Properties and relations between implication operators

Authors:
Jiaxin Han;Huacan He;Yingcang Ma
Affiliations:
School of Computer Science, Northwestern Polytechnical University, Xi'an, China;School of Computer Science, Northwestern Polytechnical University, Xi'an, China;College of Science, Xi'an University of Engineering Science and Technology, Xi'an, China
Venue:
ICIC'06 Proceedings of the 2006 international conference on Intelligent computing: Part II
Year:
2006

Citing 16
Cited 0

On the implication operator in fuzzy logic

Information Sciences: an International Journal
Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions

Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
On fuzzy implication operators

Fuzzy Sets and Systems
A new look at fuzzy connectives

Fuzzy Sets and Systems
Force implication: a new approach to human reasoning

Fuzzy Sets and Systems
Contrapositive symmetry of fuzzy implications

Fuzzy Sets and Systems
Conjunction and disjunction on ([0,1], ≤)

Fuzzy Sets and Systems - Special issue on fuzzy relations, part 1
Applicability of the fuzzy operators in the design of fuzzy logic controllers

Fuzzy Sets and Systems
A new class of fuzzy implications, axioms of fuzzy implication revisited

Fuzzy Sets and Systems
Searching for basic properties obtaining robust implication operators in fuzzy control

Fuzzy Sets and Systems
R0 implication: characteristics and applications

Fuzzy Sets and Systems - Mathematics
Automorphisms, negations and implication operators

Fuzzy Sets and Systems - Implication operators
On some new classes of implication operators and their role in approximate reasoning

Information Sciences—Informatics and Computer Science: An International Journal
On fuzzy implication in De Morgan algebras

Fuzzy Sets and Systems
Fuzzy reasoning and fuzzy relational equations

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

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

Fourteen properties and their interdependencies contributed to the analysis of six classes implication operators--S-implications, R-implications, QL-implications, Force implication, f-generated implication operator and g- generated implication operator-- are explored in this paper. It is found that all the properties can be inferred from three mutually independent properties. Then, the proven concerning which properties are true, false or satisfied for each of the six classes of implication operators is given. Based on which, the author get the property I(x(n(x)) = n (x) for all x∈[0,1] that does not hold for force implication, f-generated implication operator and g-generated implication operator.