On functional equations and inequalities related to some reasoning schemes that involve fuzzy implications

2021 ◽  
Author(s):  
Katarzyna Miś ◽  
Michał Baczyński ◽  
Piotr Helbin
Keyword(s):  
Functional Equations ◽  
Fuzzy Implications

CONTRAPOSITIVE SYMMETRY OF DISTRIBUTIVE FUZZY IMPLICATIONS

2002 ◽  
Vol 10 (supp01) ◽  
pp. 135-147 ◽  
Author(s):  
MICHAŁ BACZYŃSKI
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Strong Negation ◽  
Fuzzy Implications ◽  
Fuzzy Implication

Recently, we have examined the solutions of the system of the functional equations I(x, T(y, z)) = T(I(x, y), I(x, z)), I(x, I(y, z)) = I(T(x, y), z), where T : [0, 1]2 → [0, 1] is a strict t-norm and I : [0, 1]2 → [0, 1] is a non-continuous fuzzy implication. In this paper we continue these investigations for contrapositive implications, i.e. functions which satisfy the functional equation I(x, y) = I(N(y), N(x)), with a strong negation N : [0, 1] → [0, 1]. We show also the bounds for two classes of fuzzy implications which are connected with our investigations.

On two functional equations connected with distributivity of fuzzy implications

2016 ◽  
Vol 55 (2) ◽  
Author(s):  
Roman Ger ◽  
Marcin Emil Kuczma ◽  
Wanda Niemyska
Keyword(s):  
Functional Equations ◽  
Fuzzy Implications

ON A NEW CLASS OF IMPLICATIONS: (g,min)-IMPLICATIONS AND SEVERAL CLASSICAL TAUTOLOGIES

2012 ◽  
Vol 20 (01) ◽  
pp. 1-20 ◽  
Author(s):  
HUA-WEN LIU
Keyword(s):  
Classical Logic ◽  
Functional Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Triangular Norms ◽  
Basic Properties ◽  
New Class ◽  
Fuzzy Implications ◽  
Necessary And Sufficient

A new class of fuzzy implications, called (g, min )-implications, is introduced by means of the additive generators of continuous Archimedean t-conorms, called g-generators. Basic properties of these implications are discussed. It is shown that the (g, min )-implications are really a new class different from the known ( S , N )-, R -, QL - and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz. law of importation, contraction law and distributivity over triangular norms ( t -norms) and triangular conorms ( t -conorms) are investigated. A series of necessary and sufficient conditions are proposed, under which the corresponding functional equations are satisfied.

ON A CLASS OF DISTRIBUTIVE FUZZY IMPLICATIONS

2001 ◽  
Vol 09 (02) ◽  
pp. 229-238 ◽  
Author(s):  
MICHAŁ BACZYŃSKI
Keyword(s):  
Unknown Function ◽  
Functional Equations ◽  
System Of Functional Equations ◽  
Fuzzy Implications ◽  
Fuzzy Implication

We deal with the system of functional equations I(x,T(y,z))=T(I(x,y), I(x,z)), I(x,I(y,z))=I(T(x,y),z), where function T:[0,1]2→ [0,1] is a strict t-norm and I:[0,1]2→ [0,1] is an unknown function. Under some assumptions imposed on function I we obtain that I is almost conjugate with the Yager fuzzy implication.

On some functional equations related to derivations and bicircular projections in rings

2014 ◽  
Vol 49 (2) ◽  
pp. 313-331
Author(s):  
Maja Fošner ◽  
◽  
Benjamin Marcen ◽  
Nejc Širovnik ◽  
Joso Vukman ◽  
...  
Keyword(s):  
Functional Equations

Functional equations related to weightable quasi-metrics

2015 ◽  
Vol 4 (1047) ◽  
Author(s):  
M.J. Campion ◽  
E. Indurain ◽  
G. Ochoa
Keyword(s):  
Functional Equations
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