Fuzzy Rule Interpolation Research Papers (original) (raw)

2004, IEEE Transactions on Fuzzy Systems

The concept of fuzzy rule interpolation in sparse rule bases was introduced in 1993. It has become a widely researched topic in recent years because of its unique merits in the topic of fuzzy rule base complexity reduction. The first implemented technique of fuzzy rule interpolation was termed as α-cut distance based fuzzy rule base interpolation. Despite its advantageous properties in various approximation aspects and in complexity reduction, it was shown that it has some essential deficiencies, for instance, it does not always result in immediately interpretable fuzzy membership functions. This fact inspired researchers to develop various kinds of fuzzy rule interpolation techniques in order to alleviate these deficiencies. This paper is an attempt into this direction. It proposes an interpolation methodology, whose key idea is based on the interpolation of relations instead of interpolating α-cut distances, and which offers a way to derive a family of interpolation methods capable of eliminating some typical deficiencies of fuzzy rule interpolation techniques. The proposed concept of interpolating relations is elaborated here using fuzzy- and semantic-relations. This paper presents numerical examples, in comparison with former approaches, to show the effectiveness of the proposed interpolation methodology.

2000, IEEE Transactions on Fuzzy Systems

The first published result in fuzzy rule interpolation was the α-cut based fuzzy rule interpolation, termed as KH fuzzy rule interpolation, originally devoted for complexity reduction. Some deficiencies of this method was presented later, such as subnormal conclusion for certain configuration of the involved fuzzy sets. However, since that several conceptually different fuzzy rule interpolation techniques were proposed, none of those algorithms has such a low computational complexity than the original one. Recently, a modified version of the KH approach has been presented [1], , which eliminates the subnormality problem, while at the same time intending to maintain the advantageous computational properties of the original method. This paper presents a comprehensive analysis of the new method, which includes detailed comparison with the original KH fuzzy rule interpolation method concerning the explicit functions of the methods, preservation of piecewise linearity, stability. The fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques. All these comparisons shows that the new method preserves the advantageous properties of the KH method and alleviates its most significant disadvantage, the problem of subnormality.

2005, IEEE Transactions on Fuzzy Systems

Fuzzy rule based systems have been very popular in many engineering applications. However, when generating fuzzy rules from the available information, this may result in a sparse fuzzy rule base. Fuzzy rule interpolation techniques have been established to solve the problems encountered in processing sparse fuzzy rule bases. In most engineering applications, the use of more than one input variable is common, however, the majority of the fuzzy rule interpolation techniques only present detailed analysis to one input variable case. This paper investigates characteristics of two selected fuzzy rule interpolation techniques for multidimensional input spaces and proposes an improved fuzzy rule interpolation technique to handle multidimensional input spaces. The three methods are compared by means of application examples in the field of petroleum engineering and mineral processing. The results show that the proposed fuzzy rule interpolation technique for multidimensional input spaces can be used in engineering applications.

1997, Fuzzy Sets and Systems

The classical approaches in fuzzy control (Zadeh and Mamdani) deal with dense rule bases. When this is not the case, i.e. in sparse rule bases, one has to choose another method. Fuzzy rule interpolation (proposed first by Kóczy and Hirota [15]) offers a possibility to construct fuzzy controllers (KH controllers) under such conditions. The main result of this paper shows that the KH interpolation method is stable. It also contributes to the application oriented use of Balázs-Shepard interpolation operators investigated extensively by researchers in approximation theory. The numerical analysis aspect of the result contributes to the well-known problem of finding a stable interpolation method in the following sense.

2006

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.

2 Zsolt Csaba Johanyák and Szilveszter Kovács gaps in sparse rule bases. They can be divided into two groups depending on whether they are producing the approximated conclusion directly or a new intermediate rule is interpolated first. Relevant members of the first group are among others the α-cut based interpolation (KH) [10] proposed by Kóczy and Hirota, which was the first developed technique, the modified α-cut based interpolation (MACI) [17] introduced by Tikk and Baranyi, the fuzzy interpolation based on vague environment (FIVE) [12] developed by Kovács and Kóczy, the improved fuzzy interpolation technique for multi-dimensional input spaces (IMUL) [20] proposed by Wong, Gedeon and Tikk, the interpolative reasoning based on graduality (IRG) [2] introduced by Bouchon-Meunier, Marsala and Rifqi, the interpolation by the conservation of fuzziness (GK) [4] developed by Gedeon and Kóczy, the method based on the conservation of the relative fuzziness (CRF) proposed by Hirota, Kóczy and Gedeon, and the VKK method [19] introduced by Vass, Kalmár and Kóczy. The structure of the methods belonging to the second group can be described best by the generalized methodology of the fuzzy rule interpolation introduced by Baranyi, Kóczy and Gedeon in [1]. As other typical members of this group can be mentioned the ST method [22] introduced by Yan, Mizumoto and Qiao, the interpolation with generalized representative values (IGRV) [5] developed by Huang and Shen, the technique proposed by Jenei in [6], and the method being presented in this paper.

