This is a well-written article on fuzzy classifiers. I have the following two comments:
(1) Classification of fuzzy feature vectors: Fuzzy classifiers can handle fuzzy feature vectors (i.e., feature vectors of fuzzy numbers or linguistic values) in both the training and classification phases. This issue can be included in the article (I think that a few lines can be used for this issue in the article).
(2) Equation (1): Could you please check this equation? When the weights (i.e., the firing strengths) of rules with the Class k consequent are summed up, gk(x) can be larger than 1 (i.e., it can be outside the interval [0, 1]). Moreover, the maximum operator is not needed in this equation in this case. If gk(x) is the maximum weight (i.e., the maximum firing strength) among those rules with the Class k consequent, the summation operator is not needed in this equation.
Lucy: Many thanks for the review!
Comment (1): Done as suggested, thanks.
Comment (2): True, my mistake. The sum sign should not be there. Fixed now.
Although clearly written, unless there are page limitations, I suggest that the author extend this article. As presently written, the article does not explain enough to benefit the novice and does have enough depth to help someone already familiar wiht fuzzy classifiers, but wants to be brought up to speed on what's been happening in the field.
Lucy: Many thanks for your comments.
Lucy: Indeed, there is a limitation. I was given about 2000 words, and I am already above the limit. I would rather cut parts that may be unclear or confusing than extend the article. Bringing the reader up to speed with the current developments was not my intention. The current developments will be "old" in a couple of years time. I was rather concentrating on describing the principles and methodologies.
For example on page 2, the statement is made that "Soft labeling is free from this assumption." The author should explain what the purposes/values are for "soft labeling." If it is to make a decision or a choice, then ultimately a "soft label" has to be converted into a single decision or choice.
Lucy: This issue has been debated in the literature for ages. Soft labels versus hard labels is a matter of another article. I can only work with certain parlance and concepts; I can't justify them all in an encyclopaedia article.
On page 3, after the generic rule, the author states: "In this model every rule votes for all the classes." If this is so, then why is this "classification?"
Lucy: Same as above.
On page 4 at the end of the top paragraph, it would be beneficial to the reader to learn that there can be other architectures for fuzzy rule-based classifiers, e.g., hierarchical architectures are a way to reduce rule explosion because they partition the feature space into one or two features at a time. Exactly how to do this is problem dependent.
Lucy: I wanted to give only the very basic architectures and notions. There are many other models, but choosing from these is difficult. Favouring one group over another will require extra justification in the text. I would prefer to keep to the simple models. The first criticism by the reviewer was lack of depth and here a breadth expansion is suggested. I am not sure how I can accommodate all in a a short article.
On page 5, OWA should be referred to as "Ordered weighted averaging", and not as"weighted ordered averaging."
The section on page 5 entitled "Aggregation using fuzzy integral," introduces too many undefined terms, and surprisingly, no references are given for the Sugeno and Choquet integrals. Additionally, I did not find the sequence of steps useful, and I am already familiar wiht both of these "integrals." I might add that there is nothing fuzzy about the Choquet integral, so to call it a fuzzy integral is a misnomer.
Lucy: I was surprised myself that these have not been already included as other articles in the encyclopaedia. The "integrals" are a standard tool in fuzzy set theory, and I have been using standard terminology. Whether or not the terminology can be perceived as correct or incorrect is not for me to argue.
This article was very biased towards the authors book and work for the expense of the breadth of the whole area of fuzzy classifiers. The introductory paragraph (below the title 'Why fuzzy classifiers?') concerns classifiers in general and only in the second paragraph the reader understands that 'fuzzy classifiers are an extra tool...'. To me this is not a very strong introduction.
Some sections were very specific and unnecessary (former section 3.2 'Aggregation using fuzzy integral' for example). How many people use this technique? Do you cover all other specific techniques related to fuzzy classifiers? The limited 2000 words, in my view should be used to introduce people that might be from outside the narrow area in which the author works to the basic techniques and to the variety, not to the details and specifics of authors own work. Same applies to the lengthy section on GNPC. The readers can be simply redirected to author's book for details. At the same time, important aspects of training fuzzy classifiers were not even mentioned.
Lucy: Thanks for the corrections and especially the references. I have revised the article accordingly.
The article is now much more represnetative and informative.