Short Notes on Fuzzy Logic
Table of Contents
- What is Fuzzy Logic
- Fuzzy Inference Systems (FIS)
- Fuzzy Logic applications
- Fuzzy Logic in Python
- References
What is Fuzzy Logic
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Fuzzy Inference Systems (FIS)
Mamdani-Type and Takagi-Sugeno-Kang (TSK)-Type FIS
There are mainly two types of fuzzy inference systems, namely,
- Mamdani-type [1], [2]
- fuzzy consequents (also being called type-I)
- Singleton consequents (also being called type-II)
- TSK-type (also being called type-III) [3]
Mamdani-type FIS
Characteristics:
- A model-free approach
- Mainly based on human skills and experience (, or expert/prior knowledge)
- Possibly achieve the performance with generally satisfactory
Shortages:
- Lack of systematic approaches for the design of control systems
- Cannot guarantee the stability, controllability, parametric sensitivity and robustness [4], [5]
TSK-type FIS
Advantages:
- Any model-based technique (including a nonlinear one) can be applied to the fuzzy dynamic models
- The FL controller can be considered as a fuzzy system, usually based on a set of local linear models
Principal Design Parameters For FIS
- fuzzification strategies and the interpretation of a fuzzification operator (fuzzifier),
-
data base:
- discretization/normalization of universes of discourse,
- fuzzy partition of the input and output spaces,
- completeness,
- choice of the membership function of a primary fuzzy set;
-
rule base:
- choice of process state (input) variables and control (output) variables of fuzzy control rules,
- source and derivation of fuzzy control rules,
- types of fuzzy control rules,
- consistency, interactivity, completeness of fuzzy control rules;
-
decision making logic:
- definition of a fuzzy implication,
- interpretation of the sentence connective and,
- interpretation of the sentence connective also,
- definitions of a compositional operator,
- inference mechanism;
- defuzzification strategies and the interpretation of a defuzzification operator (defuzzifier).
Adaptive Fuzzy Systems
An adaptive fuzzy system is has a supervisory module, which can learn the data from the process to modify the components of the fuzzy system, such as [5]
- the size of the membership functions of the fuzzy sets,
- the position of the membership functions, and
- the rule weights and/or the link values.
The adaptation of the size of the membership functions is often implemented by monitoring four criteria of error correction:
- The error average value (EAV)
- Its first derivative (ΔEAV)
- Maximum value of the error (V_err)
- The average value of the output values (UAV)
The adaptation of the position of the membership functions typically uses a clustering algorithm to identify the data clusters.
The adaptation of the rule base is performed by increasing or decreasing the rule weights between 0 and 1; in addition, the adaptation of the link values is the concept derived from neutral networks and is not natural for fuzzy systems.
Fuzzy Logic applications
Fuzzy Logic controller (FLC) / control systems
Fuzzy control is originally introduced as a model-free control design approach, model-based fuzzy control has gained widespread significance in the past decade. [5]
Lee [6] gave an overview of fuzzy logic controllers by 1990. The review paper summarized the concept and the structure of fuzzy logic controllers. It also provided a survey of the methods of fuzzifying membership functions, defining the rule base, and justification of fuzzy control rules.
Some Mamdani-type FLC are listed below [5]:
- Control of machining processes
- Laser tracking systems
- Plastic injection molding
- Vibration suppression
- Manufacturing area related to robotics, such as manipulators and mobile robots
Other FLC:
- Fuzzy Statistical Process Control [7]
Fuzzy Logic in Python
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References
- E. H. Mamdani and S. Assilian, “Experiment in Linguistic Synthesis with a Fuzzy Logic Controller,” International Journal of Man-Machine Studies, vol. 7, no. 1, pp. 1–13, 1975, doi: 10.1016/S0020-7373(75)80002-2.
- E. H. Mamdani, “Advances in Linguistic-Synthesis of Fuzzy Controllers,” International Journal of Man-Machine Studies, vol. 8, no. 6, pp. 669–678, 1976, doi: 10.1016/S0020-7373(76)80028-4.
- K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets and Systems, vol. 45, no. 2, pp. 135–156, Jan. 1992, doi: 10.1016/0165-0114(92)90113-I.
- M. Sugeno, “On stability of fuzzy systems expressed by fuzzy rules with singleton consequents,” IEEE Transactions on Fuzzy Systems, vol. 7, no. 2, pp. 201–224, Apr. 1999, doi: 10.1109/91.755401.
- R.-E. Precup and H. Hellendoorn, “A survey on industrial applications of fuzzy control,” Computers in Industry, vol. 62, no. 3, pp. 213–226, Apr. 2011, doi: 10.1016/j.compind.2010.10.001.
- C.-C. Lee, “Fuzzy logic in control systems: fuzzy logic controller. I,” IEEE Transactions on Systems, Man and Cybernetics, vol. 20, no. 2, pp. 404–418, Apr. 1990, doi: 10.1109/21.52551.
- T. J. Ross, Fuzzy logic with engineering applications. Hoboken, NJ: John Wiley, 2004.