Croissant is a metadata format design to support sharing of datasets for machine learning applications. It is a platform-agnostic schema used to standardize metadata in data repositories like Hugging Face, kaggle, Dataverse and OpenML. == Structure == Croissant builds upon schema.org, uses primarily JSON-LD, and divides metadata in four "layers": Dataset Metadata, Resource, Structure and Semantic: The Dataset Metadata layer constrains which schema.org properties should be used, including additional properties, linking together the resources (files) of the dataset with general metadata, like licensing and citation information. The Resource layer describes the individual files and sets of those using two new classes, FileObject and FileSet. A FileSet may be a collection of related images. The Structure layer specifies how the files are organized in the dataset. A RecordSet class describes how resources are present, configurations that may very a lot between modality. This specification facilitates interoperability of the datasets. Finally, the Semantic layer adds information for practical reuse of the dataset, such as splits for train, test and validation subsets. It also provides a default extension for metadata related to responsible AI. The use of a standard machine-readable structure increases, for example, the discoverability of datasets in search engines such as Google Dataset Search. == History == Croissant was shared in arXiv in March 2024 and published in the proceedings of NeurIPS 2024. It started as community driven as a MLCommons Croissant Working Group, including stakeholders organizations from academia and industry, including Google, the open data institute, Sage Bionetworks and King's College London. Variations of Croissant are developed to support datasets in different areas of research, such as Geo-Croissant for geospatial datasets. Other technical extensions, such as support for RDF, soon followed.
Underwater computer vision
Underwater computer vision is a subfield of computer vision. In recent years, with the development of underwater vehicles ( ROV, AUV, gliders), the need to be able to record and process huge amounts of information has become increasingly important. Applications range from inspection of underwater structures for the offshore industry to the identification and counting of fishes for biological research. However, no matter how big the impact of this technology can be to industry and research, it still is in a very early stage of development compared to traditional computer vision. One reason for this is that, the moment the camera goes into the water, a whole new set of challenges appear. On one hand, cameras have to be made waterproof, marine corrosion deteriorates materials quickly and access and modifications to experimental setups are costly, both in time and resources. On the other hand, the physical properties of the water make light behave differently, changing the appearance of a same object with variations of depth, organic material, currents, temperature etc. == Applications == Seafloor survey Vehicle navigation and positioning Biological monitoring {possibly aquatic biomonitoring) Video mosaics as visual navigation maps Submarine pipeline inspection Wreckage visualization Maintenance of underwater structures Drowning detection systems == Medium differences == === Illumination === In air, light comes from the whole hemisphere on cloudy days, and is dominated by the sun. In water direct lighting comes from a cone about 96° wide above the scene. This phenomenon is called Snell's window. Artificial lighting can be used where natural light levels are insufficient and where the light path is too long to produce acceptable colour, as the loss of colour is a function of the total distance through water from the source to the camera lens port. === Light attenuation === Unlike air, water attenuates light exponentially. This results in hazy images with very low contrast. The main reasons for light attenuation are light absorption (where energy is removed from the light) and light scattering, by which the direction of light is changed. Light scattering can further be divided into forward scattering, which results in an increased blurriness and backward scattering that limits the contrast and is responsible for the characteristic veil of underwater images. Both scattering and attenuation are heavily influenced by the amount of organic matter dissolved or suspended in the water. Light attenuation in water is also a function of the wavelength. This means that different colours are attenuated at different rates, leading to colour degradation.with depth and distance. Red and orange light are attenuated faster, followed by yellows and greens. Blue is the least attenuated visible wavelength. === Artificial lighting === == Challenges == In high level computer vision, human structures are frequently used as image features for image matching in different applications. However, the sea bottom lacks such features, making it hard to find correspondences in two images. In order to be able to use a camera in the water, a watertight housing is required. However, refraction will happen at the water-glass and glass-air interface due to differences in density of the materials. This has the effect of introducing a non-linear image deformation. The motion of the vehicle presents another special challenge. Underwater vehicles are constantly moving due to currents and other phenomena. This introduces another uncertainty to algorithms, where small motions may appear in all directions. This can be specially important for video tracking. In order to reduce this problem image stabilization algorithms may be applied. == Relevant technology == === Image restoration === Image restoration< techniques are intended to model the degradation process and then invert it, obtaining the new image after solving. It is generally a complex approach that requires plenty of parameters that vary a lot between different water conditions. === Image enhancement === Image enhancement only tries to provide a visually more appealing image without taking the physical image formation process into account. These methods are usually simpler and less computational intensive. === Color correction === Various algorithms exist that perform automatic color correction. The UCM (Unsupervised Color Correction Method), for example, does this in the following steps: It firstly reduces the color cast by equalizing the color values. Then it enhances contrast by stretching the red histogram towards the maximum and finally saturation and intensity components are optimized. == Underwater stereo vision == It is usually assumed that stereo cameras have been calibrated previously, geometrically and radiometrically. This leads to the assumption that corresponding pixels should have the same color. However this can not be guaranteed in an underwater scene, because of dispersion and backscatter. However, it is possible to digitally model this phenomenon and create a virtual image with those effects removed == Other application fields == Imaging sonars have become more and more accessible and gained resolution, delivering better images. Sidescan sonars are used to produce complete maps of regions of the sea floor stitching together sequences of sonar images. However, sonar images often lack proper contrast and are degraded by artefacts and distortions due to noise, attitude changes of the AUV/ROV carrying the sonar or non uniform beam patterns. Another common problem with sonar computer vision is the comparatively low frame rate of sonar images.
