多目标模糊推理简单例子（周四学习卡模糊集之三角模糊数）
多目标模糊推理简单例子（周四学习卡模糊集之三角模糊数）本次推文简要介绍三角模糊数的定义及运算法则等，下期推文将介绍其在VIKOR方法中的MATLAB代码实现。//////////////////////在决策过程中往往由于认知不足或者信息属性无法给出准确的评价，如何解决这个难题呢，一起来看看吧！////////////////////// 针对决策信息不具体的多属性决策，决策者难以对方案作出准确的评价，因此模糊集的概念由此产生。最早的模糊集由Zedah于1965年提出，在文献中他作了以下解释：模糊集是一类具有连续隶属度等级的对象。这样的集合由一个隶属度(特征)函数来表征，该函数赋予每个对象一个介于0到1之间的隶属度等级。将包含、并、交、补、关系、凸等概念推广到模糊集上。由于现实决策环境往往更加复杂，再加上社会的不断发展，越来越多的模糊集理论因此诞生，如直觉模糊集、犹豫模糊集、毕达哥拉斯模糊集等。
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。
在决策过程中往往由于认知不足或者信息属性无法给出准确的评价，如何解决这个难题呢，一起来看看吧！
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针对决策信息不具体的多属性决策，决策者难以对方案作出准确的评价，因此模糊集的概念由此产生。最早的模糊集由Zedah于1965年提出，在文献中他作了以下解释：模糊集是一类具有连续隶属度等级的对象。这样的集合由一个隶属度(特征)函数来表征，该函数赋予每个对象一个介于0到1之间的隶属度等级。将包含、并、交、补、关系、凸等概念推广到模糊集上。由于现实决策环境往往更加复杂，再加上社会的不断发展，越来越多的模糊集理论因此诞生，如直觉模糊集、犹豫模糊集、毕达哥拉斯模糊集等。
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本次推文简要介绍三角模糊数的定义及运算法则等，下期推文将介绍其在VIKOR方法中的MATLAB代码实现。
三角模糊数能够有效的表示难以用精确数值描述的信息，还可以灵活的与其他模糊数进行转换，进而解决多个领域的相关问题，因此得到了众多专家学者的广泛研究。
基本概念：
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，其隶属度函数满足：
在三角模糊数的基本定义上 不少专家学者对其扩展形式也进行了研究，如有序三角模糊数、区间三角模糊数和Pythagorean三角模糊数等。
运算法则：
数据标准化：
距离测度：
VIKOR方法需要对指标与理想点之间的举例进行测量，因此三角模糊数的距离测度公式如下：
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英 文 学 习
For multi-attribute decision-making with unspecific decision information it is difficult for decision makers to make an accurate evaluation of the plan so the concept of fuzzy set arises. The earliest fuzzy set was proposed by Zedah in 1965 and he explained in the literature as follows: Fuzzy set is a class of objects with continuous membership levels. Such a set is characterized by a membership (characteristic) function which gives each object a membership level between 0 and 1. The concepts of inclusion union intersection complement relation and convexity are extended to fuzzy sets. Because the actual decision-making environment is often more complicated coupled with the continuous development of society more and more fuzzy set theories have been born such as intuitionistic fuzzy sets hesitant fuzzy sets Pythagorean fuzzy sets and so on.
This tweet briefly introduces the definition and algorithm of triangular fuzzy numbers. The next tweet will introduce its MATLAB code implementation in the VIKOR method.
Triangular fuzzy numbers can effectively represent information that is difficult to describe with precise numerical values and can be flexibly converted with other fuzzy numbers to solve related problems in many fields. Therefore it has been extensively studied by many experts and scholars.
basic concept:
Fuzzy numbers are convex fuzzy sets defined on the real number set R. For a certain fuzzy number its membership function satisfies:
On the basic definition of triangular fuzzy numbers many experts and scholars have also studied its extended forms such as ordered triangular fuzzy numbers interval triangular fuzzy numbers and Pythagorean triangular fuzzy numbers.
