Fuzzy Logic Machine Learning

[Bernice Ebesugawa]

FuzzyLogic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, instead of just the traditional values of true or false. It is used to deal with imprecise or uncertain information and is a mathematical method for representing vagueness and uncertainty in decision-making.

Fuzzy Logic is based on the idea that in many cases, the concept of true or false is too restrictive, and that there are many shades of gray in between. It allows for partial truths, where a statement can be partially true or false, rather than fully true or false.

The fundamental concept of Fuzzy Logic is the membership function, which defines the degree of membership of an input value to a certain set or category. The membership function is a mapping from an input value to a membership degree between 0 and 1, where 0 represents non-membership and 1 represents full membership.

Fuzzy Logic is implemented using Fuzzy Rules, which are if-then statements that express the relationship between input variables and output variables in a fuzzy way. The output of a Fuzzy Logic system is a fuzzy set, which is a set of membership degrees for each possible output value.

In summary, Fuzzy Logic is a mathematical method for representing vagueness and uncertainty in decision-making, it allows for partial truths, and it is used in a wide range of applications. It is based on the concept of membership function and the implementation is done using Fuzzy rules.

In the boolean system truth value, 1.0 represents the absolute truth value and 0.0 represents the absolute false value. But in the fuzzy system, there is no logic for the absolute truth and absolute false value. But in fuzzy logic, there is an intermediate value too present which is partially true and partially false.

Definition: A graph that defines how each point in the input space is mapped to membership value between 0 and 1. Input space is often referred to as the universe of discourse or universal set (u), which contains all the possible elements of concern in each particular application.

How do these four subjects differ from one another? From what I understand, they learn from numerous input data and output an estimated output. My understanding is very lacking thus me questioning these. It made no sense to me about the examples given by people such as the spam email, apple orange cat dog identification, neural network examples.

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false.1 Furthermore, when linguistic variables are used, these degrees may be managed by specific (membership) functions.

The field of AI research defines itself as the study of "intelligent agents": any device that perceives its environment and takes actions that maximize its chance of success at some goal. Colloquially, the term "artificial intelligence" is applied when a machine mimics "cognitive" functions that humans associate with other human minds, such as "learning" and "problem solving" (known as Machine Learning).

Take for example, k nearest neighbors. If you have a bunch a bunch of attributes like color: [red,blue,green,orange], temperature: [real number], shape: [round, square, triangle], you can't really fuzzify any of these except for the real numbered attribute (please correct me if I'm wrong), and I don't see how this can improve anything more than bucketing things together.

Regarding machine learning, it depends on what stage of the algorithm you want to apply fuzzy logic. It would be better applied in my opinion after the clusters are found (using traditional learning techniques) to determining the degree of membership of a certain point in the search space on each cluster, but that doesn't improve learning per see, but classification after learning.

[round, square, triangle] are mostly ideal categories, which exist primarily in geometry (i.e. in theory). In real world, some shapes might be almost square or more or less round (circular shape). There are many nuances of red, and some colors are closer to some others (ask a woman to explain turquoise, for example). Hence, also abstract categories and some specific values are useful as references, in real world the objects or values are not necessarily equals to these ones.

Fuzzy membership allow you to measure how far are some specific objects from some ideal. Using this measure lets one to avoid "no, it's not circular" (which might lead to information loss) and make use of the measure the given object is (not) circular.

In my view, fuzzy logic is not a practically viable approach to anything unless you are building a purpose build fuzzified controller or some rule based structure like for compliance/policies. Although, fuzzy implies dealing with everything between and including 0 and 1. It, however, I find is a bit flawed when you approach more complicated problems where you need to apply fuzzy logic aspects in 3 dimensional spaces. You can still approach multivariate without having to look at fuzzy logic. Unfortunately, for me having studied fuzzy logic I found myself disagreeing with the principles approached in fuzzy sets in large dimensional spaces it seems infeasible, unpractical, and not very logically sound. The natural language base that you would be applying in your fuzzy set solution will also be very adhoc what exactly is [very,few, many] this is all what you define in your application. Alot, of machine learning aspects you will find that you don't even have to go so far as to build natural language underpinnings into your model. In fact, you will find you can achieve even better results without having to apply fuzzy logic into any aspect of your model.

just too irritate you a bit by forcibly adding fuzziness to this. if instead of the "shape" attribute you had a "number of sides" attribute which would have been further divided into "less", "medium", "many" and "uncountable". the square could have been a part of "less" and "medium" both given the appropriate membership function. in place of the "color" attribute, if you had "red" attribute, then using the RGB code, a membership function could have been made. so as my experience in data mining says, every method can be applied to every dataset, what works, works.

It's not clear to me what you're trying to accomplish in the example you give (shapes, colors, etc.). Fuzzy logic has been used successfully with machine learning, but personally I think it is probably more often useful in constructing policies. Rather than go on about it, I refer you to an article I published in the Mar/Apr-2002 issue of "PC AI" magazine, which hopefully makes the idea clear:

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I remember in the late 1980s my mom was telling me about how Fuzzy Logic would make our new washer, by Siemens I believe, a lot more efficient by adjusting its water intake, rotation speed, and program duration based on the weight of the laundry load, how dirty the laundry was, and how sensitive to hot water. All of a sudden this made watching the laundry cool (at least for me). Why? Because this was the first time I observed an electronic device automatically respond to human input, even if it was just a load of dirty laundry. Keep in mind, that at the time these washers only had three sensors (for weight, water input, and rotation speed) built-in, while the rest of the input parameters had to be set by pressing buttons. But even this very simple system was based on making incremental changes based on feedback. At the time, there was no actual feedback learning, as the washer simply adjusted water intake, heat, and rotation speed in real time, without retaining data for the next run. Simply speaking, this was an industrial controller that applied a simply algorithm to a few input signals and then automatically changed the behavior of the machine it was controlling. The algorithm itself also was simple and due to a lack of CPU power in household devices of the 1980s, it must have looked up pre-calculated settings from a table, instead of running correlations in real-time.

In 2020, the core principle behind Fuzzy Logic is still the same, but today we can leverage an array of cheap sensors to provide the washer with a lot more input than just weight, water amount and rotation speed. Sensors can even determine the nature of stains in the clothes, so that the washer can add more or different detergent, automatically as needed. Modern washer motors, I believe they do not need sensors for that but I could be wrong, can alert the controller of irregularities in the drum rotation, pointing toward an ill-balanced load of laundry. The controller can then decide to gradually try to even out the load by applying a specific rotation patterned that was provided in the initial software, as it had shown to be effective for shifting laundry.

Fuzzy logic simply uses an algorithm that translates a set of input factors into action, based on a set of rules provided by a human. In the 1980s, I believe, these rules were provided in the form of simple tables, while today's cheap CPU power probably allows washers and other devices to execute a set of complex correlation analytics during the washing cycle. The core principle of fuzzy logic remains the same, but of course modern washers are able to make a lot more adjustments a lot more gradually and frequently compared to the antiques we used to wash our clothes in the 1980s. What's fuzzy about this? The term "fuzzy" simply refers to the machine's ability to continuously respond to input data and then adjust to how its response changed that data.

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