On the Direct Decomposability of Fuzzy Connectives, Negations and Implications Based on T-Norms and T-Conorms on Product Lattices

Graded dominance and related graded properties of fuzzy connectives

Fuzzy Sets and Systems ◽

10.1016/j.fss.2014.04.025 ◽

2015 ◽

Vol 262 ◽

pp. 78-101 ◽

Cited By ~ 10

Author(s):

Libor Běhounek ◽

Ulrich Bodenhofer ◽

Petr Cintula ◽

Susanne Saminger-Platz ◽

Peter Sarkoci

Keyword(s):

Graded Properties ◽

Fuzzy Connectives

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Fuzzy Connectives for Efficient Image Reduction and Speeding Up Image Analysis

IEEE Access ◽

10.1109/access.2018.2879473 ◽

2018 ◽

Vol 6 ◽

pp. 68403-68414 ◽

Cited By ~ 2

Author(s):

Gleb Beliakov ◽

Gita Das ◽

Huy Quan Vu ◽

Tim Wilkin ◽

Yong Xiang

Keyword(s):

Image Analysis ◽

Fuzzy Connectives

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A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms

Fuzzy Sets and Systems ◽

10.1016/s0165-0114(83)80073-6 ◽

1983 ◽

Vol 11 (1-3) ◽

pp. 115-134 ◽

Cited By ~ 356

Author(s):

Siegfried Weber

Keyword(s):

General Concept ◽

Fuzzy Connectives

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Learning the Fuzzy Connectives of a Multilayer Network Using Particle Swarm Optimization

2007 IEEE Symposium on Foundations of Computational Intelligence ◽

10.1109/foci.2007.371532 ◽

2007 ◽

Cited By ~ 4

Author(s):

Gaurav Parekh ◽

James M. Keller

Keyword(s):

Particle Swarm Optimization ◽

Particle Swarm ◽

Multilayer Network ◽

Swarm Optimization ◽

Fuzzy Connectives

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REVISITING Xor-IMPLICATIONS: CLASSES OF FUZZY (CO)IMPLICATIONS BASED ON f-Xor (f-XNor) CONNECTIVES

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488513500414 ◽

2013 ◽

Vol 21 (06) ◽

pp. 899-925 ◽

Cited By ~ 3

Author(s):

BENJAMÍN BEDREGAL ◽

RENATA HAX SANDER REISER ◽

GRAÇALIZ PEREIRA DIMURO

Keyword(s):

Boundary Conditions ◽

Unit Interval ◽

End Points ◽

Triangular Norms ◽

Fuzzy Implications ◽

Classical Definition ◽

Definition Of ◽

Exclusive Or ◽

Intrinsic Definition ◽

Fuzzy Connectives

The main contribution of this paper is the introduction of an intrinsic definition of the connective “fuzzy exclusive or” E (f-Xor E), based only on the properties of boundary conditions, commutativity and partial isotonicity-antitonicity on the the end-points of the unit interval U = [0,1], in a way that the classical definition of the boolean Xor is preserved. We show three classes of the f-Xor E that can be also obtained from the composition of fuzzy connectives, namely, triangular norms, triangular conorms and fuzzy negations. A discussion about extra properties satisfied by the f-Xor E is presented. Additionally, the paper introduces a class of fuzzy equivalences that generalizes the Fodor and Roubens's fuzzy equivalence, and four classes of fuzzy implications induced by the f-Xor E, discussing their main properties. The relationships between those classes of fuzzy implications and automorphisms are explored. The action of automorphisms on f-Xor E is analyzed.

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