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Bart Kosko claims in Fuzziness vs. Probability [32] that probability theory is a subtheory of fuzzy logic, as questions of degrees of belief in mutually-exclusive set membership in probability theory can be represented as certain cases of non-mutually-exclusive graded membership in fuzzy theory.
The approximate reasoning formalism proposed by fuzzy logic can be used to obtain a logic in which the models are the probability distributions and the theories are the lower envelopes. [7] In such a logic the question of the consistency of the available information is strictly related with the one of the coherence of partial probabilistic ...
Note that unlike possibility, fuzzy logic is compositional with respect to both the union and the intersection operator. The relationship with fuzzy theory can be explained with the following classic example. Fuzzy logic: When a bottle is half full, it can be said that the level of truth of the proposition "The bottle is full" is 0.5.
Under the distribution semantics, a probabilistic logic program defines a probability distribution over interpretations of its predicates on its Herbrand universe. The probability of a ground query is then obtained from the joint distribution of the query and the worlds: it is the sum of the probability of the worlds where the query is true. [2 ...
Type-2 fuzzy sets and systems generalize standard Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy, since that word has the connotation of much uncertainty.
Fuzzy logic has been applied to the problem of predicting cement strength. [89] It looks like fuzzy logic will eventually be applied in almost every aspect of life, even if people are not aware of it, and in that sense fuzzy logic is an astonishingly successful invention. [90]
Any Stochastic Partial Information SPI(p), which can be considered as a solution of a linear inequality system, is called Linear Partial Information LPI(p) about probability p. It can be considered as an LPI-fuzzification of the probability p corresponding to the concepts of linear fuzzy logic.
Fuzzy logic is based on the fuzzy sets concepts proposed by Lotfi Zadeh. [21] The degree of membership concept is central to fuzzy sets. The fuzzy sets differ from crisp sets since they allow an element to belong to a set to a degree (degree of membership). This approach finds good applications for control problems. [22]