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I may not be correct but it seems that the leading operations research and management science journals (Informs OR and MS) do not publish any works on fuzzy logic or fuzzy sets. I could find only three papers in MS and zero papers in OR that have "fuzzy" in their title. The first of the three papers in MS is from Zadeh and Richard Bellman (who are well known for their contributions) and has been cited over nine thousand times. The last of the three papers is published in 1983 as can be seen in the picture.

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Does it mean that fuzzy sets have nothing to do with OR? I don't understand why an OR paper relevant to fuzzy sets cannot or should not be submitted to such journals.

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Generally, fuzzy sets are not appreciated by the operations research community, particularly in the United States. The topic is not included in any of the standard OR textbooks (like Taha "Operations Research" or Winston "Operations Research: Applications and Algorithms") nor is it part of the curriculum of any undergraduate or graduate program I have seen.

Operations research journals seem to differ as to whether they will look at fuzzy set papers. The OP mentions the INFORMS journals "Operations Research" and "Management Science" as not publishing fuzzy set papers. Another journal (non-US) I know which is good, but not top tier, will not send fuzzy set papers out for review and simply returns them to the author. But European Journal of Operational Research will publish fuzzy set papers, as will the UK Journal of the Operational Research Society. I do not know if UK or European curricula are more likely to include the topic.

Inclusion of "fuzzy sets" in operations research seems itself to be fuzzy.

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  • $\begingroup$ Hmm, interesting. So why are the sets not appreciated? I understand that the mathematics differs from standard set theory, but I suspect that for certain types of uncertainty they may make good sense to be used. Am I wrong? $\endgroup$ – Richard Sep 22 '19 at 17:33
  • $\begingroup$ That sounds like a great question to ask! $\endgroup$ – Michael Trick Sep 23 '19 at 22:37
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Disclaimer: The following is based on my own thoughts and discussions with colleagues, hence not supported with hard data. Also, I'm no expert in fuzzy theory, but I've good experience with robust optimization and stochastic programming.

One line research in OR, which is relatively very active, is the fuzzification of MADM methods (e.g., fuzzy AHP or fuzzy TOPSIS). Another line of research is the fuzzification of DEA models. In addition, I've seen many papers on SCM considering fuzzy input.

Regarding the possible publication venues, as @michael-trick already mentioned, journals such as EJOR, JORS, and OMEGA publish papers in this area on a regular basis. In addition, journals dedicated to artificial intelligence (e.g., Expert Systems with Application and Information Science) or OR applications (e.g., Computers & Industrial Engineering) usually publish a good number of fuzzy papers.

About why fuzzy is relatively neglected by North American researchers, here is my two cents. Fuzzy sets were originally intended for modeling ambiguity. Fuzzy sets are a better tool to be used in soft-OR models (usually advocated by European researchers), as opposed to hard-OR models (usually advocated by North American researchers). To clarify this, I've to explain the idea behind fuzzy sets. For this matter, a classical example is that different people have different perceptions of hot, warm, and cold water and those perceptions are not necessarily related to the water temperature. This idea is not very consistent with the input data used usually used in optimization models. Following the fuzzy terminology, numbers used in optimization are crisp by nature and usually have no ambiguity in them. For example, consider customer's demand in a supply chain model. Perhaps you don't know what the future demand would be, however the demand itself is crisp. In other words, the fact that you cannot measure the future demand does not make it ambiguous. It's just unknown.

Finally, I do not think that optimization models with fuzzy parameters and stochastic programming (or even robust optimization models) are very comparable. The types of uncertainty considered by each method are very different (fuzzy membership function vs. probability distribution or uncertainty intervals). Also, stochastic programming and robust optimization models have structural properties for modeling the uncertainty and how to deal with it, while, AFAIK, fuzzy models lack such properties. For details, please see a relatively similar question on OR-X, available from here.

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    $\begingroup$ I strongly agree with the last paragraph. Fuzziness is a matter of semantic uncertainty, for which there is usually no underlying probability distribution (as in, "good" v. "ok" v. "bad" outcome). Stochastic optimization handles randomness, where there is an underlying distribution and where the possible values of the random thing are unambiguous (5 orders for widgets v. 6 orders, where we assume everyone agrees on what 5 means). $\endgroup$ – prubin Sep 25 '19 at 20:51
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In my opinion, fuzzy sets inherently suggest a notion of uncertainty, e.g. a statement may be “half-true” as it cannot be clearly determined whether it is true or not.

This type of uncertainty is very often dealt with in OR through e.g. stochastic programming. So I don’t think there is any limitation of using fuzzy sets in OR, for as long as it solves the problem. In fact, I for one would be curious to see what type of use fuzzy sets could have in our community.

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  • $\begingroup$ Optimization models with fuzzy parameters and stochastic programming (or even robust optimization models) are not very comparable. Please see here for details. $\endgroup$ – Ehsan Sep 22 '19 at 19:02
  • $\begingroup$ Maybe not as methods, but they all can be used to address uncertainty in mathematical modeling, correct? $\endgroup$ – Richard Sep 22 '19 at 19:09
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    $\begingroup$ SP and RO models are designed to deal with uncertainty. However, fuzzy sets were proposed to deal with ambiguity. Hence, I don't think fuzzy mathematical programming models are a plausible way to deal with uncertainty. $\endgroup$ – Ehsan Sep 22 '19 at 19:22
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    $\begingroup$ True, SO and RO were designed with uncertainty in mind, but we always “steal” ideas from other fields when they make sense. I can very much envision fuzzy sets to be relevant for certain type of models. $\endgroup$ – Richard Sep 23 '19 at 5:19

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