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Towards sparse rule base generation for fuzzy rule interpolation

Towards sparse rule base generation for fuzzy rule interpolation

This paper presents an initial investigation of a novel data-driven rule base generation approach for FRI, which is able to directly generate a compact sparse rule base from data. In particular, the proposed approach first partitions the problem domain into a number of sub-regions based on the given training data set and fuzzy partitions the problem domain accordingly, such that each sub-region is represented by a corresponding fuzzy rule. Then, the profile curvature of each sub-region is calculated to represent the extent to which the sub-region deviates from being ‘flat’ or ‘straight’. Given a threshold, those sub-regions which have higher curvature values are then identified, and the corresponding rules will be selected to initialise the rule base. From this, the membership functions of the fuzzy sets involved in the initialised rule base are fine-tuned using a genetic algorithm (GA) optimisation method. The experiment shows that the proposed approach can directly generate a sparse rule base for FRI from a given data set, generating results that are comparable with those of [14].
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improving rule base quality with rule classification PCAI 2003

improving rule base quality with rule classification PCAI 2003

Classifications Using Structures Call-tree analysis of a rule-base can classify rules based on their level in this tree. A fact is a fact in fact-base. A bottom rule does not call any other rule and should therefore be as efficient as possible, since it is potentially used by many rules. A top rule is not called by any other rule. An intermediate rule is neither a top rule nor a bottom rule and its use should be minimized, since these rules are often the most unclear. An interface rule, which interfaces the rule- base with some external systems e.g., database, should be a bottom rule, if possible. A library rule is not specific to anything in the rule- base and is safely reused in other rule-based systems.
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Towards Sparse Rule Base Generation for Fuzzy Rule Interpolation

Towards Sparse Rule Base Generation for Fuzzy Rule Interpolation

This paper presents an initial investigation of a novel data-driven rule base generation approach for FRI, which is able to directly generate a compact sparse rule base from data. In particular, the proposed approach first partitions the problem domain into a number of sub-regions based on the given training data set and fuzzy partitions the problem domain accordingly, such that each sub-region is represented by a corresponding fuzzy rule. Then, the profile curvature of each sub-region is calculated to represent the extent to which the sub-region deviates from being ‘flat’ or ‘straight’. Given a threshold, those sub-regions which have higher curvature values are then identified, and the corresponding rules will be selected to initialise the rule base. From this, the membership functions of the fuzzy sets involved in the initialised rule base are fine-tuned using a genetic algorithm (GA) optimisation method. The experiment shows that the proposed approach can directly generate a sparse rule base for FRI from a given data set, generating results that are comparable with those of [14].
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Rule-base reduction in Fuzzy Rule Interpolation-based Q-learning

Rule-base reduction in Fuzzy Rule Interpolation-based Q-learning

considered being a cardinal rule, therefore it has to stay in the rule base (see Fig. 2.). Depending on the actual problem, difference in the cumulative rewards could be allowed to some degree, till the problem is still solved and produces the same or near the same rewards. Various thresholds can be used in defining „near the same‟ depending on the task and requirements. Close matches of the rewards should result in approximately the same steps as were the original incrementally constructed full rule base, when using the final reduced rule base. Accepting relatively greater (depending on the exact reward function), but still valid, differences between the rewards could result in a different step-by-step solution, but the overall task will still be solved.
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Curvature-Based Sparse Rule Base Generation for Fuzzy Rule Interpolation

Curvature-Based Sparse Rule Base Generation for Fuzzy Rule Interpolation

therefore, they are likely to cause performance deteri- oration along with the size reduction of the rule base. This paper presents a data-driven rule base gener- ation approach for FRI based on the initial work re- ported in [21], which directly generates sparse rule bases from data sets by effectively using curvature values traditionally utilised in geography. Different to the conventional fuzzy rule base generation ap- proaches, the proposed approach discriminates rules by calculating their curvature values. Note that cur- vature values are only workable in three-dimensional spaces (or a rule with two antecedents and one conse- quence) and thus cannot be directly used for higher- order problems. As a solution, for any given higher- order problem, the proposed approach firstly decom- poses the higher-order space into a number of three- dimensional spaces, and then approximates the im- portance of the higher-order spaces by aggregating the curvature values of the corresponding decomposed three-dimensional ones. From this, the most important rules are selected to form a raw rule base, which is then optimised using a general optimisation approach, such as the genetic algorithm. The proposed approach is val- idated and evaluated by two experiments; the results demonstrate that the proposed approach is promising.
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Automated rule base completion as Bayesian concept induction

