萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）

小君 2023-04-14 19:16:37 352

萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）本期推文阅读时长大约5分钟，欢迎您的用心访问，亲爱的您，这里是LearningYard学苑。今天小编为大家带来的主题是MATLAB学习——三角模糊数，

不同属性值下的标准VIKOR方法代码实现

Standard VIKOR method code implementation under different attribute values

萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）(1)

分享兴趣，传播快乐，

增长见闻，留下美好！

亲爱的您，这里是LearningYard学苑。

今天小编为大家带来的主题是

MATLAB学习——三角模糊数，

欢迎您的用心访问，

本期推文阅读时长大约5分钟，

请您耐心阅读。

Share interest spread happiness

Increase knowledge and leave good news!

Dear you this is LearningYard Academy.

Today the theme I bring to you is

MATLAB learning - triangular fuzzy numbers

Welcome your visit with heart

This tweet is about 5 minutes long to read.

Please read with patience.

模糊数是模糊数学中最基础的概念之一。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，如果两个模糊子集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).

定义

模糊数是定义在实数集R上的凸模糊集，若对于某一模糊数ŕ，其隶属度函数满足：

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:

萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）(2)

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，因其简易性和实用性受到了学术界的广泛关注，是决策理论研究者在学术道路上定要掌握的一环。

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.

运算法则

令A=(a1 am an)与B=(b1 bm bn)为任意两个三角模糊数，则它们的运算法则如下：

Let A=(a1 am an) and B=(b1 bm bn) be any two triangular fuzzy numbers then their algorithms are as follows:

萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）(3)

数据标准化

令Ã为标准化后的结果，则：

若A为效益型指标：

萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）(4)

若为成本型指标：

萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）(5)

距离测度

VIKOR方法需要对指标与理想点之间的距离进行测量，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)为任意两个三角模糊数，定义范数||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

萌说新语MATLAB入门学习8（萌说新语MATLAB入门学习8）(6)