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
