I went through several literature on fuzzy logic and found that authors have used any kind of membership function for their work (most common are triangular or trap. type). I want to know
1. Is there any basis to choose type of membership functions for inputs and output data in fuzzy logic, or any of these can be chosen?
2. Whether for one analysis, mix of these membership functions type may be used? for ex one input in triangular and other input in trap. form?
2.Whether in single input mix of these membership functions type may be used?
Thanks in advance.
You can choose it depending on the distribution of the available data and the output you want. For example, if your data is in a normal distribution, the Gaussian membership function is used, if there is a single peak value, the triangular membership function is used, if it remains constant after a certain value, the trapezoidal membership function is used. It depends on the type of variable you are fuzzyfication, expert opinion and your intuition.
Dear Alok Pandey,
I suggest you to see links on topic.
https://www.tutorialspoint.com/fuzzy_logic/fuzzy_logic_membership_function.htm
https://www.philadelphia.edu.jo/academics/qhamarsheh/uploads/Lecture%2018_Different%20Types%20of%20Membership%20Functions%201.pdf
https://www.brighthubengineering.com/diy-electronics-devices/48950-types-of-membership-functions/
https://www.tutorialspoint.com/fuzzy_logic/fuzzy_logic_inference_system.htm
https://www.tutorialspoint.com/fuzzy_logic/fuzzy_logic_inference_system.htm
https://www.mathworks.com/help/fuzzy/foundations-of-fuzzy-logic.html
Best regards
Dear Alok Pandey
I recommend you, have a look at the following link:
https://www.researchgate.net/post/What-is-the-best-way-for-choosing-membership-function-in-fuzzy-logic
Hi Dr. Alok Pandey
There are no fixed rules. The designer makes judgement on a case-by-case basis. For example, I want to model the four seasons for the temperate zones in the northern hemisphere. But I'm not a meteorologist and I don't have "data" to make the distribution. So, I can try embedding my experience directly into the fuzzy system, by taking the linguistic approach.
I use the Gaussian membership functions (MFs) to describe the fuzzy sets of the seasons because I prefer a smooth function that is infinitely differentiable. There are six fuzzy sets over the 12-month period because the Fall20 and Winter21 MFs are included to account for the seasonal cycle. The top subplot shows the Winter MF is blue, Spring MF is green, Summer MF is red, and Fall MF is gold.
I use the Sugeno fuzzy system and the following if–then rules are used in the modeling:
- R1: If Month is Fall20, then Heat Index is Medium (0.5).
- R2: If Month is Winter20, then Heat Index is Low (0.0).
- R3: If Month is Spring21, then Heat Index is Medium (0.5).
- R4: If Month is Summer21, then Heat Index is High (1.0).
- R5: If Month is Fall21, then Heat Index is Medium (0.5).
- R6: If Month is Winter21, then Heat Index is Low (0.0).
The bottom subplot shows the Heat Index over the 12-month period. Low index values are indicated by the cold color gradient, and high index values are indicated by the warm color gradient. Rising index implies Spring and Falling index implies Fall. Try comparing my no-data fuzzy model with the observatory data:
https://earthobservatory.nasa.gov/biome/graphs.php
There is no special reason to select the membership function, it can be dependent on your research problem and the background of the study.
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