22 key points

to bring trust to

AI-driven decisions

Reasoning AI


Augmented Fuzzy Symbolic AI

Xtractis is a Generalized “Fuzzy Symbolic AI” as it implements innovative mathematics based on the Theory of Fuzzy Relations of order N [Zalila 1993]. It is the result of over 250 scientist-years of high-level R&D in fuzzy mathematics and automatic induction.

This non-standard mathematics enables reasoning with continuous logics, which are more suitable than classic binary logic for modeling complex real-world problems, i.e., problems mixing imprecision, subjectivity, and epistemic uncertainty.


Knowledge-Generating AI

Xtractis is an “Augmented Fuzzy Symbolic AI” because it automatically discovers implicit knowledge in data and structures it into decision systems based on fuzzy rules.

It exhibits all the knowledge synthesized from the information included in the learning dataset. It allows domain experts to understand their processes and enrich their knowledge.


Collective & Evolving AI

Xtractis robots infinitely perfect their induction (resp. abduction) strategies to discover increasingly efficient models (resp. increasingly satisfactory solutions) without human supervision, first in competition, then in cooperation.


Frugal AI

Xtractis uses evenly small or big data. It manages low-quality or low-quantity data without imputation, i.e., without introducing bias in data before processing.
When the volume of data is limited, it induces models with higher predictive capacity than the best open-source AI techniques. The predictive capacity is also higher when comparing the models from different techniques at iso-complexity (similar model structure).

Human-Centric AI


Replicating Human Reasoning

Xtractis instantiates the three human reasoning modes in three software robots:

XTRACTIS REVEAL uses fuzzy induction to discover intelligible cause and effect models, as human scientists, thanks to the Experimental Scientific Method.

XTRACTIS PREDICT uses fuzzy deduction for its predictive analysis, calculating the predictions from the induced models rationally and deterministically.

XTRACTIS OPTIMIZE uses fuzzy abduction for its prescriptive analysis, discovering the most optimal solutions to meet a non-linear multi-objective request from induced or analytical models.


Enabling Audit & Certification of AI Decision Systems

Users and experts can validate their models before pushing to end-use, or audit them before submission to certification to comply with AI regulations for high-risk applications.


Enhancing Knowledge
& Augmenting Experts

Xtractis-induced models are fully auditable by the domain expert who confirms the correctness of the decisions of the AI system to be deployed. It rationally explains each decision made. The deductive reasoning followed to calculate each prediction is automatically drawn in a detailed report.


Highlighting Biases
& Deploying Ethical Transparent AI Systems

Xtractis induces rules that confirm the presence of noise deliberately introduced into the reference data or explain any conscious or unconscious bias that a decision-making process may contain. It also refuses to deliver a prediction if it is highly uncertain of its decision (for offline systems).

Trusted AI


Robust Models

Xtractis discovers highly accurate knowledge from data: induced top-models have sustained high predictive capacity, at least equal to that of the best open-source AI techniques. The platform includes an intensive model validation process to ensure their level of reliability in the end-use and an intensive benchmark versus the best challenging techniques. It also detects any noise in data, by highlighting the measured values that are strongly different from the predicted ones.


Intelligible & Explainable Models

Xtractis-induced models are natively transparent: they are systems of fuzzy "IF…THEN" unchained rules which only use native predictor variables (no synthetic ones). Their internal decision-making logic is obvious and each of their decision is easily explained and traced.


Stable Models

Xtractis-induced models have native formal stability: firstly, no prediction will come out of an interval determined in advance from the structure of the rules; second, any slight variation of a predictive variable will lead to a gradual variation of the fuzzy prediction. Still, strong non-linearities inherent to the complex process or pheomena under study are recognized and addressed when necessary.


Holistic Modeling

Xtractis considers in first intention all the available variables and their interactions to retain weak signals. Then, it automatically discards non-impacting variables. The complexity of the complex process or pheomena under study is naturally discovered ex-post. As models are multifactorial, their predicted decisions for each new case are highly personalized.

