想点之间的距离举行 丈量，因此三角模糊数的距离测度公式如下所示：
令A=(a1,am,au)与B=(b1,bm,bu)为恣意 两个三角模糊数，界说范数||A-B||为三角模糊数A与B之间的距离为
The VIKOR method needs to measure the distance between the indicator and the ideal point, so the distance measurement formula of the triangular fuzzy number is as follows:
Let A=(a1,am,au) and B=(b1,bm,bu) be any two triangular fuzzy numbers, and define the norm ||A-B|| as the distance between A and B of the triangular fuzzy numbers as
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