Soft Computing Lecture 4 Fuzzy logic linguistic variables

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