n-Dimensional Intervals and Fuzzy S-implications

Zanotelli, Rosana; Reiser, Renata; Bedregal, Benjamín R. C.

doi:10.1109/fuzz-ieee.2018.8491580

Cited by 7 publications

(4 citation statements)

References 24 publications

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“…This section studies n -dimensional fuzzy implications on the lattice

introduced in [46] extending this work investigating construction methods of n -dimensional fuzzy implications from fuzzy implications preserving their main properties. Additionally, if

2

, the n -dimensional fuzzy implications are the usual interval-valued fuzzy implications as investigated in [1] , [9] , [16] and therefore, their corresponding properties are investigated in the more general n -dimensional interval space.…”

Section: Fuzzy Implications Onmentioning

confidence: 99%

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n-Dimensional (S,N)-implications

Zanotelli

Reiser

Bedregal

2020

International Journal of Approximate Reasoning

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The n -dimensional fuzzy logic ( n -DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, n -DFL provides a consolidated logical strategy for applied technologies since the ordered evaluations provided by decision makers impact not only by selecting the best solutions for a decision making problem, but also by enabling their comparisons. In such context, this paper studies the n -dimensional fuzzy implications ( n -DI) following distinct approaches: (i) analytical studies, presenting the most desirable properties as neutrality, ordering, (contra-)symmetry, exchange and identity principles, discussing their interrelations and exemplifications; (ii) algebraic aspects mainly related to left- and right-continuity of representable n -dimensional fuzzy t-conorms; and (iii) generating n -DI from existing fuzzy implications. As the most relevant contribution, the prospective studies in the class of n -dimensional interval (S,N)-implications include results obtained from t-representable n -dimensional conorms and involutive n -dimensional fuzzy negations. And, these theoretical results are applied to model approximate reasoning of inference schemes, dealing with based-rule in n -dimensional interval fuzzy systems. A synthetic case-study illustrates the solution for a decision-making problem in medical diagnoses.

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“…This section studies n -dimensional fuzzy implications on the lattice

introduced in [46] extending this work investigating construction methods of n -dimensional fuzzy implications from fuzzy implications preserving their main properties. Additionally, if

2

Section: Fuzzy Implications Onmentioning

confidence: 99%

“… [46, Propositions 6 and 11] A representable n-DI

verifies the property

, for

16810

if and only if each

, with

, verifies the corresponding property Ik .…”

Section: Fuzzy Implications Onmentioning

confidence: 99%

n-Dimensional (S,N)-implications

Zanotelli

Reiser

Bedregal

2020

International Journal of Approximate Reasoning

Self Cite

View full text Add to dashboard Cite

show abstract

“…Technique Contribution Class n-Dimensional Intervals and Fuzzy Simplications [31] Study main properties characterizing the class of Simplications on Ln(U ) TR Towards the study of main properties of n-Dimensional QL-implicators [32] n-dimensional QL-implicators are studied considering duality and conjugation operators.…”

Section: Fuzzy Negations On L N (U )mentioning

confidence: 99%

“…[31, Def.7] A function I : L n (U ) 2 → L n (U ) is a n-dimensional fuzzy implicator (n-DI) if I meets the boundary conditions:I0(a): I(/1/, /1/)= I(/0/, /1/)=I(/0/, /0/) = /1/; I0(b): I(/1/, /0/)=/0/. Other properties of an implicator I are as follows: I1: x ≤ z → I(x, y) ≥ I(z, y); I2: y ≤ z → I(x, y) ≤ I(x, z); I3: I(/1/, y) = y; I4: I(/x/, /x/) = /1/; I5 I(x, /0/) = N (x); I6: I(x, I(y, z)) = I(y, I(x, z)); I7: I(x, y) = /1/ ⇔ x ≤ y.…”

mentioning

confidence: 99%