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Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
A first course in fuzzy logic
Interval arithmetic: From principles to implementation
Journal of the ACM (JACM)
On the relationship between some extensions of fuzzy set theory
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Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Formal Aspects of Correctness and Optimality of Interval Computations
Formal Aspects of Computing
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Analyzing Properties of Fuzzy Implications Obtained via the Interval Constructor
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Interval Additive Generators of Interval T-Norms
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Fuzzy Implications
On interval fuzzy S-implications
Information Sciences: an International Journal
Interval valued QL-implications
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Fuzzy Sets and Systems
Interval valued fuzzy coimplication
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
On averaging operators for Atanassov's intuitionistic fuzzy sets
Information Sciences: an International Journal
Generation of interval-valued fuzzy implications from Kα operators
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
The standard completeness of interval-valued monoidal t-norm based logic
Information Sciences: an International Journal
On the representation of intuitionistic fuzzy t-norms and t-conorms
IEEE Transactions on Fuzzy Systems
Algebraic structures of interval-valued fuzzy ( S,N)-implications
International Journal of Approximate Reasoning
Information Sciences: an International Journal
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The Smets-Magrez axiomatic is usually used to define the class of fuzzy continuous implications which are both S and R-implications (Lukasiewicz implications). Another approach is the construction of such class starting from a basic implication and applying automorphisms. Literature has shown that there is a harmony between those approaches, however in this paper we show that the extension of the Lukasiewicz implication defined on [0,1] for interval values cannot be applied in a direct way. We show that the harmony between the Smets-Magrez axiomatic approach and the one that comes from the generation by automorphisms is not preserved when such extension is done. One of the main consequences lies on the fact that the automorphism approach induces the loss of R-implications from the resulting class of implicators. More precisely, we show that the interval version of such approaches produce two disjunct classes of implicators, meaning that, unlike the usual case, the choice of the respective approach is an important step.