Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Fuzzification of set inclusion: theory and applications
Fuzzy Sets and Systems
Fuzzy implication operators and generalized fuzzy method of cases
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Inclusion grade and fuzzy implication operators
Fuzzy Sets and Systems
Inclusion-Based Approximate Reasoning
ICCS '01 Proceedings of the International Conference on Computational Science-Part II
A fuzzy inference methodology based on the fuzzification of set inclusion
Recent advances in intelligent paradigms and applications
Image and Vision Computing
Fuzzy lattice reasoning (FLR) classifier and its application for ambient ozone estimation
International Journal of Approximate Reasoning
Information Sciences: an International Journal
Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality
Journal of Mathematical Imaging and Vision
On two qualitative approaches to tolerant inclusion operators
Fuzzy Sets and Systems
Fuzzy rough approximations of process data
International Journal of Approximate Reasoning
On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering
Computers & Mathematics with Applications
Reasoning about actions with imprecise and incomplete state descriptions
Fuzzy Sets and Systems
Determining Significance of Attributes in the Unified Rough Set Approach
RSFDGrC '07 Proceedings of the 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
About approximate inclusion and its axiomatization
Fuzzy Sets and Systems
Elicitation of fuzzy association rules from positive and negative examples
Fuzzy Sets and Systems
Using similarity measures for histogram comparison
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
On representation and analysis of crisp and fuzzy information systems
Transactions on rough sets VI
On possible and necessary inclusion of intuitionistic fuzzy sets
Information Sciences: an International Journal
Relationship between inclusion measure and entropy of fuzzy sets
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
An approach to parameterized approximation of crisp and fuzzy sets
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
Generalized fuzzy morphological operators
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part II
Automatic selection of data analysis methods
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Definition and construction of fuzzy DI-subsethood measures
Information Sciences: an International Journal
HAIS'12 Proceedings of the 7th international conference on Hybrid Artificial Intelligent Systems - Volume Part II
Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral
Mathematical and Computer Modelling: An International Journal
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Inclusion for fuzzy sets was first introduced by Zadeh in his seminal 1965 paper. Since it was found that the definition of inclusion was not in the true spirit of fuzzy logic, various researchers have set out to define alternative indicators of the inclusion of one fuzzy set into another. Among these alternatives, the indicator proposed by Sinha and Dougherty stands out as an intuitively appealing one, as it is built up with a strong but appropriate collection of axioms in mind. Starting from a very general expression depending on four functional parameters for such an indicator, those authors proposed conditions they claimed to be necessary and sufficient to satisfy the axioms. This paper aims to revisit this material by exposing it in a clearer way, correcting errors along the way while pinpointing some nasty pitfalls that Sinha and Dougherty overlooked. This results in a new, easier to handle and more consistent framework for the axiomatic characterization of inclusion grades for fuzzy sets, advantageous to the further development of practical applications. In the end, a link is established with Kitainik's results on the fuzzification of set inclusion, allowing amongst others the derivation of a sufficient and necessary characterization of the Sinha-Dougherty axioms.