Fuzzy programming
Authors: Kyle Clark, Matt Schweider, Tommy Sheehan, Jared Melancon (SYSEN 6800, Fall 2020)
Steward: TA's name, Fengqi You
Introduction
Fuzzy Programming is an optimization model that deals with performing optimization in the presence of uncertainty. This optimization technique is used when determining the exactness of a system's performance criteria/parameters and decision variables is not possible. Specifically, the truth values associated with the system can be completely false (0), completely true (1), or some value between the two extremes. This aims to capture the concept of partial truth. One approach to account for uncertainty in a system is to model the uncertainty using probability distributions, also know as statistical analysis. However, sometimes uncertainty can be better described using qualitative adjectives, or 'Fuzzy' statements, such as young or old, and hot or cold, because clear boundaries do not necessarily exist [1]. Fuzzy Programming is built on the concept of Fuzzy Logic. The motivation for Fuzzy Logic, or more precisely Fuzzy Set Theory, is to accurately model and represent real world data which is often 'Fuzzy' due to uncertainty. This uncertainty can be introduced into a system by a number of factors such as imprecision in measurement tools or due to the use of vague language. The examples present below will show these concepts [2].
Methodology
While Boolean Logic is used to describe situations as completely true or completely false, Fuzzy Logic allows for a mathematical representation of partial truth or partial falsehood. For instance, let's say that we have a set of integers that describe the ages of a group of people and we wanted to categorize them as either young or old. In Boolean logic, we would create two sets, a young set and an old set. We could say that ages 0 - 25 years old belong to the young set and ages 26+ belong to the old set. However,
Applications
Example
Conclusion
The optimization technique of Fuzzy Programming is useful when qualitative adjectives are the only available descriptors for a system's performance criteria/parameters and decision variables.
References
[1] https://ecommons.cornell.edu/bitstream/handle/1813/2804/05_chapter05.pdf?sequence=16&isAllowed=y [2] https://books.google.com/books?id=IkajJC9iGxMC&pg=PA73#v=onepage&q&f=false