# Fuzzy mathematical programming vs stochastic programming

 1 Dear all As we know, there are some approaches to tackle uncertainty in mathematical programming amongst with stochastic programming, robust optimization, and fuzzy mathematical programming. To the best of my knowledge, SP is used when there are enough data to estimate the probability distribution function, RO is used when we just know the interval that data varies (continuous form), and FMP is used when data are vague, ambiguous, or when data are not sufficient to estimate PDF of data. There are a lot of problem in operations management in which there is no historical data, such supply chain network design, location of warehouses and so on. In this situation, it seems more appropriate to use FMP while in most prestigious journals such as Management science, Operations Research, etc, SP and RO are more acceptable while these approaches increase the complexity of model and in some cases make them nonlinear. Can anyone tell me why SP and RO are more desirable to model uncertainty in these journals and North of America? Thanks asked 01 Oct '16, 16:06 Amin-Sh 61●1●7 accept rate: 0%

 4 Disclaimer: Similar to Paul, 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 relatively more experience with RO and SP. Originally, fuzzy theory was proposed to deal with ambiguous data. For example, how you define coldness or hotness of water is ambiguous. However, most of data we use in our optimization models are by nature crisp (e.g., price, time, demand, etc). 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. Following the previous point, FMP community has abused FMP to a great extent. I've seen papers published in good journals that are absolutely outrageous. For example in some scheduling studies, the authors have considered due dates to be fuzzy parameters. This means that even customers are not sure which date they need their order. AFAIK, FMP models, at least basic ones, have no structural property that models the uncertainty. For example, some FMP models are built on the idea of $$\alpha$$-cut that is very similar to the expected value models (i.e., nominal models in RO terminology), and we already know they are not as good as stochastic models. Recently, I've seen efforts to extend FMP models to consider notions of robustness and chance constraints (e.g., possibilistic models). However, I don't know about their rigor. Fuzzy data is based on experts' opinion. I don't know how you can derive a membership function from the expert's mind. However, asking people for scenarios and intervals seems more natural. answered 05 Oct '16, 08:20 Ehsan ♦ 4.8k●3●11●22 accept rate: 16% Thank you dear Ehsan. The first reason was so surprising for me. (07 Oct '16, 06:20) Amin-Sh
 toggle preview community wiki

By Email:

Markdown Basics

• *italic* or _italic_
• **bold** or __bold__
• image?![alt text](/path/img.jpg "Title")
• numbered list: 1. Foo 2. Bar
• to add a line break simply add two spaces to where you would like the new line to be.
• basic HTML tags are also supported

Tags: