## Augmented Fuzzy Artificial intelligence

The xtractis technology is based on Fuzzy Relations of Order N Theory coupled with proprietary algorithms of Inductive Machine Reasoning

## Fuzzy Theory + Inductive Reasoning

##### The DNA of xtractis robots

## Some key ideas about Fuzzy Theory

1- Fuzzy theory 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.

2- Fuzzy knowledge is information-rich: transforming it in the beginning of the data processing into binary knowledge induces a bias which inevitably affects the quality of the decision. It is preferable to maintain the fuzziness throughout the data processing and to decide only at the end of the process (final transition from fuzzy decision to crisp decision)

3- Fuzzy logic and fuzzy set theory are used for the gradual and nuanced modeling of expert knowledge, by replicating their mode of reasoning, while allowing the definition of categories with ill-defined limits. Fuzzy logic is part of the approach of Symbolic / Cognitive Fuzzy AI. By integrating both imprecision and uncertainty, it makes it possible to design decision-support systems that are more effective than conventional expert systems: an expert will be all the more certain of their assertions if she/he is authorized to be imprecise and will be all the more uncertain if he/she is forced to be precise. It also offers a high-performance alternative approach for modeling complex processes and non-linear phenomena.

4- **Fuzzy arithmetic** allows modeling and processing of imprecise numerical quantities. It enables the design of more accurate predictive analytical models which are more faithful to reality.

5- Dual measures of **possibility** and **necessity** replace the measure of probability when the decision maker must assess the occurrence of an event, on which he/she has little historical data or poor quality data. This appears in particular in multi-criteria decision-making problems or operational safety problems, when the decision-maker uses information from human sensors (judgment, expert opinion). The theory of possibility is thus adapted to take into account the epistemic uncertainty linked to the lack of information, when the theory of probability is rather linked to the stochastic uncertainty characterizing a presence of “blind chance”. In particular, it allows the estimation of the occurrence of imprecise events.

## The concept of Fuzzy Relation of order N

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 an infinite number of logical operators of conjunction, disjunction, negation, inference and anchor-composition. It shows how to create an infinity of fuzzy measures of possibility and necessity, using the FR-N fusion composition operators.

This theory defines new original algebraic structures, while exhibiting the corresponding maximum algebraic structures, according to the operators used. Compared to other AI techniques, it thus allows larger margin in non-linear non-convex non-connected non-monotonous and non-decomposable modeling of complex processes and phenomena.

## A fuzzy-rule based xtractis model

An “IF…THEN” fuzzy rule is a local non-linear model linking nuanced variables. Mathematically, it is defined by an FR-N, i.e. a non-linear multidimensional function connecting N-1 input variables to the output variable.

An xtractis model is a collection of fuzzy rules covering the decision space. Any occurence in this space leads to the simultaneous and gradual triggering of certain rules, then the interpolation of their decisions: local rules interact with each other 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 the real level of complexity of the process under study: **to discover the most robust and compact model**.

xtractis paradoxically succeeds in **explaining** -through explicit decision rules using original variables- **knowledge that cannot be explained** by a human, such as knowledge used in perception or sensory evaluation.

## Inductive, Collective & Evolutionary Automated Machine Reasoning

From a set of structured data collected on the process to be modeled and characterized by a set of potentially predictive variables, xtractis robots discover the underlying models, by Inductive Automatic Reasoning.

More precisely, it is an Inductive Collective Competitive Reflective Cooperative and Evolutionary Reasoning! This means that several robots are launched in competition to process the same problem, each robot having a distinct learning strategy, among the infinite family of strategies at their disposal. After completing their respective inductive reasoning, the robots systematically, objectively and intensively assess the robustness of the models discovered.

Once each robot has selected its top models, the xtractis robots enter a cooperation phase to build, without supervision, new inductive reasoning strategies that are more advanced and more efficient than those of robots of the previous generation, and this at infinity. Unlike Open Source AI algorithms which are fixed a priori by the modeler, our robots are able to learn alone to reason better. Consequently, on a set of learning data which does not change, the more they will have induction energy (computational power x time), the more they will be able to discover more and more efficient and more compact predictive models, therefore the most explicable.

## Robustness needs processing time

Although it needs a lot of computing time, the robustness assessment step is crucial because it makes it possible to estimate **the predictive capacity of the model**, i.e. the reliability of the predictions delivered by the deployed model when it is used in real/unknown situations. For one model, this robustness calculation can take from 50 to 10,000 times the time it took to generate it, but it is an essential step to avoid falling into the trap of over-learning. Indeed, although necessary, a high descriptivity or descriptive capacity is not sufficient, because it does not guarantee that the model is robust: by learning “by memory” (overlearning), the model would have a very high descriptivity, but would often make wrong decisions when processing situations that were not part of its learning dataset.

Therefore, **it is impossible to carry out robust predictive modeling in real time**. However, in deployment, the predictions deduced from a robust model are delivered in real time.

## A technology suitable for Complex Processes

Ultimately, Fuzzy theory expands the range of modeling, prediction and evaluation methods, while simplifying the interpretability of complex processes.

xtractis Augmented Fuzzy AI approach can manage:

- multi-dimensionality and non-linearity while proposing local models which, combined, make it possible to cover the whole of the decision-making or operating space;
- all types of data: quantitative or qualitative, digital or symbolic, objective or subjective, certain or uncertain, precise or imprecise, entered or missing;
**Regression**(predicting the value of a numeric variable),**Multiclassification**(predicting the class to which a new profile would belong),**Scoring**(predicting the risk of occurrence of the event studied) or**Clustering**(identifying stable segments in data).