Assume the risk to have a value from 0 (no risk) to 10 (immediate safety risk). Assume also that there are also four linguistic descriptions of risk: "no risk", "potential risk", "normal risk", and "immediate risk", in which each linguistic term could have a range of values between 0 to 10, depending on the person being interviewed. What is the best method or approach in sampling and modeling fuzzy variables for this by combining all samples from interviewees?
I don't think there is a "best" approach that can be found that easily. It always depends on what your variables are and your approach. Do you want to be optimistic, or do you prefair to be pesimistic? Fuzzy modelling can "simulate" your way of thinking and can give you many different answers. Do you know what your boundaries are? Are you sure which answers and possible situations give you the highest risk? After setting your rules, each method will give you almost the same answer in ranking your interviewees between each other. After this point, it all depends on how "strict" you want your model to be and how many of those interviewees should be ranked as "immediate risk".
There are several techniques available in the literature. In my opinion technique for order preference by similarity to ideal solution based on trapezoidal hesitant fuzzy sets will be suitable in this case. It is a useful and practical technique for selection and ranking of alternatives through distance measure.
The p-fuzzy dynamical systems obtained by means of a Mamdani controller,
evidently produce approximate solutions of the studied phenomenon and such solutions are more trustworthy if we get more information on the phenomenon. Thus, as much information we have, more refined will be the families of successive fuzzy subsets used in the base of fuzzy rules.
The Mamdani method can induce non linearity in the response (output), but this fact does not harm the induced dynamic process in the p-fuzzy system because it simply uses the values of
response (output) after the defuzzification method. Moreover, the Mamdani method favors the attainment of a field of directions (responses) that can be used to establish parameters of deterministic systems originated by variational equations.
The uncertainty may be of type I, caused mainly by randomness, addressed with statistics and also of type II, caused by our lack of knowledge, addressed with fuzzy logic. Type I needs previously accumulated data, type II needs experts able to guess the future (no direct data available, just generic knowledge and personal experience). However, using statistics when designing fuzzy logic systems is very effective. You could simply ask several experts to tune your parameters and to fusion their answers. You could apply the test of the universal specialist, involving engineers but also managers, members of the target group of your project, etc.
There is a suitable method called Fuzzy inference system
Fuzzy systems are based on fuzzy If-Then rules that are stored in a fuzzy rule base. A fuzzy If-Then rule is a conditional expression in which some of the words are defined by membership functions The different parts of a fuzzy system are as follows:
Fuzzification
Fuzzy rule base
Fuzzy inference
engine
Defuzzification
Fuzzification projects a point to a fuzzy set. Although finding an appropriate way to assign numbers to all of the members of a fuzzy set is very difficult, assigning number 1 to a member means complete membership in that set and assigning number 0 to a member means that the member does not belong to
that set at all. Other numbers between 0 and 1 represent partial membership in that set. An inference engine is present for deducing logic and principles. Deducing means obtaining new expressions and results based on a combination of existing expressions. An inference engine leads to fuzzy results using
the exertion of fuzzy rules on a combination of existing conditions in a fuzzy rule base. Defuzzification projects fuzzy results that are obtained from an inference engine to a certain point.
The flexibility, simplicity, and computational speed of fuzzy models do not imply a loss of accuracy. Moreover, the size of a fuzzy rule base could be adjusted to match the amount and accuracy of the data. In contrast to crisp rules, fuzzy rules provide the ability to perform partial and simultaneous fulfillment of rules. In other words, instead of the ordinary (crisp) distinction of an applying or a not applying a rule, a
rule could be partially applied.
There are two major methods for implementing fuzzy systems (the Mamdani method and the Sugeno method), which differ in small ways .
I think that opinion of prof. Tsataltzinos is proper start point for Your task. As to proper tools for that Mamdani controller seems to be good.
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