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As complexity rises, precise statements lose meaning and meaningful statements lose precision. ( Lofti Zadeh ). Fuzzy logic deals with reasoning that is approximate rather than fixed and exact. This may make the reasoning more meaningful for a human: Fuzzy logic is an extension of Boolean logic by Lotfi Zadeh in 1965 based on the mathematical theory of ...


22

Fuzzy logic is based on regular boolean logic. Boolean logic means you are working with truth values of either true or false (or 1 or 0 if you prefer). Fuzzy logic is the same apart from you can have truth values that are in-between true and false, that is to say, you are working with any number between 0 (inclusive) and 1 (inclusive). The fact that you can ...


9

It's analogous to analogue versus digital, or the many shades of gray in between black and white: when evaluating the truthiness of a result, in binary boolean it's either true or false (0 or 1), but when utilizing fuzzy logic, it's an estimated probability between 0 and 1 (such as 0.75 being mostly probably true). It's useful for making calculated decisions ...


9

A classical example of fuzzy logic in an AI is the expert system Mycin. Fuzzy logic can be used to deal with probabilities and uncertainties. If one looks at, for example, predicate logic, then every statement is either true or false. In reality, we don't have this mathematical certainty. For example, let's say a physician (or expert system) sees a ...


4

You've obviously never heard of fuzzy logic washing machines. ● Typically, fuzzy logic controls the washing process, water intake,water temperature, wash time, rinse performance, and spin speed. This optimises the life span of the washing machine. More sophisticated machines weigh the load (so you can’t overload the washing machine), advise on the ...


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This was a somewhat hotly debated question in the 1980s. The debate was more-or-less ended with papers like Cheeseman's In Defense of Probability. The short answer is that Fuzzy Logic does not just assign a continuous value to sentences, what it does is assign degrees of membership in different fuzzy sets. These degrees of membership range between 0 and 1. ...


3

No, you can't extract any probability from a fuzzy membership grade. The uncertainty expressed by fuzzy logic is about partial truth, not about probability. $ \mu_S(x) = 0.9 $ doesn't mean that "$ x $ is tall" is true with a probability of 0.9, but that "$ x $ is tall" is 90% true (notice the difference in semantics). You have to think ...


3

Fuzzy logic seems to have multiple of applications historically in Automotive Engineering. I found an interesting article on the subject from 1997. This excerpt provides an interesting rationale: The key reason for fuzzy logic’s success in automotive engineering lies in the implications of its paradigm shift. Previously, engineers spent much time ...


2

My impression is that fuzzy logic has mostly declined in relevance and probabilistic logic has taken over its niche. (See the comparison on Wikipedia.) The two are somewhat deeply related, and so it's mostly a change in perspective and language. That is, fuzzy logic mostly applies to labels which have uncertain ranges. An object that's cool but not too cool ...


2

First I need to note that there is no prescribed/best way to choose the shape of membership function in fuzzy systems, that's the fuzziness in it. One could argue that the best way is to ask an expert in the field where you are going to apply your fuzzy solution but those are not always available. With that said, fuzzy membership functions are used to ...


2

They are unrelated. There is a possibility of interpreting fuzzy values as probabilities, but strictly speaking they are different: fuzzy values are vague, while probabilities reflect likelihood (see Wikipedia entry for Fuzzy Logic) While rolling a particular number on a six-side die has a probability of $1 \over 6$, a roll can actually only ever have one ...


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The site FuzzyTECH lists an array of applications: Industrial Automation Monitoring Glaucoma Coal Power Plant Complex Chilling Systems Refuse Incineration Plant Fuzzy Logic Design Practical Design Water Treatment System Truck Speed Limiter Medical Shoe Fuzzy in Appliances Automotive Engineering Antilock Braking System ...


2

We can assume without loss of generality that \begin{equation} \min\{\mu_A(r), \mu_A(s)\} = \mu_A(r) = \alpha. \end{equation} $\implies$ a-cut of fuzzy set $A$ is on $R^n$ is convex. A-cut can be defined as \begin{equation} A = \{x \in R^n| \mu_A(x) \geq \alpha\} \end{equation} If we take two elements $r$ and $s$, by the definition of convex set, number $\...


1

Its not required, you can have $m=1$, actually it can be any number $\geq 1$. Now the better question is why to have it? The answer is that it adds a smoothing effect. Lets look at it in each of the limits ($\lim m \rightarrow 1$ and $\lim m \rightarrow \infty$) Towards $\infty$, it makes $u_{ij}$ equal to $\frac{1}{c}$, making each point have equal ...


1

Fuzzy logic is not down trending. It's a common architecture selection for systems that require the representation of uncertainty in changing rules. The domains include work-flow control, aeronautics, chemical plant engineering, automated defense of cyber-attack, building systems, and business intelligence. In natural language processing, it's up-trending ...


1

There is absolutely no doubt that fuzzy logic can contribute to the reliability and accuracy of real time diagnostics of mechanical, thermodynamic, and electro-magnetic devices. I can state this with assurance because it exists in aeronautics products today. One of the senior PhDs at the research facility wanted to acquire data via standard techniques and ...


1

After re-reading Jang's original (1993?) paper on ANFIS, I learned he recommended simply squaring the b-parameter to deal with the notion that b could be changed to a negative value when using back-propagation. While this solves the negative domain issue, the issue still remains that if b is a non-integer, then the bell function loses its intended shape. I ...


1

Recently, I needed to develop a Fuzzy Logic algorithm to made inferences of any data entrance; the real case applied was in Oil and Gas Industry, that the code needs to infere Joint Types in Fluid Pipelines. But with this Algorithm, the Computer Science Developer can infere any problems data, follow the link bellow: https://www.codeproject.com/Articles/...


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You need some sort of interpretation abstraction before your mathematical reasoning. While the text might read "123", you need to parse this into a literal of type Natural Number or Integer. Similarly, "x" could be a member variable. Then your deduction becomes, is literal 123 a Natural Number? Yes. As for the second statement, you should hopefully be able ...


1

A human has an abstract concept of numbers in mind. So 456 is a unique entity which is by definition unlike any other number because that are other unique entities. If you give ∃x ∈ ℕ: x==123 to your system it could check the property of natural numbers by counting from 0 to 123 to conclude that the statement is true. A human does it in another way. A human ...


1

Fuzzy Logic is a way of dealing with uncertainties, which is something that computers don't do naturally which human do very well. The way we instantly think of dealing with things and the way that computers tend to deal with certain things is 'True' or 'False', or '1 or '0'. For example, you might classify someone is alive as alive ('True') or has passed ...


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It is making deductions based on probability and statistics, like humans make decisions all the time. We are never 100% sure the decision we have made is the right one but there is always some doubt present. Ai will definitely need to use it in some form.


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Why is it useful? Many things we don't know for sure. We estimate and are often uncertain, but nearly never 100% sure. It may seem like a weakness, but because of this fuzzy approach we can function in this complex world and even behave quite intelligently. Hence it's a way to simplify things. And it gives you some leeway to fill the gaps appropriately, e....


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