8/28/16

Relations & Similarity in Computing & Mathematics.

Data Collections & Relations, Relation Criteria.

We can organize data in for example databases, then check how these relate with each other.

For example we can have a set of 'words':
 { 'plane', 'helicopter', 'plate', 'dish', 'cup', 'star', 'knife', 'place' }.

We can define 'greater length of word' relation for example, that states that a 'word' is in this relation with another 'word' if it consits of more 'characters'.

For example word 'helicopter' with it's 10 'characters' is in 'greater length relation' with 'plate' with it's 5 'characters'; but 'plate' is not in the same relation with a 'helicopter' word' - we can say that this relation is 'not reversible'.

We can define other relations as well, for example minimal amount of the same 'characters' at the same positions in a 'word'.

We can define a 'minimum of 3 same character in a same length word' relation; then 'plane', 'plate' & 'place' words are in this relation; this a relation is reversible.

Let's note that amount of the same 'characters' at the same position is 4 for the above 'words' - therefore lesser amount criteria in regards of character similarity at positions are met as well.

We can define a lot of different relation criteria - for similarity relations or for other relations - using programming languages for example.

Relation criteria is a function that accepts a zero, one, two, or more objects (their ordering is meaningful & important in this case) then returns a boolean value (true or false) depending on whether these criteria are met or not; this has uses in data categorization & sorting for example as well, as well as in defining conditional instructions & preconditions; perhaps more as well.


Relations & Similarity in the Relational Databases.

In relational databases we have a 'like' operator & more.

Relations are also called 'tables', for data meeting 'in relation' criteria can be grouped into a well-defined tables; it's semantics (meaning) is that they are in relation if they are in the same table or in the same view.

If we have a table with semantic similarity, then this can be used as well.

For example, we can have 'air vehicles' table - similarity relation nevertheless - that can contain { 'plane', 'helicopter' } data set; we can say that both 'plane' & 'helicopter' are similar semantically (according to their meanings) because they are 'air vehicles'.

If something is not in this table (for example: 'air drone') then this does not mean so strongly that it is dissimilar yet - only that it's in 'uncertain dissimilarity relation'; we can call 'uncertain dissimilarity relation' a 'weak dissimilarity relation' as well; Computers can fairly well see semantic similarities if they are programmed well & have enough of well-structured data; there are fields of Artificial Intelligence that are responsible for data discovery & learning from databases, to handle database(s)' unknown or partly-unknown structure.

There's much more of mathematics in that as well, including 'Relational Model' Theory.


Similarity Relation with Regular Expressions.

Character strings can be analyzed using Regular Expressions.

Regular Expressions can be used to form 'Patterns', then we can analyze if a character string(s) 'match this a pattern'.

When two or more character strings match the same pattern, then we can say they are similar that way.

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