2000

A major issue in the field of fuzzy applications is the complexity of the algorithms used. In order to obtain efficient methods, it is necessary to reduce complexity without losing the easy interpretability of the components. One of the possibilities to achieve complexity reduction is to combine fuzzy rule interpolation with the use of hierarchical structured fuzzy rule bases, as proposed by Sugeno et al. (1991). For interpolation, the method of Koczy and Hirota (1993) is used, but other techniques are also suggested. The difficulty of applying this method is that it is often impossible to determine a partition of any subspace of the original state space so that in all elements of the partition the number of variables can be locally reduced. Instead of this, a sparse fuzzy partition is searched for and so the local reduction of dimensions will be usually possible. In this case however, interpolation in the sparse partition itself, i.e. interpolation in the meta-rule level is necessary. This paper describes a method how such a multilevel interpolation is possible

2006, 7th International Symposium of Hungarian Researchers on Computational Intelligence

Fuzzy rule interpolation-based reasoning methods are the most common choices for cases when the applied rule base is not dense. This paper presents a new techniquecalled LESFRI, which is based on the method of least squares. Its central idea is theconservation of the shape type specific to a fuzzy partition. The method has lowcomputational complexity.
Keywords: fuzzy rule interpolation, LESFRI, sparse fuzzy rule base

2007, 11th IEEE International Conference of Intelligent Engineering Systems (IEEE INES 2007)

This paper aims the introduction and comparison of two novel fuzzy system generation methods that implement theconcept of incremental Rule Base Extension (RBE). Bothmethods automatically obtain from given input-output data a lowcomplexity fuzzy system with a sparse rule base.
Keywords-rule base generation; sparse rule base; fuzzy ruleinterpolation; rule base extension

2009, 2009 5th International Symposium on Applied Computational Intelligence and Informatics

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 Qlearning 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 Qlearning (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. I.

2011, 2011 IEEE 12th International Symposium on Computational Intelligence and Informatics (CINTI)

The Virtual Collaboration Arena (VirCA) is a modular, easy to use 3D framework supporting the development of augmented (real and virtual) reality applications. To apply the services provided by VirCA, special VirCA interfaces are needed in the actual programming environment. Native interface does not exist for some special environments, like e.g. for MATLAB, which is a commonly used for implementing complex models. The goal of the paper is to introduce a possible method for interconnecting the prototype spatial ETO-MOTOR model implemented in MATLAB with the 3D VirCA augmented reality environment. This is achieved by a newly developed adapter application, which translates between the two environments and uses standardized network protocols for communication. The ETO-MOTOR is a behaviour model based upon ethological studies. In the case of the example application, the type of the ETO-MOTOR is a "spatial ETO-MOTOR", i.e. it can directly send spatial coordinates or heading directions to the virtual actors of the model. The prototype of the spatial ETO-MOTOR is constructed as a Fuzzy Rule Interpolation (FRI) based fuzzy automaton. In the example of the paper the ETO-MOTOR describes the behaviour of a dog in an unknown environment. In the original version of the model implementation, it has a very simple proof-of-concept user interface, which is sufficient for basic testing only, but very far from real world experiences. The personal interaction with the model thanks to the 3D VirCA augmented reality environment can yield much more direct observations and hence more profit for ethologists. The developed MATLAB-VirCA connector application provided with this paper can be easily modified to suit the needs of other third party applications too.

2007, BULETINUL STIINTIFIC al Universitatii “Politehnica” din Timisoara, ROMANIA,Seria AUTOMATICA si CALCULATOARE

Fuzzy modeling has great adaptability to thevariations of system configuration and operation conditions. This paper investigates the fuzzy modeling of a laboratory scale system of anaerobic tapered fluidized bed reactor (ATFBR). The studied system is the anaerobic digestion of synthetic wastewater derived from the starch processing industries. The experiment was carried out in a mesophilic ATFBR reactor with mesoporous granulated activated carbon as bacterial support.The fuzzy system was generated and trained by a modified version of the Projection based Rule Extraction (PRE) method using the obtained experimental data, and it applies the inference technique Fuzzy Rule Interpolation based on Polar Cuts (FRIPOC).The output parameters predicted by the tuned system have been found to be very close to the correspondingexperimental ones and the model was validated by replicative testing. Keywords: fuzzy modeling, FRIPOC, Anaerobic Tapered Fluidized bed Reactor, OLR, COD, BOD, pH

2007, 5th Slovakian-Hungarian JointSymposium on Applied Machine Intelligence and Informatics (SAMI2007)

The aim of this paper is to introduce a novel two-step Fuzzy Rule InterpolationTechnique (FRIT) “VEIN”, based on the concept of Vague Environment. The strength of FRIT against classical fuzzy reasoning methods is the ability of gaining conclusion even incase where the knowledge is represented by sparse fuzzy rule bases. The FRIT “VEIN”introduced in this paper is following the structure the Generalized Methodology of fuzzyrule interpolation [1], by adapting the concept of Vague Environment [4] for approximatedescription of fuzzy partitions [6].
Keywords: Vague Environment, Fuzzy Rule Interpolation, Fuzzy Set Interpolation, Single Rule Reasoning

