Interval valued fuzzy sets based on normal forms
Fuzzy Sets and Systems
Interval-valued fuzzy sets and “compensatory AND”
Fuzzy Sets and Systems
Type I and type II fuzzy system modeling
Fuzzy Sets and Systems - Special issue on fuzzy modeling and dynamics
Analysis of the weighting exponent in the FCM
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
Information Sciences: an International Journal
Development of fuzzy and control charts using α-cuts
Information Sciences: an International Journal
Decision making with imprecise parameters
International Journal of Approximate Reasoning
Fuzzy clustering of time series in the frequency domain
Information Sciences: an International Journal
Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization
Information Sciences: an International Journal
MiniMax ε-stable cluster validity index for Type-2 fuzziness
Information Sciences: an International Journal
A fuzzy minimax clustering model and its applications
Information Sciences: an International Journal
The range of the value for the fuzzifier of the fuzzy c-means algorithm
Pattern Recognition Letters
Information Sciences: an International Journal
Functional fuzzy clusterwise regression analysis
Advances in Data Analysis and Classification
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The level of fuzziness is a parameter in fuzzy system modeling which is a source of uncertainty. In order to explore the effect of this uncertainty, one needs to investigate and identify effective upper and lower boundaries of the level of fuzziness. For this purpose, Fuzzy c-means (FCM) clustering methodology is investigated to determine the effective upper and lower boundaries of the level of fuzziness in order to capture the uncertainty generated by this parameter. In this regard, we propose to expand the membership function around important information points of FCM. These important information points are, cluster centers and the mass center. At these points, it is known that, the level of fuzziness has no effect on the membership values. In this way, we identify the counter-intuitive behavior of membership function near these particular information points. It will be shown that the upper and lower values of the level of fuzziness can be identified. Hence the uncertainty generated by this parameter can be encapsulated.