Deep learning speech synthesis
Deep learning speech synthesis refers to the application of deep learning models to generate natural-sounding human speech from written text (text-to-speech) or spectrum (vocoder). Deep neural networks are trained using large amounts of recorded speech and, in the case of a text-to-speech system, the associated labels and/or input text. == Formulation == Given an input text or some sequence of linguistic units Y {\displaystyle Y} , the target speech X {\displaystyle X} can be derived by X = arg max P ( X | Y , θ ) {\displaystyle X=\arg \max P(X|Y,\theta )} where θ {\displaystyle \theta } is the set of model parameters. Typically, the input text will first be passed to an acoustic feature generator, then the acoustic features are passed to the neural vocoder. For the acoustic feature generator, the loss function is typically L1 loss (Mean Absolute Error, MAE) or L2 loss (Mean Square Error, MSE). These loss functions impose a constraint that the output acoustic feature distributions must be Gaussian or Laplacian. In practice, since the human voice band ranges from approximately 300 to 4000 Hz, the loss function will be designed to have more penalty on this range: l o s s = α loss human + ( 1 − α ) loss other {\displaystyle loss=\alpha {\text{loss}}_{\text{human}}+(1-\alpha ){\text{loss}}_{\text{other}}} where loss human {\displaystyle {\text{loss}}_{\text{human}}} is the loss from human voice band and α {\displaystyle \alpha } is a scalar, typically around 0.5. The acoustic feature is typically a spectrogram or Mel scale. These features capture the time-frequency relation of the speech signal, and thus are sufficient to generate intelligent outputs. The Mel-frequency cepstrum feature used in the speech recognition task is not suitable for speech synthesis, as it reduces too much information. == History == In September 2016, DeepMind released WaveNet, which demonstrated that deep learning-based models are capable of modeling raw waveforms and generating speech from acoustic features like spectrograms or mel-spectrograms. Although WaveNet was initially considered to be computationally expensive and slow to be used in consumer products at the time, a year after its release, DeepMind unveiled a modified version of WaveNet known as "Parallel WaveNet," a production model 1,000 faster than the original. This was followed by Google AI's Tacotron 2 in 2018, which demonstrated that neural networks could produce highly natural speech synthesis but required substantial training data—typically tens of hours of audio—to achieve acceptable quality. Tacotron 2 used an autoencoder architecture with attention mechanisms to convert input text into mel-spectrograms, which were then converted to waveforms using a separate neural vocoder. When trained on smaller datasets, such as 2 hours of speech, the output quality degraded while still being able to maintain intelligible speech, and with just 24 minutes of training data, Tacotron 2 failed to produce intelligible speech. In 2019, Microsoft Research introduced FastSpeech, which addressed speed limitations in autoregressive models like Tacotron 2. FastSpeech utilized a non-autoregressive architecture that enabled parallel sequence generation, significantly reducing inference time while maintaining audio quality. Its feedforward transformer network with length regulation allowed for one-shot prediction of the full mel-spectrogram sequence, avoiding the sequential dependencies that bottlenecked previous approaches. The same year saw the release of HiFi-GAN, a generative adversarial network (GAN)-based vocoder that improved the efficiency of waveform generation while producing high-fidelity speech. In 2020, the release of Glow-TTS introduced a flow-based approach that allowed for fast inference and voice style transfer capabilities. In March 2020, the free text-to-speech website 15.ai was launched. 15.ai gained widespread international attention in early 2021 for its ability to synthesize emotionally expressive speech of fictional characters from popular media with minimal amount of data. The creator of 15.ai (known pseudonymously as 15) stated that 15 seconds of training data is sufficient to perfectly clone a person's voice (hence its name, "15.ai"), a significant reduction from the previously known data requirement of tens of hours. 15.ai is credited as the first platform to popularize AI voice cloning in memes and content creation. 15.ai used a multi-speaker model that enabled simultaneous training of multiple voices and emotions, implemented sentiment analysis using DeepMoji, and supported precise pronunciation control via ARPABET. The 15-second data efficiency benchmark was later corroborated by OpenAI in 2024. == Semi-supervised learning == Currently, self-supervised learning has gained much attention through better use of unlabelled data. Research has shown that, with the aid of self-supervised loss, the need for paired data decreases. == Zero-shot speaker adaptation == Zero-shot speaker adaptation is promising because a single model can generate speech with various speaker styles and characteristic. In June 2018, Google proposed to use pre-trained speaker verification models as speaker encoders to extract speaker embeddings. The speaker encoders then become part of the neural text-to-speech models, so that it can determine the style and characteristics of the