Soft Computing

Lecture 4

Fuzzy logic, linguistic variables, pseudo-physical logics

8.3 Linguistic variable 8.3.1 Definition of linguistic variable When we consider a variable, in general, it takes numbers as its value. If the variable takes linguistic terms, it is called “linguistic variable”.

Definition(Linguistic variable) The linguistic variable is defined by the following quintuple. Linguistic variable = (x, T(x), U, G, M) x:• x - name of variable• T(x): set of linguistic terms which can be a value of the variable• U: set of universe of discourse which defines the characteristics of the Variable• G: syntactic grammar which produces terms in T(x)• M: semantic rules which map terms in T(x) to fuzzy sets in U

Fuzzy predicate

Fuzzy modifier

Pseudo-physical logics

• Spatial– Deal with description of objects and its

positions in space

• Temporary– Deal with description of time, events, time

domain

• Causal– Deal with description of reasons and

consequences, causal links between them

Spatial logic

• Set of basis relations

• Set of rules defining features basis relations

• Set of rules for descriptions of derivative relations

• Set of rules for descriptions of connections between relations

Kinds of relations

• Determined• Fuzzy

• Topological• Metrical

– Based on metric scale• Absolute• Relative• Egocentric• External

Kinds or parts of spatial logic

• Logic of position of objects

• Logic of positional relationship of objects

• Logic of directions

• Logic of distances

Examples of basis relations in logic of positional relationship of objects

• Under(X,Y) – x is situated under y• Inside(X,Y) – x is situated into y• At_left(X,Y) – x is situated at left from y• On(X,Y) – x is situated on y• Vertical(X) – x is vertical• Touch(X,Y) – x touches with y• Near(X,Y) – x is near y• Far(X,Y) – x is far from y• Hang(X,Y) – x hang on y

Examples of features of relations

• Touch(X,Y) -> touch(Y,X) symmetry

• Under(X,Y) -> not under(Y,X) antisimmetry

• under(X,Y) -> under(X,Z)&under(Z,Y) transitivity

• Near(X,X) reflexivity

• and so on

Examples of derivative relations

• Stand_on(X,Y) -> on(X,Y) & vertical(X)

• Lie_on(X,Y) -> on(X,Y) & horizontal(X)

Examples of connections between relations

• Far(X,Y) -> not touch(X,Y)

• Under(X,Y) -> Above(Y,X)

• Touch(X,Y) -> near(X,Y)

• On(X,Y) -> above(X,Y)

• And so on

Examples of relations in temporary logic

• Simultaneously(X,Y)

• Earlier(X,Y)

• Pass_in(X,Y) x passes in temporary interval y

• Finish_in(X,Y) interval X finishes in interval y

• And so on

Examples of causal logic

• Reason(X,Y) x is reason of y

• Help_to(X,Y) x is helper for y

• Consequence(X,Y) x is Consequence of y

• Prevent(X,Y) x prevent to y

• Goal(x,y) x is goal of y

• And so on