Algorithm:
Data standardization:
Distance measure:
The VIKOR method needs to measure the example between the index and the ideal point so the distance measurement formula of the triangular fuzzy number is as follows
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英文翻译：谷歌翻译
参考资料：
[1]周师兄学习文档
[2]谭春桥 张晓丹. 基于后悔理论的不确定风险型多属性决策VIKOR方法[J].统计与决策 2019(1):47-51.
[3]王柯. 面向故障诊断的三角模糊数决策方法研究[D].齐鲁工业大学 2021.
本文由LearningYard学苑原创，仅代表作者个人观点，如有侵权请联系删除。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。
在决策过程中往往由于认知不足或者信息属性无法给出准确的评价，如何解决这个难题呢，一起来看看吧！
//////////////////////
针对决策信息不具体的多属性决策，决策者难以对方案作出准确的评价，因此模糊集的概念由此产生。最早的模糊集由Zedah于1965年提出，在文献中他作了以下解释：模糊集是一类具有连续隶属度等级的对象。这样的集合由一个隶属度(特征)函数来表征，该函数赋予每个对象一个介于0到1之间的隶属度等级。将包含、并、交、补、关系、凸等概念推广到模糊集上。由于现实决策环境往往更加复杂，再加上社会的不断发展，越来越多的模糊集理论因此诞生，如直觉模糊集、犹豫模糊集、毕达哥拉斯模糊集等。
//////////////////////
本次推文简要介绍三角模糊数的定义及运算法则等，下期推文将介绍其在VIKOR方法中的MATLAB代码实现。
三角模糊数能够有效的表示难以用精确数值描述的信息，还可以灵活的与其他模糊数进行转换，进而解决多个领域的相关问题，因此得到了众多专家学者的广泛研究。
基本概念：
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，其隶属度函数满足：
在三角模糊数的基本定义上 不少专家学者对其扩展形式也进行了研究，如有序三角模糊数、区间三角模糊数和Pythagorean三角模糊数等。
运算法则：
数据标准化：
距离测度：
VIKOR方法需要对指标与理想点之间的举例进行测量，因此三角模糊数的距离测度公式如下：
//////////////////////
英 文 学 习
For multi-attribute decision-making with unspecific decision information it is difficult for decision makers to make an accurate evaluation of the plan so the concept of fuzzy set arises. The earliest fuzzy set was proposed by Zedah in 1965 and he explained in the literature as follows: Fuzzy set is a class of objects with continuous membership levels. Such a set is characterized by a membership (characteristic) function which gives each object a membership level between 0 and 1. The concepts of inclusion union intersection complement relation and convexity are extended to fuzzy sets. Because the actual decision-making environment is often more complicated coupled with the continuous development of society more and more fuzzy set theories have been born such as intuitionistic fuzzy sets hesitant fuzzy sets Pythagorean fuzzy sets and so on.
This tweet briefly introduces the definition and algorithm of triangular fuzzy numbers. The next tweet will introduce its MATLAB code implementation in the VIKOR method.
Triangular fuzzy numbers can effectively represent information that is difficult to describe with precise numerical values and can be flexibly converted with other fuzzy numbers to solve related problems in many fields. Therefore it has been extensively studied by many experts and scholars.
basic concept:
Fuzzy numbers are convex fuzzy sets defined on the real number set R. For a certain fuzzy number its membership function satisfies:
On the basic definition of triangular fuzzy numbers many experts and scholars have also studied its extended forms such as ordered triangular fuzzy numbers interval triangular fuzzy numbers and Pythagorean triangular fuzzy numbers.
Algorithm:
Data standardization:
Distance measure:
The VIKOR method needs to measure the example between the index and the ideal point so the distance measurement formula of the triangular fuzzy number is as follows
//////////////////////
英文翻译：谷歌翻译
参考资料：
[1]周师兄学习文档
[2]谭春桥 张晓丹. 基于后悔理论的不确定风险型多属性决策VIKOR方法[J].统计与决策 2019(1):47-51.
[3]王柯. 面向故障诊断的三角模糊数决策方法研究[D].齐鲁工业大学 2021.
本文由LearningYard学苑原创，仅代表作者个人观点，如有侵权请联系删除。