Powerful AI


General Purpose Behavioral AI

Xtractis is perfectly suited to non-linear modeling, whether it concerns human decisions or the behavior of artificial or natural processes: industrial or socio-economic phenomena, conscious or unconscious human decisions, sensory perception… You can quickly develop high-risk predictive applications regardless of your activity sector (Finance, Banking, Insurance, Health, Pharma, Biotech, Sciences, Smart Industry, Defense, Security, Cyber, Legal, Autonomous Machines, ADAS…), and your department (Management, Marketing, R&D, Domain Expertise...).


Sovereign AI

XTRACTIS REVEAL, PREDICT, OPTIMIZE, and MONITOR algorithms are 100% proprietary, designed and developed in France, and independent of open-source AI code licenses. Only Benchmark features use open-source frameworks.
Licenses are hosted by an independant host and are accessible hrough a private and secure PaaS.


Compliant AI for High-Risk Applications

Xtractis already establishes higher requirements than the future European regulation "AI Act" relating to the deployment of high-risk AI applications. It also respects the WHO guiding principles for the use of AI in Health.


Mentalist AI!

With its innovative Reverse Engineering process, Xtractis can decipher the hidden behavior of a black-box AI system by inducing an Xtractis white-box model of at least equivalent performance.


Globally Unique AI

Xtractis is the only AI that natively discovers knowledge from data in a fully operational way.

Easy to Use AI


No-Code All-in-One Ready-to-Use Platform

You only use the mouse to control the Xtractis interface, even for Benchmark feature. You do not need to program, or have extensive Data Science skills.


Scalable Induction Power

You "hire" more Xtractis robots if you need to handle more complex problems or to get your results faster. Only CPU is used, no need of GPU; thus, more eco-friendly, and cheaper hardware.


Access in Private PaaS

Dedicated physical servers upon request.
Maximum Security to access your data and models.
Servers can be located on your site.


Prediction in Real-Time

Predictions running at a very high frequency on basic CPU: up to 70,000 predictions per second, on an Intel i7 @2.5Ghz with 8 physical cores.


Easy Deployment

Special licenses to exploit models via API or embedded codes.

FAQ about Fuzzy AI Concepts

Fuzzy Theory or Fuzzy Mathematics proposes formally rigorous concepts, techniques, and methods to model and deal with multidimensional knowledge and fuzzy data, i.e., real-world data that include imprecision, uncertainty, and/or subjectivity. It is made up of several branches.


Fuzzy knowledge is information-rich: transforming it into binary knowledge at the beginning of the data processing induces a bias that inevitably affects the quality of the decision. Maintaining the fuzziness throughout the data processing and deciding only at the end of the process (final transition from a fuzzy decision to a binary decision) is much more adequate for accurate decisions.


In Fuzzy Theory, dual measures of Possibility and Necessity replace the measure of Probability when the decision maker must assess the occurrence of an event on which they have little historical data or poor-quality data (e.g., will I draw a reddish ball out of the bag?). This appears particularly in multi-criteria decision-making when information comes from human sensors (judgment, expert opinion).


Theory of Possibility is thus adapted to account for the epistemic uncertainty linked to the lack of information. Particularly, it allows the estimation of the occurrence of fuzzy events, when the Theory of Probability is rather linked to the stochastic uncertainty of precise but random event.

Fuzzy Logic and Fuzzy Set theory are branches of Fuzzy Mathematics. They are used for the gradual and nuanced modeling of expert knowledge, by replicating the human reasoning while allowing the definition of fuzzy categories, i.e., with ill-defined boundaries.

By integrating both imprecision and uncertainty, it makes it possible to design decision-support systems that are more effective than conventional expert systems: experts will be even more confident of their assertions if they are authorized to be imprecise and will be all the more uncertain if they are forced to be precise.

