模糊集的常见操作及示例和代码

本文概述

Python3
Python3
Python3
Python3

什么是模糊集？
模糊是指不清楚或模糊的事物。因此, 模糊集是一个集合, 其中每个键都与值相关联, 该值基于确定性介于0到1之间。此值通常称为隶属度。模糊集在常规集符号的顶部用波浪号表示。
用代码对模糊集进行运算：
1.并集或合集：
考虑由A和B表示的2个模糊集, 然后让Y成为它们的并集, 那么对于A和B的每个成员, Y将是：

degree_of_membership(Y)= max(degree_of_membership(A), degree_of_membership(B))

范例：
Python3

# Example to Demonstrate the # Union of Two Fuzzy Sets A = dict () B = dict () Y = dict ()A = { "a" : 0.2 , "b" : 0.3 , "c" : 0.6 , "d" : 0.6 } B = { "a" : 0.9 , "b" : 0.9 , "c" : 0.4 , "d" : 0.5 }print ( 'The First Fuzzy Set is :' , A) print ( 'The Second Fuzzy Set is :' , B)for A_key, B_key in zip (A, B): A_value = https://www.lsbin.com/A[A_key] B_value = B[B_key]if A_value > B_value: Y[A_key] = A_value else : Y[B_key] = B_valueprint ('Fuzzy Set Union is :' , Y)

输出如下

The First Fuzzy Set is : {'a': 0.2, 'b': 0.3, 'c': 0.6, 'd': 0.6} The Second Fuzzy Set is : {'a': 0.9, 'b': 0.9, 'c': 0.4, 'd': 0.5} Fuzzy Set Union is : {'a': 0.9, 'b': 0.9, 'c': 0.6, 'd': 0.6}

2.交集：
考虑2个用A和B表示的模糊集, 然后让Y视为它们的交集, 那么对于A和B的每个成员, Y将是：

degree_of_membership(Y)= min(degree_of_membership(A), degree_of_membership(B))

范例：
Python3

# Example to Demonstrate # Intersection of Two Fuzzy Sets A = dict () B = dict () Y = dict ()A = { "a" : 0.2 , "b" : 0.3 , "c" : 0.6 , "d" : 0.6 } B = { "a" : 0.9 , "b" : 0.9 , "c" : 0.4 , "d" : 0.5 }print ( 'The First Fuzzy Set is :' , A) print ( 'The Second Fuzzy Set is :' , B)for A_key, B_key in zip (A, B): A_value = https://www.lsbin.com/A[A_key] B_value = B[B_key]if A_value < B_value: Y[A_key] = A_value else : Y[B_key] = B_value print ('Fuzzy Set Intersection is :' , Y)

输出如下

The First Fuzzy Set is : {'a': 0.2, 'b': 0.3, 'c': 0.6, 'd': 0.6} The Second Fuzzy Set is : {'a': 0.9, 'b': 0.9, 'c': 0.4, 'd': 0.5} Fuzzy Set Intersection is : {'a': 0.2, 'b': 0.3, 'c': 0.4, 'd': 0.5}

3.补集：
考虑用A表示的模糊集, 然后将Y视为它的补集, 那么对于A的每个成员, Y将是：

degree_of_membership(Y)= 1 - degree_of_membership(A)

范例：
Python3

# Example to Demonstrate the # Difference Between Two Fuzzy Sets A = dict () Y = dict ()A = { "a" : 0.2 , "b" : 0.3 , "c" : 0.6 , "d" : 0.6 }print ( 'The Fuzzy Set is :' , A)for A_key in A: Y[A_key] = 1 - A[A_key]print ( 'Fuzzy Set Complement is :' , Y)

输出如下

The Fuzzy Set is : {'a': 0.2, 'b': 0.3, 'c': 0.6, 'd': 0.6} Fuzzy Set Complement is : {'a': 0.8, 'b': 0.7, 'c': 0.4, 'd': 0.4}

4.差集：
考虑2个用A和B表示的模糊集, 然后让Y视为它们的交集, 那么对于A和B的每个成员, Y将是：

degree_of_membership(Y)= min(degree_of_membership(A), 1- degree_of_membership(B))

范例：
Python3

# Example to Demonstrate the # Difference Between Two Fuzzy Sets A = dict () B = dict () Y = dict ()A = { "a" : 0.2 , "b" : 0.3 , "c" : 0.6 , "d" : 0.6 } B = { "a" : 0.9 , "b" : 0.9 , "c" : 0.4 , "d" : 0.5 }print ( 'The First Fuzzy Set is :' , A) print ( 'The Second Fuzzy Set is :' , B)for A_key, B_key in zip (A, B): A_value = https://www.lsbin.com/A[A_key] B_value = B[B_key] B_value = 1 - B_valueif A_value < B_value: Y[A_key] = A_value else : Y[B_key] = B_valueprint ('Fuzzy Set Difference is :' , Y)

输出如下

The First Fuzzy Set is : {"a": 0.2, "b": 0.3, "c": 0.6, "d": 0.6} The Second Fuzzy Set is : {"a": 0.9, "b": 0.9, "c": 0.4, "d": 0.5} Fuzzy Set Difference is : {"a": 0.1, "b": 0.1, "c": 0.6, "d": 0.5}