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Fuzzy Rule Interpolation Matlab Toolbox - FRI Toolbox

In most fuzzy systems, the completeness of the fuzzy rule base is required to generate meaningful output when classical fuzzy reasoning methods are applied. This means, in other words, that the fuzzy rule base has to cover all possible inputs. Regardless of the way of rule base construction, be it created by human experts or by an automated manner, often incomplete rule bases are generated. One simple solution to handle sparse fuzzy rule bases and to make infer reasonable output is the application of fuzzy rule interpolation (FRI) methods. In this paper, we present a Fuzzy Rule Interpolation Matlab Toolbox, which is freely available. With the introduction of this Matlab Toolbox, different FRI methods can be used for different real time applications, which have sparse or incomplete fuzzy rule base.

Fuzzy Rule Interpolation Based on Polar Cuts

Systems applying fuzzy logic are rule based ones. The collection of the rules the so called rule base can be characterized as dense or sparse depending on whether there exist rules for all the possible observations. In the sparse case for some observations there are no rules whose antecedent part would overlap the observation at least partially. Therefore the classical compositional reasoning methods can not produce an acceptable conclusion. The inference techniques based on fuzzy rule interpolation are developed for especially this purpose. This paper proposes a new fuzzy rule interpolation based inference technique applying the concept of linguistic term shifting and polar cut. It is called FRIPOC (Fuzzy Rule Interpolation based in POlar Cuts) and it is applicable in the case of sparse and dense rule bases, too. Its main advantages are its comprehensibility, extrapolation capability and its applicability even if the height of one or more fuzzy sets is smaller than one. The rest of this paper is organized as follows. Section 1 gives a brief overview on the relevant fuzzy rule interpolation techniques grouping them depending on the main steps they are following. Section 2 presents the main structure and the steps and stages that characterize the method FRIPOC. Section 3 introduces the concept of the polar cut and a fuzzy set interpolation technique called FEAT-p based on it as a possible implementation for the first and third stage of the first step. In section 4 the authors propose a technique for the determination of the position of the consequent sets that is an extension and adaptation of the Shepard 2D interpolation [15]. Section 5 introduces a new polar cut based single rule inference method for the determination of the conclusion. In section 6 some relevant features of the new method are outlined through some numerical examples.

Extending the Fuzzy Rule Interpolation "FIVE" by Fuzzy Observation

Some difficulties emerging during the construction of fuzzy rule bases are inherited from the type of the applied fuzzy reasoning. In fuzzy systems, when classical methods (e.g. the Compositional Rule of Inference) are applied, the completeness of the fuzzy rule base is required to generate meaningful output. This means, that the fuzzy rule base has to cover all possible inputs. The way of building a complete rule base is not always straightforward. One simple solution to handle sparse fuzzy rule bases and to make infer reasonable output is the application of fuzzy rule interpolation (FRI) methods. On the other hand most of the FRI methods share the burden of high computational demand. However there is a method “FIVE” (Fuzzy Interpolation based on Vague Environment, originally introduced in [8], [11] and [12]) which is simple and quick enough to fit even the requirements of direct control, where the conclusions are applied as real-time control actions, too. Beyond the simplicity and therefore the high reasoning speed, “FIVE” has two obvious drawbacks, the lack of the fuzziness on the observation and conclusion side. The main contribution of this paper is the introduction of a way for handling fuzzy observations by extending the original “FIVE” concept with the ability of merging vague environments.

Sparse Fuzzy System Generation by Rule Base Extension

This paper aims the introduction and comparison of two novel fuzzy system generation methods that implement the concept of incremental Rule Base Extension (RBE). Both methods automatically obtain from given input-output data a low complexity fuzzy system with a sparse rule base.

Fuzzy rule interpolation and extrapolation techniques: Criteria and evaluation guidelines

This paper comprehensively analyzes Fuzzy Rule Interpolation and extrapolation Techniques (FRITs). Because extrapolation techniques are usually extensions of fuzzy rule interpolation, we treat them both as approximation techniques designed to be applied where sparse or incomplete fuzzy rule bases are used, i.e., when classical inference fails. FRITs have been investigated in the literature from aspects such as applicability to control problems, usefulness regarding complexity reduction and logic. Our objectives are to create an overall FRIT standard with a general set of criteria and to set a framework for guiding their classification and comparison. This paper is our initial investigation of FRITs. We plan to analyze details in later papers on how individual techniques satisfy the groups of criteria we propose. For analysis,MATLAB FRI Toolbox provides an easy-to-use testbed, as shown in experiments.