It also offers a high-performance alternative approach for modeling complex processes and non-linear phenomena. Fuzzy Logic is the basis of Fuzzy Symbolic / Cognitive AI.

Fuzzy Arithmetic is a branch of Fuzzy Mathematics. It allows the modeling and processing of approximate numerical quantities. It enables the design of more accurate predictive analytical models that are more faithful to reality. It also allows solving complex Operational Research problems by introducing fuzzy constraints, i.e., which could be more or less satisfied.

The Fuzzy Relation of order N (FR-N) generalizes the concepts of scalar of [0,1] (FR-0), fuzzy set (FR-1), of fuzzy two-dimensional relation (FR-2) and extends them to an N-dimensional space. An FR-N thus defines a non-linear multi-dimensional equation.


FR-N Theory introduces infinite fuzzy logical operators of conjunction, disjunction, negation, implication, and anchor-composition. It shows how to create an infinity of fuzzy measures of possibility and necessity using the FR-N fusion composition operators. And thus how to create an infinity of fuzzy deductive, inductive and abductive reasoning algorithms.


This theory defines new original algebraic structures while exhibiting the corresponding maximum algebraic structures according to the operators used. FR-N Theory extends Fuzzy Logic, Fuzzy Set Theory and Theory of Possibility, and merges them into a single theory.


Compared to the other binary AI techniques, it thus allows a larger margin in modeling non-linear non-monotonous non-convex non-connected, and non-decomposable complex processes and phenomena.

An “IF…THEN” fuzzy rule is a non-linear equation relating the causes to the effect or a local non-linear model linking nuanced variables. Mathematically, it is defined by an FR-N, i.e., a non-linear multidimensional function relating N-1 interacting input variables to the output variable, thanks to fuzzy operators of conjunction, disjunction, negation and implication.


The fuzzy deductive inference of fuzzy rules is based on the anchor-composition of FR-N.

A fuzzy model/system is a collection of fuzzy rules covering the decision space. Any occurrence in this space leads to the simultaneous and gradual triggering of specific rules, then the interpolation of their decisions: local rules interact and cooperate to calculate the most appropriate final decision.
The more the model is composed of fuzzy rules and the more it uses input variables, the more it will succeed in accurately describing the behavior of a complex process. The feat of XTRACTIS is to find automatically the actual level of complexity of the process under study: when enough information is included in the dataset, XTRACTIS always succeeds in discovering the most robust AND compact model, i.e., the most intelligible model with the highest predictive and real performances.

Induction is the human reasoning mode that makes it possible to discover general laws (i.e., a model) from observing given facts about causes and their consequences.

Deduction is the human reasoning mode that finds the consequence of given causes from general laws.

Abduction is the human reasoning mode that searches for particular possible causes for a given consequence from general laws.

The model's robustness refers to its predictive performance or ability to make correct predictions for unknown situations (cases that are not part of the training set) or for noisy situations.

Not to be confused with the descriptive performance (descriptiveness), which is its ability to make correct predictions for known situations (cases of the training set).

An INTELLIGIBLE model is composed of an optimal finite number of pieces of knowledge: it is a white-box or transparent model. We can therefore understand the entire internal logic of its deductive reasoning for the infinity of possible cases.


An EXPLAINABLE model is a model whose decision can be locally justified for a specific case of prediction. It can be a black-box model.


An intelligible model is necessarily explainable, but the converse is false. Because they are intelligible, XTRACTIS models are also explainable.

XTRACTIS has 3 Machine Learning challengers among the non-linear AI techniques: Neural Networks, Boosted Trees, and Random Forests.
Despite their widespread use, these open-source AI techniques produce unintelligible models whose stability cannot be formally proved.
Conversely, XTRACTIS models are intelligible and formally stable due to the theoretical foundations of our algorithms. In addition, their robustness is at least equivalent to that of the models obtained from other AI techniques.