On contradiction in fuzzy logic

Abstract

We clarify which space of functions in [0, 1] E would be reasonable in fuzzy logic in order to avoid selfcontradiction.

Measures of self-contradiction on Atanassov's intuitionistic fuzzy sets: An axiomatic model

“…In fact, it is sufficient to consider other sequences of rectangular regions with vertices not only on the line α 2 = 1−α 1 2 , but on any line containing the points 1 L and (0, α), with α ∈ (0, 1), and even on curves given by continuous and strictly decreasing functions. ) n , whereas C (χ i ) = (…”

“…These papers formalize the idea that a set is self-contradictory, or contradictory for short, if it violates the principle of noncontradiction, that is, the statement "If x is P, then x is not P" has some degree of truth. They established that the fuzzy set associated with the predicate P determined by the membership function μ P is contradictory if "μ P (x) → μ ¬P (x) for all x", representing the implication "→" by means of the reticular order ≤ of [0,1] and the negation through a strong fuzzy negation N. Thus μ P is selfcontradictory regarding N, or N-self-contradictory, if μ P ≤ N • μ P . Note that such an inequality is true in classical logic if and only if μ P = μ ∅ .…”

A normal form which preserves tautologies and contradictions in a class of fuzzy logics

“…For that we believe that the approach pointed out in Section 5 is a suitable start point. We should also summarize this work considering several different notions of logical consequence and contradictions (see for example [48]). In another setting, we must also study classes of fuzzy logics where the CNF and DNF preserve tautologies and contradictions as considered here as well as other weaker notions of tautologies and contradictions.…”

Approximate robotic mapping from sonar data by modeling perceptions with antonyms

“…Involution: In considering a pair (P, Q) of antonyms, Q is an antonym of P, and P is an antonym of Q P ¼ aðaPÞ and Q ¼ aðaQ Þ: 2. Coherence with the negation: Pairs of antonyms (P, Q) are N-contradictory [48,25], for certain strong negation; it is expressed by: P 6 not Q ; and Q 6 not P (see for example the pair of antonyms (Far, Near) in Fig. 1 or (None, Some) in Fig.…”