output speech. This procedure has shown the community that it is possible to use only a single model to generate speech with multiple styles. == Neural vocoder == In deep learning-based speech synthesis, neural vocoders play an important role in generating high-quality speech from acoustic features. The WaveNet model proposed in 2016 achieves excellent performance on speech quality. Wavenet factorised the joint probability of a waveform x = { x 1 , . . . , x T } {\displaystyle \mathbf {x} =\{x_{1},...,x_{T}\}} as a product of conditional probabilities as follows p θ ( x ) = ∏ t = 1 T p ( x t | x 1 , . . . , x t − 1 ) {\displaystyle p_{\theta }(\mathbf {x} )=\prod _{t=1}^{T}p(x_{t}|x_{1},...,x_{t-1})} where θ {\displaystyle \theta } is the model parameter including many dilated convolution layers. Thus, each audio sample x t {\displaystyle x_{t}} is conditioned on the samples at all previous timesteps. However, the auto-regressive nature of WaveNet makes the inference process dramatically slow. To solve this problem, Parallel WaveNet was proposed. Parallel WaveNet is an inverse autoregressive flow-based model which is trained by knowledge distillation with a pre-trained teacher WaveNet model. Since such inverse autoregressive flow-based models are non-auto-regressive when performing inference, the inference speed is faster than real-time. Meanwhile, Nvidia proposed a flow-based WaveGlow model, which can also generate speech faster than real-time. However, despite the high inference speed, parallel WaveNet has the limitation of needing a pre-trained WaveNet model, so that WaveGlow takes many weeks to converge with limited computing devices. This issue has been solved by Parallel WaveGAN, which learns to produce speech through multi-resolution spectral loss and GAN learning strategies.
HYPO CBR
HYPO is a computer program, an expert system, that models reasoning with cases and hypotheticals in the legal domain. It is the first of its kind and the most sophisticated of the case-based legal reasoners, which was designed by Kevin Ashley for his Ph.D dissertation in 1987 at the University of Massachusetts Amherst under the supervision of Edwina Rissland. HYPO's design represents a hybrid generalization/comparative evaluation method appropriate for a domain with a weak analytical theory and applies to tasks that rarely involve just one right answer. The domain covers US trade secret law, and is substantially a common law domain. Since Anglo-American common law operates under the doctrine of precedent, the definitive way of interpreting problems is of necessity and case-based. Thus, HYPO did not involve the analysis of a statute, as required by the Prolog program. Rissland and Ashley (1987) envisioned HYPO as employing the key tasks performed by lawyers when analyzing case law for precedence to generate arguments for the prosecution or the defence. HYPO was a successful example of a general category of legal expert systems (LESs), it applies artificial intelligence (A.I.) techniques to the domain of legal reasoning in patent law, implementing a case-based reasoning (CBR) system, in contrast to rule based systems like MYCIN, or mixed-paradigm systems integrating CBR with rule-based or model-based reasoning like IKBALS II. A legal case-based reasoning essentially reasons from prior tried cases, comparing the contextual information in the current input case with that of cases previously tried and entered into the system. As noted by Ashley and Rissland (1988) CBR is used to "... capture expertise in domains where rules are ill-defined, incomplete or inconsistent". The HYPO project set out to model the creation of hypotheticals in law, where no case matches well enough. HYPO uses hypotheticals for a variety of tasks necessary for good interpretation: "to redefine old situations in terms of new dimensions, to create new standard cases when an appropriate one doesn’t exist, to explore and test the limits of a concept, to refocus a case by excluding some issues and to organize or cluster cases". Hypotheticals can include facts that support two conflicting lines of reasoning. So, it makes and responds to arguments from competing viewpoints about who should win the dispute. HYPO use heuristics such as making a case weaker or stronger, making a case extreme, enabling a near-miss, disabling a near-hit to generate hypotheticals in the context of an argument by using the dimensions mechanism. Dimensions have a range of values, along which the supportive strength that may shift from one side to the other. What differentiated this expert system from others was its facility not only to return a primary to best-case response but to return near-best-fit responses also. == Components == Legal knowledge in HYPO is contained in: the case-knowledge-base (CKB) and the library of dimensions. The CKB contains HYPO's base of known cases that are highly structured objects and sub-objects both real and hypothetical in the area of trade secret law. Each case is represented as a hierarchical set of frames whose slots are important facets of the case (e.g. Plaintiff, defendant, secret knowledge, employer/employee data).Ashley’s HYPO system used a database of thirty cases in the area indexed by thirteen dimensions. A key mechanism in HYPO is a dimension i.e. a mechanism to allow retrieval from the CKB, in order to represent legal cases. Ashley's dimensions are composed