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--- tanszek:oktatas:techcomm:information_-_basics:description_of_information [2023/10/26 20:45] – létrehozva knehez
+++ tanszek:oktatas:techcomm:information_-_basics:description_of_information [2024/09/30 17:43] (current) – knehez
@@ Line 1: / Line 1: @@
-The mathematical set is the totality of well-defined objects.
+Mathematical //set// is the totality of well-defined objects. The objects which belong to the set are called the //elements//.
-The objects which belong to the set are called the 'elements'.
 This state of belonging to a given set is called relation, which has the following sign: a∈X
@@ Line 15: / Line 13: @@
 The elements (which belong to a given set) can be defined by enumeration or by giving an exact principle of how they belong to that set.
-For example:
+**For example**:
 The set of natural numbers:
-Z={1,2,3,4,5..} you may define the elements by writing them
+$$ Z = \{1, 2, 3, 4, 5, ...\} $$
-List the natural, odd integers from one to ten:
+You may define the elements by writing them: List the natural, odd integers from one to ten:
-H={1,3,5,7,9}
+$$ A = \{1, 3, 5, 7, 9\} $$
 or
-H={n : n positive, odd number and n < 1O}
+$$  A = \{x \mid x \text{ is an odd integer and } 1 \leq x < 10 \} $$
+or in modern C++:
+<sxh c++>
+std::set<int> mySet = {1, 2, 3};
+</sxh>
+or in Python:
+<sxh Python>
+my_set = {1, 2, 3}
+</sxh>
+The sets (and their belongings) are usually set in a sharp way.
+{{:tanszek:oktatas:techcomm:information_-_basics:pasted:20231026-204536.png}}
+In information technology it is possible to use sets which contain fuzzy elements as well.
+In these cases the value of how an element is connected to a given set is defined by a '//membership function//'
+μm(x)
+{{:tanszek:oktatas:techcomm:information_-_basics:pasted:20240930-173642.png}}
+//Fuzzy sets// are a generalization of classical sets used in mathematics and logic to //handle uncertainty// and //partial membership//. Unlike classical sets where an element either belongs or does not belong to a set (membership is binary: 0 or 1), fuzzy sets allow for degrees of membership, represented by values between 0 and 1.
+Further reading: [[https://towardsdatascience.com/a-very-brief-introduction-to-fuzzy-logic-and-fuzzy-systems-d68d14b3a3b8|A very brief introduction to fuzzy-logic]]