Relation To Fuzzy Logic
Multi-valued logic is closely related to fuzzy set theory and fuzzy logic. The notion of fuzzy subset was introduced by Lotfi Zadeh as a formalization of vagueness; i.e., the phenomenon that a predicate may apply to an object not absolutely, but to a certain degree, and that there may be borderline cases. Indeed, as in multi-valued logic, fuzzy logic admits truth values different from "true" and "false". As an example, usually the set of possible truth values is the whole interval . Nevertheless, the main difference between fuzzy logic and multi-valued logic is in the aims. In fact, in spite of its philosophical interest (it can be used to deal with the Sorites paradox), fuzzy logic is devoted mainly to the applications. More precisely, there are two approaches to fuzzy logic. The first one is very closely linked with multi-valued logic tradition (Hajek school). So a set of designed values is fixed and this enables us to define an entailment relation. The deduction apparatus is defined by a suitable set of logical axioms and suitable inference rules. Another approach (Goguen, Pavelka and others) is devoted to defining a deduction apparatus in which approximate reasonings are admitted. Such an apparatus is defined by a suitable fuzzy subset of logical axioms and by a suitable set of fuzzy inference rules. In the first case the logical consequence operator gives the set of logical consequence of a given set of axioms. In the latter the logical consequence operator gives the fuzzy subset of logical consequence of a given fuzzy subset of hypotheses.
Read more about this topic: Many-valued Logic
Famous quotes containing the words relation to, relation, fuzzy and/or logic:
“Concord is just as idiotic as ever in relation to the spirits and their knockings. Most people here believe in a spiritual world ... in spirits which the very bullfrogs in our meadows would blackball. Their evil genius is seeing how low it can degrade them. The hooting of owls, the croaking of frogs, is celestial wisdom in comparison.”
—Henry David Thoreau (1817–1862)
“Every word was once a poem. Every new relation is a new word.”
—Ralph Waldo Emerson (1803–1882)
“Even their song is not a sure thing.
It is not a language;
it is a kind of breathing.
They are two asthmatics
whose breath sobs in and out
through a small fuzzy pipe.”
—Anne Sexton (1928–1974)
“What avail all your scholarly accomplishments and learning, compared with wisdom and manhood? To omit his other behavior, see what a work this comparatively unread and unlettered man wrote within six weeks. Where is our professor of belles-lettres, or of logic and rhetoric, who can write so well?”
—Henry David Thoreau (1817–1862)