of (i) prerequisites, which are a set of factual predicates that must be satisfied for the dimension to apply (ii) focal slots, which accommodate one or two of the dimension's prerequisites designated as being indicative of the case's strength along that dimension and (iii) range information, which tells how a change in focal slot value effects the strength of a party's case along a given dimension. Dimensions focus attention on important aspects of cases. In HYPO's domain of misappropriation of trade secrets the dimension called “secrets voluntary disclosed” captures the idea that the more disclosures the plaintiff has made of his/her putative secret, the less convincing is his/her argument that the defendant is responsible for letting the secret. HYPO, like any other CBR system has also the following components: Similarity/relevancy metrics: that is, standards by which to evaluate the closeness of cases, judge their relevancy to the instant case, and select “most on point” cases. Half-Order Theory of the Application Domain: that is, hierarchies and taxonomies of knowledge, especially regarding the application domain. Precedent-based argumentation abilities: that is, capabilities to generate and evaluate precedent-based arguments. Knowledge to generate hypotheticals: that is, the ability to generate hypothetical cases to deal with various circumstances, like testing the validity of an interpretation or argument by providing gedanken experiments such as test cases or to fill in a weak CKB. == Functions == HYPO's method of creating an argument and justifying a solution or position has several steps. HYPO begins its processing with the current fact situation (cfs) which is direct input by the user into HYPO's representation framework. Once the user inputs the case, HYPO begins its legal analysis. The cfc is analyzed for relevant factors. Based on these factors HYPO selects the relevant cases and produces a case-analysis-record that records which dimensions apply to the cfc and which nearly apply (i.e. are "near misses"). The combined list of applicable and near miss dimensions is called the D-list. At this point the fact gathered module may request additional information from the user in order to draw a legal conclusion. Once all the facts are in the case-positioner module it uses the case-analysis record to create the claim lattice. This is a technique that organizes the relevant retrieved cases from the point of view of the cfc and makes it easy for HYPO to ascertain the most-on point cases (mopc) and to least on-point-cases. HYPO's arguments are 3ply, leading to the construction of the skeleton of an argument: it makes a point for one side, drawing the analogy between the problem and the precedent, responds with an argument for the opponent side, endeavoring to differentiate the cited case and citing other cases as counterarguments. Then it makes a final rebuttal, attempting to differentiate the counterarguments. The claim lattice also enables the HYPO-generator module to produce legally hypotheticals. With its use of dimension-based heuristics, the HYPO-generator does a heuristic search of the space of all possible cases. Lastly, the Explanation module expands upon the argument skeleton and provides explanation and justification for the different lines of analysis and cases found by HYPO. == An intelligent legal tutoring system == Legal expert systems are specifically designed to teach an area of law and are useful for pedagogical purposes. Ashley's work was mainly concerned to build tools to help students understand legal reasoning. Explanation and argument are the bases of the case method used in many professional schools in the U.S., first introduced by the Dean of the Harvard Law School, Christopher Columbus Langdell in 1870. The case method focuses on close readings of cases and principles; it involves students in pointed Socratic dialogue and makes strong use of hypotheticals (hypos). Thus, CATO (Aleven 1997) was a research project to device and test an intelligent, case-based tutorial program for teaching law students how to argue with cases implementing the HYPO program. Within the tutor system, Ashley and Aleven (1991) proposed to leverage an understanding of legal reasoning against the standard case-based tutoring methodology. What makes this tutoring system stand out is the additional levels of abstraction involved in its results. The system presents exercises, including the facts of a problem and a set of on-line cases and instructions to make, or respond to, a legal argument about the problem. The student/user will have a set of tools to analyze the problem and fashion an answer comparing it to other cases. Instead of simply generating precedent cases, the system works to interpret student responses, comparing them against a list of possibilities and responding to student entries, for example, by citing counterexamples, and providing feedback on a student's problem solving activities with explanations of correctness or giving further hints as to what may be wrong with evaluating a student's ability to perform legal reasoning and argument, examples and follow-up assignments by employing HYPO's model of case-based structure. == HYPO’s progeny == The quality of HYPO's results speak for themselves, in that a number of sequent legal reasoning systems are either directly based upon H
Eden: It's an Endless World!
