What can a fuzzy model do that cannot usually be replicated by a conventional simulation
model?
Describe the facts in a way that is comprehensible to all. You can also specify an example
for the solution.
Fuzzy models are used when a numerical or mathematical description in a model is difficult or does not represent the facts in an appropriate way
For example, the boundaries for water temperature are defined as: hot = 100°C and cold = 0°C. Then, a temperature of 49°C would be defined as cold, even though it is not really cold, and a temperature of 51° would be defined as hot, even though it is not hot and not very different to 49° degrees.
Therefore, a fuzzy model includes imprecisions and uncertainties and not crisp numbers or states in order to reduce a systems complexity.
To create a fuzzy model, the first step is the fuzzification, i.e. the process of changing a crisp number or value (scalar) into a fuzzy value (here: cold, warm, hot). Then the fuzzy interferences need to be defined by using fuzzy logic (IF the water is hot, THEN I should not put my hand in it.) At last, we need to defuzzicate the model by converting the fuzzy values (linguistic terms) into crisp numbers or values again.
Mostly, the best way to model ecological systems is by using fuzzy logic models because of the systems complexities.
Describe briefly and concisely the main differences between a fuzzy model and a
conventional deterministic simulation model.
Deterministic simulation model:
Sharp date (numbers) as input
Clear ranges → boundaries between states
Based on (mathematical) algorithms with mathematical connections
90% of the models are deterministic
Fuzzy Model
Can process fuzzy / imprecise data & range → linguistic variables instead of numbers
Includes imprecisions and uncertainties
imprecise ranges → boundaries are weakened
(Only suitable for less than 100 input values)
Your task is to give a classification for precipitation intensities between 0 and 20 mm/h.
The following boundaries should be applied:
0 - 2 mm/h => low intensity
2 - 5 mm/h => medium intensity
5 - 10 mm/h => big intensity
> 10 mm/h => very big intensity
Present this classification once on the basis of classical set theory and once as a
membership function for fuzzy logic.
Specify which condition(s) must be fulfilled whenever two contiguous membership
functions meet?
The sum of both membership functions must be 100% at these points. Both have 50% membership at the interfaces! The slope angles must be equal.
You should create a rulebase for a fuzzy logic precipitation runoff model.
Input variables for your model are precipitation and evaporation; output is runoff.
Define descriptive classes for the input variables and define at least 2 rules that determine
the relationship between the input variables and the output.
EXTRA
You should create a rulebase for a fuzzy logic model for the quality of a spawning habitat for fish. Define 2 input variables with 3 descriptive classes.
Explain fuzzyfication, fuzzy inference and defuzzyfication. Give examples in each case!
III Describe the 3 steps of the fuzzy model: what do the 3 steps do, explain the steps and give specific examples
• Fuzzification: process of changing a real scalar (numerical) value into a fuzzy value → e.g. water temperature = [cold, warm, hot]
• Fuzzy inference: process of formulating the mapping from a given input to an output of linguistic variables using fuzzy logic (if…, then…), i.e. the fuzzy interefenerences between states are defined → e.g. IF the water is hot, THEN I should not put my hand in it
• Defuzzification: process of
FUZZY SUMMARY
❑ Fuzzy logic models can use fuzzy and uncertain information to make accurate decisions.
❑ In contrast to traditional Boolean logic, which only recognises clear and unambiguous truth values (true/false),
fuzzy logic works with fuzzy, unspecific and incomplete data.
❑ Benefits of fuzzy logic models:
▪ Allows for uncertainty and fuzziness in available information/processes
▪ Ability to model based on linguistic context
▪ Extension of traditional Boolean logic with partial truth values
▪ Suitable for modelling complex systems and problems that cannot be accurately described numerically
▪ Ability to incorporate expert knowledge and human judgement into modelling
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