A Layperson Reflection on Sorites

Trillas, Enric; García-Honrado, Itziar

doi:10.1007/978-3-642-36527-0_15

Cited by 6 publications

(2 citation statements)

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“…A "crisp kernel of antonymy" of P can be reached, once an antonym aP is known, through the set A P = {x ∈ X : p(x) ≤ p a (x)}, containing those elements of X showing "P less than aP " [10], those that are more covered by aP than by P . For instance, provided X is an interval Provided P is precise, it is A P = {x ∈ X : 1 = p a (x)}, that, if p a is not coincidental with p (P is regular), cannot be coincidental with the crisp complement of the crisp set specified by P in X.…”

Section: 2mentioning

confidence: 99%

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A reflection on fuzzy “complements”

Trillas

Soto

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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A fuzzy set can be seen as a measure of the meaning of a predicate in a given universe. Generally, a predicate covers some elements of the universe and not others. In this paper the problem of determining the properties a fuzzy set should check to cover elements not covered by a predicate represented by a fuzzy set is reviewed. Thus the problems of determining the negation and antonym of a predicate and the possibility of finding a good measure to represent them are studied, and new concepts as the kernel of an antonymy are introduced.

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Section: 2mentioning

confidence: 99%

“…P specifies the crisp set [0, 5), and [5,10] Hence, fuzzy logic opens a door to newly looking at opposites by even offering a methodology able to obtain antonyms without words for them in language.…”

Section: Non-regular Precise Predicatesmentioning

confidence: 99%