Eden: It's an Endless World!, also known simply as Eden (stylized in all caps), is a Japanese science fiction manga series written and illustrated by Hiroki Endo. It was serialized in Kodansha's seinen manga magazine Monthly Afternoon from September 1997 to June 2008, with its chapters collected in 18 tankōbon volumes. == Premise == The story is set in the near future, following the "closure virus" pandemic has killed 15 percent of the world's population, crippled or disfigured many more, with catastrophic effect on global politics. Its themes and many character names are taken from Gnostic mythology. == Plot == The series begins with a long introduction, with the characters Ennoia and Hannah living a peaceful life on a remote and isolated island called Eden, with researcher Lane Morris, who is their guardian and a victim of the pandemic. The events that led to this situation are revealed in flashbacks, leading up to the return of Ennoia's father, along with the forces of the Propater Federation. Following this, the story moves forwards twenty years, and focuses on Ennoia's son, Elijah, the main character, and his own conflict with the powerful and monopolistic Propater federation to save his sister, Mana Ballard, kidnapped by Propater when he was very young. She is being held to threaten Ennoia Ballard, father of the two characters, who has become a powerful drug lord in South America, feared and despised by many, including, to an extent, his own family. During a terrorist attack, Elijah, aged 15, is separated from his mother and his sister is kidnapped, along with his mother Hannah and now has to handle things on his own. Eden is about his coming-of-age as a man and trying to survive both bodily and morally in world that is too complex for mere "black and white". He encounters many other characters, both allies and enemies, all sharing the same struggle to survive in a post-apocalyptic dystopian world. Many stories are included of the people Elijah meets, telling their past or following life, sometimes volumes later, furthering understanding of the characters and giving increased depth to the world of the book as a whole. Later in the series, the story once again moves forwards in time, jumping four more years ahead. The Closure Virus, the cause of the original pandemic, mutates, this time assimilating non-organic matter as well as organic, known as "colloid" (or "Disclosure Virus"). The story rejoins Elijah, now 19 years old, as well as many other old characters, and some new, as the world begins to deal with this new threat that is swallowing many cities in the world, leaving lakes and craters, and many people. It is later discovered that the several colloids in the world, are linked with a net of underground auto-built "cables," and that the colloid itself, stores all the memories of the people it swallows. == Characters == Elijah Ballard (エリヤ・バラード, Eriya Barādo) Elijah is introduced while on the run from Propater. He becomes involved in his father's criminal activities, and undergoes a coming of age into adulthood. Ennoia Ballard (エンノイア・バラード, Ennoia Barādo) Elijah's father. Hannah Mayall (ハナ・メイオール, Hana Meiōru) Elijah's mother. Mana Ballard (マナ・バラード, Mana Barādo) Elijah's sister, who remains in Propater hands whilst her mother is rescued. Elijah's fight to free her is a focus of the later parts of the story. Nazarbaiev Khan (ナザルバイエフ・カーン, Nazarubaiefu Kān) Colonel Khan is an old soldier from Azerbaijan. He leads the Nomad group (including Kenji and Sophia) fleeing Propater at the start of the series. Khan became Kenji's mentor after killing his brother, and the two share a slightly strained, but at the same time, trusting, relationship. Sophia Theódores (ソフィア・テオドレス, Sofia Teodoresu) A powerful Greek computer hacker, and full-body cyborg. Maya (マーヤ, Māya) A nearly godlike AI, which seems to roughly correspond to the savior of Gnostic mythology. Kenji Asai (ケンジ・アサイ) The brother of a low-level yakuza boss. Helena Montoya (ヘレナ・モントーヤ, Herena Montōya) A prostitute now working in a brothel. Has a complex relationship with Elijah and acts as a surrogate big sister. == Media == === Manga === Eden: It's an Endless World! was written and illustrated by Hiroki Endo. The series