Automated rule base completion as Bayesian concept induction

Considerable attention has recently been devoted to the prob- lem of automatically extending knowledge bases by applying some form of inductive reasoning. While the vast majority of existing work is centred around so-called knowledge graphs, in this paper we consider a setting where the input consists of a set of (existential) rules. To this end, we exploit a vec- tor space representation of the considered concepts, which is partly induced from the rule base itself and partly from a pre-trained word embedding. Inspired by recent approaches to concept induction, we then model rule templates in this vector space embedding using Gaussian distributions. Unlike many existing approaches, we learn rules by directly exploit- ing regularities in the given rule base, and do not require that a database with concept and relation instances is given. As a result, our method can be applied to a wide variety of on- tologies. We present experimental results that demonstrate the effectiveness of our method.
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Automated Rule Base Completion as Bayesian Concept Induction

Automated Rule Base Completion as Bayesian Concept Induction

Considerable attention has recently been devoted to the prob- lem of automatically extending knowledge bases by applying some form of inductive reasoning. While the vast majority of existing work is centred around so-called knowledge graphs, in this paper we consider a setting where the input consists of a set of (existential) rules. To this end, we exploit a vec- tor space representation of the considered concepts, which is partly induced from the rule base itself and partly from a pre-trained word embedding. Inspired by recent approaches to concept induction, we then model rule templates in this vector space embedding using Gaussian distributions. Unlike many existing approaches, we learn rules by directly exploit- ing regularities in the given rule base, and do not require that a database with concept and relation instances is given. As a result, our method can be applied to a wide variety of on- tologies. We present experimental results that demonstrate the effectiveness of our method.
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Adaptive Rule-Base Influence Function Mechanism for Cultural Algorithm

Adaptive Rule-Base Influence Function Mechanism for Cultural Algorithm

using the feedback gained from the search space. This update mechanism continues until the rule- based system learns the features of behavior of individuals in the search space and is parallel to the search mechanism. The simulation results show that convergence of the update of rule-base is faster than the search mechanism. In other words, this rule based finds its optimal values before the search process ends. As soon as the rule-based converges to its optimal state, the update process stops and the search mechanism uses the optimized rule-based to find the optimal solution. The update algorithm for the rule base is based on GA and is presented in details in section 3. The proposed cultural algorithm is evaluated on six unimodal and multimodal benchmark functions. The algorithm is compared with several other optimization algorithms such as previous version of CA, PSO and GA. The obtained results show that CA which benefits from a rule-based system outperforms these algorithms in terms of global optimality. In section 2 the components of CA are reviewed. Section 3 presents the optimization procedure of rule based system in details. In section 4 we experimentally compare the proposed algorithm with existing CA and various optimization algorithms using a set of benchmark functions. Discussions and further investigation on the proposed method are made in this section. Finally conclusion points are pointed out in section 5.
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Experience-based Rule Base Generation and Adaptation for Fuzzy Interpolation

Experience-based Rule Base Generation and Adaptation for Fuzzy Interpolation

Experience-based Rule Base Generation and Adaptation for Fuzzy Interpolation Jie Li, Hubert P. H. Shum, Xin Fu, Graham Sexton, Longzhi Yang Abstract —Fuzzy modelling has been widely and successfully applied to control problems. Traditional fuzzy modelling re- quires either complete experts’ knowledge or large data sets to generate rule bases such that the input spaces can be fully covered. Although fuzzy rule interpolation (FRI) relaxes this requirement by approximating rules using their neighbouring ones, it is still difficult for some real world applications to obtain sufficient experts’ knowledge and/or data to generate a reasonable sparse rule base to support FRI. Also, the generated rule bases are usually fixed and therefore cannot support dynamic situations. In order to address these limitations, this paper presents a novel rule base generation and adaptation system to allow the creation of rule bases with minimal a priori knowledge. This is implemented by adding accurate interpolated rules into the rule base guided by a performance index from the feedback mechanism, also considering the rule’s previous experience information as a weight factor in the process of rule selection for FRI. In particular, the selection of rules for interpolation in this work is based on a combined metric of the weight factors and the distances between the rules and a given observation, rather than being simply based on the distances. Two digitally simulated scenarios are employed to demonstrate the working of the proposed system, with promising results generated for both rule base generation and adaptation.
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RULE BASE IDS FOR APPLICATION LAYER USING FUZZY LOGIC