Incremental Rule Base Creation with Fuzzy Rule Interpolation-Based Q-Learning

Reinforcement Learning (RL) is a widely known topic in computational intelligence. In the RL concept the problem needed to be solved is hidden in the feedback of the environment, called rewards. Using these rewards the system can learn which action is considered to be the best choice in a given state. One of the most frequently used RL method is the Q-learning, which was originally introduced for discrete states and actions. Applying fuzzy reasoning, the method can be adapted for continuous environments, called Fuzzy Q-learning. An extension of the Fuzzy Q-learning method with the capability of handling sparse fuzzy rule bases is already introduced by the authors. The latter suggests a Fuzzy Rule Interpolation (FRI) method to be the reasoning method applied with Q-learning, called FRIQ-learning. The main goal of this paper is to introduce a method which can construct the requested FRI fuzzy model from scratch in a reduced size. The reduction is achieved by incremental creation of an intentionally sparse fuzzy rule base. Moreover an application example (cart-pole problem simulation) shows the promising results of the proposed rule base reduction method.

Application of interpolation-based fuzzy logic reasoning in behaviour-based control structures

Some difficulties emerging during the construction of fuzzy behaviour-based control structures are inherited from the type of the applied fuzzy reasoning. The fuzzy rule base requested for many classical reasoning methods needed to be complete. In case of fetching fuzzy rules directly from expert knowledge e.g. for the behaviour coordination module, the way of building a complete rule base is not always straightforward. One simple solution for overcoming the necessity of the complete rule base is the application of interpolation-based fuzzy reasoning methods, since interpolation-based fuzzy reasoning methods can serve usable (interpolated) conclusion even if none of the existing rules is hit by the observation. These methods can save the expert from dealing with derivable rules and help to concentrate on cardinal actions only. To demonstrate the applicability of the interpolation-based fuzzy reasoning methods in behaviour-based control structures, a simple interpolation-based fuzzy reasoning method and its adaptation for behaviour-based control are introduced briefly in this paper.

Interpolation based fuzzy automaton for human-robot interaction

Abstract One way of handling Human-Robot Interaction (HRI) is based on the concept, that the robot acts like an animal companion to human. According to this paradigm the Robot should not be molded to mimic the human being, and form human-to-human like communication, but to follow the existing biological examples and form inter-species interaction. The 20.000 year old human-dog relationship is a good example for this paradigm of the HRI, as interaction of different species. One good reason of this approach in HRI is the lack of the “uncanny valley” effect i.e. increasing similarity of robots to humans will actually increase the chances that humans refuse interaction (will be frightened). In this paper, for ethologically inspired HRI model implementation, a fuzzy model structure built upon the framework of low computational demand Fuzzy Rule Interpolation (FRI) methods and fuzzy automaton is suggested. The application of FRI methods fits well the conceptually “spare rule-based” structure of the existing descriptive verbal ethological models. (In case of the descriptive verbal ethological models, the “completeness” of the rule-base is not required). The main benefit of the FRI method adaptation in ethological model implementation is the fact, that it has a simple rule-based knowledge representation format. Because of this, even after numerical optimization of the model, the rules are still “human readable”, and helps the formal validation of the model by the ethological experts. On the other side due to the FRI base, the model has still low computational demand and fits directly the requirements of the embedded implementations. For demonstrating the applicability of the proposed structure, some components of a human-dog interaction FRI model, which also suitable for HRI, will be briefly introduced in this paper.

Fuzzy Rule Interpolation-based Q-learning

Reinforcement learning is a well known topic in computational intelligence. It can be used to solve control problems in unknown environments without defining an exact method on how to solve problems in various situations. Instead the goal is defined and all the actions done in the different states are given feedback, called reward or punishment (positive or negative reward). Based on these rewards the system can learn which action is considered the best in a given state. A method called Q-learning can be used for building up the state-action-value function. This method uses discrete states. With the application of fuzzy reasoning the method can be extended to be used in continuous environment, called Fuzzy Q-learning (FQ-Learning). Traditional Fuzzy Q-learning uses 0-order Takagi-Sugeno fuzzy inference. The main goal of this paper is to introduce Fuzzy Rule Interpolation (FRI), namely the FIVE (Fuzzy rule Interpolation based on Vague Environment) to be the model applied with Q-learning (FRIQ-learning). The paper also includes an application example: the well known cart pole (reversed pendulum) problem is used for demonstrating the applicability of the FIVE model in Q-learning.

Linearity and the cnf property in linear fuzzy rule interpolation

It is an important question if rule interpolation is done whether the theoretical shape of the membership function of the calculated conclusion is exactly or approximately linear between two neighboring /spl alpha/-levels in the breakpoint set, or it has a very different shape. In the latter case, interpolation for only a few (as e.g. 0 and 1) levels is not satisfactory, which fact might increase the computational time necessary for generating the conclusion by a large constant factor. It is also examined if the conclusion has a convex and normal membership function, i.e. whether the calculated infima exceed the calculated suprema of the given /spl alpha/-cut or not.<<ETX>>