ran in Kodansha's Monthly Afternoon magazine from September 25, 1997, to June 25, 2008. Kodansha collected its chapters into 18 tankōbon volumes, released from April 21, 1998, to July 23, 2008. In July 2005, Dark Horse Comics announced in San Diego Comic-Con that it has licensed Eden for North American distribution, with publication to begin in November of that year. As of March 2014, 14 volumes were released in total. ==== Volumes ==== == Reception == Eden was named Wizard magazine's best manga of 2007. In his review of another work by Hiroki Endo titled Hiroki Endo's Tanpenshu, David F. Smith of Newtype USA has called Eden one of the best manga American money can buy.
Irwin Sobel
Irwin Sobel (born September 12, 1940) is a scientist and researcher in digital image processing. == Biography == Irwin Sobel was born in New York City. He graduated from MIT in 1961 and completed his Ph.D. research at the Stanford Artificial Intelligence Project (SAIL) with thesis Camera Models and Machine Perception. His Ph.D. advisor was Jerome A. Feldman. Starting in 1973, he spent nine years doing postdoctoral research at Columbia University. After 1982, he worked as a Senior Researcher at HP Labs. == Sobel operator == In 1968, Sobel gave a talk entitled "An Isotropic 3x3 Image Gradient Operator" at SAIL; this method became known as the Sobel operator. It was developed jointly with a colleague, Gary Feldman, also at SAIL.
Defuzzification
Defuzzification is the process of producing a quantifiable result in crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems. These systems will have a number of rules that transform a number of variables into a fuzzy result, that is, the result is described in terms of membership in fuzzy sets. For example, rules designed to decide how much pressure to apply might result in "Decrease Pressure (15%), Maintain Pressure (34%), Increase Pressure (72%)". Defuzzification is interpreting the membership degrees of the fuzzy sets into a specific decision or real value. The simplest but least useful defuzzification method is to choose the set with the highest membership, in this case, "Increase Pressure" since it has a 72% membership, and ignore the others, and convert this 72% to some number. The problem with this approach is that it loses information. The rules that called for decreasing or maintaining pressure might as well have not been there in this case. A common and useful defuzzification technique is center of gravity. First, the results of the rules must be added together in some way. The most typical fuzzy set membership function has the graph of a triangle. Now, if this triangle were to be cut in a straight horizontal line somewhere between the top and the bottom, and the top portion were to be removed, the remaining portion forms a trapezoid. The first step of defuzzification typically "chops off" parts of the graphs to form trapezoids (or other shapes if the initial shapes were not triangles). For example, if the output has "Decrease Pressure (15%)", then this triangle will be cut 15% the way up from the bottom. In the most common technique, all of these trapezoids are then superimposed one upon another, forming a single geometric shape. Then, the centroid of this shape, called the fuzzy centroid, is calculated. The x coordinate of the centroid is the defuzzified value. == Methods == There are many different methods of defuzzification available, including the following: AI (adaptive integration) BADD (basic defuzzification distributions) BOA (bisector of area) CDD (constraint decision defuzzification) COA (center of area) COG (center of gravity) ECOA (extended center of area) EQM (extended quality method) FCD (fuzzy clustering defuzzification) FM (fuzzy mean) FOM (first of maximum) GLSD (generalized level set defuzzification) ICOG (indexed center of gravity) IV (influence value) LOM (last of maximum) MeOM (mean of maxima) MOM (middle of maximum) QM (quality method) RCOM (random choice of maximum) SLIDE (semi-linear defuzzification) WFM (weighted fuzzy mean) The maxima methods are good candidates for fuzzy reasoning systems. The distribution methods and the area methods exhibit the property of continuity that makes them suitable for fuzzy controllers.