Fuzzy logic

These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty.

[5][6] Fuzzy logic has been applied to many fields, from control theory to artificial intelligence.

In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum.

In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts.

[12] It uses the following rules: Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership.

For example, in the image below, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale.

The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge.

In the paper (Zaitsev, et al),[16] a criterion has been formulated to recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum.

Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers.

The TSK system[19] is similar to Mamdani, but the defuzzification process is included in the execution of the fuzzy rules.

Hence, TSK is usually used within other complex methods, such as in adaptive neuro fuzzy inference systems.

Fuzzy logic is used in control systems to allow experts to contribute vague rules such as "if you are close to the destination station and moving fast, increase the train's brake pressure"; these vague rules can then be numerically refined within the system.

A first notable application was on the Sendai Subway 1000 series, in which fuzzy logic was able to improve the economy, comfort, and precision of the ride.

Nowhere in that process is there anything like the sequences of either-or decisions which characterize non-fuzzy mathematics, computer programming, and digital electronics.

The former approach uses binary logic, matching the hardware on which it runs, but despite great efforts it did not result in intelligent systems.

Neural networks, by contrast, did result in accurate models of complex situations and soon found their way onto a multitude of electronic devices.

Since medical and healthcare data can be subjective or fuzzy, applications in this domain have a great potential to benefit a lot by using fuzzy-logic-based approaches.

Fuzzy logic can be used in many different aspects within the medical decision making framework.

The biggest question in this application area is how much useful information can be derived when using fuzzy logic.

This is why fuzzy logic is a highly promising possibility within the medical decision making application area but still requires more research to achieve its full potential.

[27] One of the common application areas of fuzzy logic is image-based computer-aided diagnosis in medicine.

[28] Computer-aided diagnosis is a computerized set of inter-related tools that can be used to aid physicians in their diagnostic decision-making.

Indeed, the following theorem holds true (provided that the deduction apparatus of the considered fuzzy logic satisfies some obvious effectiveness property).

Another open question is to start from this notion to find an extension of Gödel's theorems to fuzzy logic.

While both fuzzy logic and probability theory can represent degrees of certain kinds of subjective belief, fuzzy set theory uses the concept of fuzzy set membership, i.e., how much an observation is within a vaguely defined set, and probability theory uses the concept of subjective probability, i.e., frequency of occurrence or likelihood of some event or condition [clarification needed].

The concept of fuzzy sets was developed in the mid-twentieth century at Berkeley[30] as a response to the lack of a probability theory for jointly modelling uncertainty and vagueness.

Lotfi A. Zadeh argues that fuzzy logic is different in character from probability, and is not a replacement for it.

Like fuzzy logic, they are methods used to overcome continuous variables or systems too complex to completely enumerate or understand discretely or exactly.

FML allows modelling a fuzzy logic system in a human-readable and hardware independent way.

IEEE STANDARD 1855–2016 uses the W3C XML Schema definition language to define the syntax and semantics of the FML programs.