Similarity versus Preference in Fuzzy Set-Based Logics

Case-Based Reasoning for Insulin Bolus Advice

“…Case retrieval. Several similarity measurement metrics can be found in the literature, [16][17][18] which are commonly integrated within CBR and can be used for case retrieval. ABC4D uses the k-nearest neighbor (k-NN) 19 classifier to retrieve the most similar case when compared to the current meal scenario.…”

Fuzzy-Set Based Logics — an History-Oriented Presentation of their Main Developments

“…However it does not mean that all logics of graded truth are compositional (for instance, similarity logics using crisp propositions fuzzified by a fuzzy proximity relation (as done in [Ruspini, 1991]), are not compositional [Dubois and Prade, 1998b]. The information system paradigm underlying Zadeh's view of fuzzy truth values nevertheless questions the comparison made in [Gaines, 1978] between probabilistic logics which are not compositional, and a particular (max-min) many-valued logic which is truth-functional.…”

“…The formula (q(x), µ P (x)) then expresses a piece of information of the form "the more x is P , the more certain q(x) is true". A fuzzy restriction on the scope of an existential quantifier can be also introduced in the following way [Dubois et al, 1998]. From the two classical first order logic premises "∀x ∈ A, ¬p(x, y) ∨ q(x, y)", and "∃x ∈ B, p(x, c)", where c is a constant, we can conclude that "∃x ∈ B, q(x, c)" provided that B ⊆ A.…”

“…Then, using both |= α and |= α K , a deductive notion of interpolation based on gradual rules, as described in Section 2.5, can be captured inside a logical setting. The relations and the differences between similarity-based logics and possibilistic logic are discussed in and in [Dubois and Prade, 1998b]. The presence of a similarity relation on the set of interpretation suggests a modal logic setting for similarity-based reasoning where each level cut S α of S is an accessibility relation.…”

A logic of the similarity with prototypes and its relationship to fuzzy logic

“…This is a well-known interpretation of fuzzy sets; "similarity" is the key notion. For the similaritybased interpretation of fuzzy sets as well as other possible interpretations, we refer, e.g., to [5,6]. The idea to understand fuzzy sets as crisp sets together with a similarity relation is furthermore developed in [7].…”