RULE BASE IDS FOR APPLICATION LAYER USING FUZZY LOGIC

visual.sangi@gmail.com Abstract: The objective of this paper is to develop a Fuzzy Rule-Base Based Intrusion Detection System on Application Layer which works in the application layer of the network stack. It consists of semantic IDS and Fuzzy based IDS. Rule based IDS looks for the specific pattern which is defined as malicious. A non-intrusive regular pattern can be malicious if it occurs several times with a short time interval. At application layer, HTTP traffic’s header and payload are analyzed for possible intrusion. In the proposed misuse detection module, the semantic intrusion detection system works on the basis of rules that define various application layer misuses that are found in the network. An attack identified by the IDS is based on a corresponding rule in the rule-base. An event that doesn’t make a ‘hit’ on the rule-base is given to a Fuzzy Intrusion Detection System (FIDS) for further analysis. In a Rule-based intrusion detection system, an attack can either be detected if a rule is found in the rule base or goes undetected if not found. If this is combined with FIDS, the intrusions went undetected by RIDS can further be detected. These non-intrusive patterns are checked by the fuzzy IDS for a possible attack. The non-intrusive patterns are normalized and converted as linguistic variable in fuzzy sets. These values are given to Fuzzy Cognitive Mapping (FCM). If there is any suspicious event, then it generates an alarm to the client/server. Results show better performance in terms of the detection rate and the time taken to detect. The detection rate is increased with reduction in false positive rate for a specific attack.
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A New Rule - Base Modification Scheme For The Time Delay Systems

A New Rule - Base Modification Scheme For The Time Delay Systems

[15] 3.5. The Rule-Base Shifting Scheme For the controller developed in Section 2, several shifting schemes are investigated for many time delay values and performance indexes. Some of the shifted versions of the rule-base of Table 2.1 are given in Table 3.1. The shifting amounts are equal and opposite in direction in lower and upper sides of Δe = Z (zero) row. For instance, in Table 3.1.b., all the rows are not shifted equally; that is, the neighbouring rows of Δe equals to ‘Zero’ are not shifted, and the others are shifted for one cell in appropriate directions. This shifting scheme is coded as 011(shifted number of cells from low values to high values of Δe) and the corresponding controller is abbreviated as FLC_011. Table 3.1 includes four shifting schemes for FLCs that will be compared throughout the paper.
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MODIFICATION OF FUZZY LOGIC RULE BASE IN THE OPTIMIZATION OF TRAFFIC LIGHT CONTROL SYSTEM

MODIFICATION OF FUZZY LOGIC RULE BASE IN THE OPTIMIZATION OF TRAFFIC LIGHT CONTROL SYSTEM

& Yarahmadi, 2014; Babangida, Peter & Luhutyit, 2017). In all these approaches the dynamic ATLS generally out performs the static ATLS. In the dynamic ATLS approach that improves on the static ATLS using the fuzzy inference system, the fuzzy rule base is of paramount importance in designing a fuzzy logic controller for the scheduling of traffic. When the size of the fuzzy rule base is very high, the problem of computational burden leads to performance issues. There should be a balance between the size of the rule base and the performance of the system. The most recent work reported in Babangida et al., (2017) presented a rule base size of 49 rules and the average percentage improvement of the dynamic ATLS (DPSTLS) over the static ATLS (SPSTLS) system was obtained as 65.35% waiting time.
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Designing of rule base for a TSK- fuzzy system using bacterial foraging optimization algorithm (BFOA)

Designing of rule base for a TSK- fuzzy system using bacterial foraging optimization algorithm (BFOA)

The rest of paper is organized as follows: in section 2 the BFOA is described. Section 3 is about modelling the problem. In section 4 BFOA based algorithm is used to construct the rule base of a fuzzy controller system and the results of achieved fuzzy system via BFOA based method (that is called BSO) are shown in comparison with some available heuristic methods and finally section5 is the conclusion of using this method in comparison with PSO algorithm.

