Store:FLes03

Set theory

As mentioned in the previous chapter, the basic concept of fuzzy logic is that of multivalence, i.e., in terms of set theory, of the possibility that an object can belong to a set even partially and, therefore, also to several sets with different degrees. Let us recall from the beginning the basic elements of the theory of ordinary sets. As will be seen, in them appear the formal expressions of the principles of Aristotelian logic, recalled in the previous chapter.

Quantifiers

• Membership: represented by the symbol $\in$ (belongs), - for example the number 13 belongs to the set of odd numbers $\in$ $13\in Odd$
• Non-membership: represented by the symbol $\notin$ (It does not belong)
• Inclusion: Represented by the symbol $\subset$ (is content), - for example the whole $A$ it is contained within the larger set $U$, $A\subset U$ (in this case it is said that $A$ is a subset of $U$)
• Universal quantifier, which is indicated by the symbol $\forall$ (for each)
• Demonstration, which is indicated by the symbol $\mid$ (such that)