2007, InternationalSymposium on Applied Computational Intelligence and Informatics (SACI 2007)

One of the most critical steps during the developmentof a fuzzy system is the identification of the fuzzy rule base andthe fuzzy partitions, the so-called “tuning”. This paper intends topresent a comparative study of three different fuzzy partitionparameter identification methods with respect to the effect of different fuzzy partition parameterization strategies.
Keywords-fuzzy system tuning; rule base optimization; sparse rule base; fuzzy rule interpolation

2008, 2008 IEEE International Conference on Computational Cybernetics

Relatively few Fuzzy Rule Interpolation (FRI) techniques can be found among the practical fuzzy rule based applications. Many of them have limitations from the direct application point of view, for example they can be applied only in one dimensional case, or defined based on the two closest surrounding rules of the actual observation. Additionally the FRI methods can dramatically simplify the building of fuzzy rule bases by enabling the application of sparse rule bases. FRI methods can provide reasonable (interpolated) conclusions even if none of the existing rules fires under the current observation. These methods can help the expert to concentrate on the cardinal actions only.

2012, Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments - HCCE '12

This paper presents human-robot interaction interfaces based on ethological studies. An ethological test procedure was modeled with the application of a fuzzy rule interpolation based fuzzy automaton. This fuzzy automaton was loaded with rules formed from the extracted ethological knowledge. Using the behaviours supplied by the fuzzy automaton as conclusions, different interfaces can be defined for the incarnation of the model. The ethological test procedure and its modeling technique based on the fuzzy automaton will be shortly introduced in the pap er, and then the various human-robot interfaces based on the former will be presented. These include interfaces of simulated environments and also interfaces as real robot hardware with their supplemental devices (sensors, cameras, etc.).

2019, International Journal of Computer Sciences and Engineering

Humans make use of facial expression to communicate in their day to day interactions with each other, which comes naturally without much effort. Facial expression is essentially a communication and interaction between humans and where other information like speech is not available; it becomes what one can depend on to transmit emotion or reactions of an individual. Hence, human expression recognition with high recognition is still an interesting task. This study is aimed at implementing face detection and expression recognition using fuzzy rule interpolation (FRI) technique. This follows through a development of specifications for fuzzy rule interpolation in emotion recognition using the viola jones algorithm as the detection algorithm and local binary pattern (LBP) algorithm for the feature extraction. The extended Cohn Kanade (CK+) face database was used for the experimentation of the system. The classification of the various expressions was achieved by the image category classifier of Matlab.

2010

Fuzzy Q-learning, the fuzzy extension of the Reinforcement Learning (RL) is a well known topic in computational intelligence. It can be used to tackle control problems in unknown continuous environments without defining an exact method on how to solve it explicitly. In the RL concept the problem needed to be solved is hidden in the feedback of the environment, called reward or punishment (positive or negative reward). From these rewards the system can learn which action is considered to be the best choice in a given state. One of the most frequently applied RL method is the "Q-learning". The goal of the Q-learning method is to find an optimal policy for the system by building the state-actionvalue function. The state-action-value-function is a function of the expected return (a function of the cumulative reinforcements), related to a given state and a taken action following the optimal policy. The original Q-learning method was introduced for discrete states and actions. With the application of fuzzy reasoning the method can be adapted for continuous environment, called Fuzzy Q-learning (FQ-Learning). Traditional Fuzzy Qlearning embeds the 0-order Takagi-Sugeno fuzzy inference and hence inherits the requirement of the state-action-value-function representation to be a complete fuzzy rule base. An extension of the traditional fuzzy Q-learning method with the capability of handling sparse fuzzy rule bases is already introduced by the authors, which suggests a Fuzzy Rule Interpolation (FRI) method, namely the FIVE (Fuzzy rule Interpolation based on Vague Environment) technique to be the reasoning method applied with Q-learning (FRIQ-learning). The main goal of this paper is the introduction of a method which can construct the requested FRI fuzzy model in a reduced size. The suggested reduction is achieved by incremental creation of an intentionally sparse fuzzy rule base.

Several Fuzzy Rule Interpolation (FRI) techniques have limitations from the direct application point of view, for example their applicability is limited to the one dimensional case, or they can be defined only based on the two closest surrounding rules of the actual observation. This is the reason why relatively few FRI methods can be found among the practical fuzzy rule based applications. With the application of FRI methods sparse rule bases can be used, which substantially simplify the construction of fuzzy rule bases, because FRI methods can provide reasonable (interpolated) conclusions even if none of the existing rules fires under the gathered observation. Compared to the classical fuzzy CRI (compositional rule of inference), by eliminating the derivable rules, the number of the fuzzy rules needed in the rule base could be dramatically reduced. This paper provides a brief overview of several FRI methods and in more details an application oriented simple and quick FRI method "FIVE" will be introduced. For the demonstration of the benefits of the interpolation-based fuzzy reasoning as systematic approach, a robot guidance application is presented, where the robot is able to cycle through defined waypoints while avoiding collision with obstacles and walls. All of the controlling parts were accomplished with fuzzy rule bases of the "FIVE" FRI method.