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On-Line Construction and Rule Base Simplification by Replacement in Fuzzy Systems Applied to a Wastewater Treatment Plant

On-Line Construction and Rule Base Simplification by Replacement in Fuzzy Systems Applied to a Wastewater Treatment Plant

Fig. 9. Membership functions of the first input variable with rule-base simplification. 5. CONCLUSIONS The on-line learning (eTS) and the rule-base simplification techniques presented in this paper have a great potential for building computational intelligence systems for monitoring and controlling industrial plants. This work presented the application of these techniques to a wastewater plant of a pulp and paper mill allowing the construction of partially interpretable models with reasonable accuracy. The conditions for new rule creation need tuning and further work to develop formal methods for rule simplification in the general case is under investigation.
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An Extended Takagi-Sugeno-Kang Inference System (TSK+) with Fuzzy Interpolation and Its Rule Base Generation

An Extended Takagi-Sugeno-Kang Inference System (TSK+) with Fuzzy Interpolation and Its Rule Base Generation

3.2 Extended TSK inference Given a rule base as specified in Eq. 1 and an input vec- tor (A ∗ 1 , . . . , A ∗ m ), the TSK+ performs inferences using the same steps as those detailed in Sect. 2.1 except that Eq. 3 is replaced by Eq.7. According to the third property of the mod- ified similarity measure discussed above, S(A ∗ s , A sr ) > 0 unless A ∗ s and A sr take boundary crisp values 0 and 1. This means the firing strength of any rule R r is always greater than 0, i.e. α r > 0, except for the special case when only boundary crisp values are involved. As a result, every rule in the rule base contributes to the final inference result to a certain degree. Therefore, even if the given observation does not overlap with any rule antecedent in the rule base, certain inference result can still be generated, which significantly improves the applicability of the conventional TSK inference system.
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RULE-BASE DATA MINING SYSTEMS FOR

RULE-BASE DATA MINING SYSTEMS FOR

Fig 1 ERP-CRM Model 3.1 CRM Model CRM Model is responsible for receiving and sending requests and responses to the customer directly. These requests include queries, complaints, suggestions and orders are forwarded to the Enterprise Resource Planning (ERP) through the query generator. After taking corrective action automatic response generated will be forwarded through the CRM Model. These transactions will be saved in the database for knowledge rule-base conception.

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Curvature-based sparse rule base generation for fuzzy rule

interpolation

Curvature-based sparse rule base generation for fuzzy rule interpolation

There are two breakthroughs or improvements during this piece of PhD work. One breakthrough is to apply curvature values into fuzzy rule base generation and to extend the three-dimensional curvature idea into high-dimensional problems. However, given that traditional curvature values only work with three-dimensional data, the most challenging part is to develop an approach to calculate the artificial ‘curvature’ values in a high-dimensional space. In this work, by regarding a higher-dimensional complex problem as a collection of three dimensional problems with basic case solution, any high-dimensional problems can thus be addressed by applying the proposed basic case solutions multiple times. The second breakthrough is the design of an efficient framework to innovatively apply curvature based sparse rule base generation method into real-world problems, including real-world image classification problem. The key idea is inspired by an intuitive fact that to describe an unseen instance the most straightforward way is to relate it to previously seen classes. Therefore, an efficient framework was proposed and it can recognise unseen classes with light-weight simile annotations, as explained as in Fig. 4.6. Semantic concepts are complex and structured whereas the label space for most of current supervised learning consists of discrete and disjoint one-hot category vectors. Therefore, in traditional machine-learning methods the associations between classes are imposed to be neglected and the labelling work is always inefficient. Compared to attributes or texts, similes are more visual-related and do not involve extra concepts, thus lead to less information loss. Assigning only two similes for each seen class and using curvature values to select important rules, the proposed method makes the image representation more interpretable and discriminative, with results significantly boost the ZSL performance.
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Fuzzy modelling using a simplified rule base

Fuzzy modelling using a simplified rule base

The conventional conjunctive form of if-then rule assumes that both input variables-(in this case, the quality of service andjbod) must be present in order to contribu[r]

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RULE BASE DATA MINING SYSTEMS FOR CUSTOMER QUERIES

RULE BASE DATA MINING SYSTEMS FOR CUSTOMER QUERIES

Fig 1 ERP-CRM Model 3.1 CRM Model CRM Model is responsible for receiving and sending requests and responses to the customer directly. These requests include queries, complaints, suggestions and orders are forwarded to the Enterprise Resource Planning (ERP) through the query generator. After taking corrective action automatic response generated will be forwarded through the CRM Model. These transactions will be saved in the database for knowledge rule-base conception.

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Dynamic-link rule base in fuzzy inference system

Dynamic-link rule base in fuzzy inference system

A dynamic-link rule base (DLRB) was introduced into the conventional fuzzy inference system for the purpose of dynamically skipping the unfired rules and linking the f[r]

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