Dendritic cell algorithm (DCA) is an immune-inspired classification algorithm which is developed for the purpose of anomaly detection in computer networks. The DCA uses a weighted function in its context detection phase to process three categories of input signals including safe, danger and pathogenic associated molecular pattern to three output context values termed as co-stimulatory, mature and semi-mature, which are then used to perform classification. The weighted function used by the DCA requires either manually pre-defined weights usually provided by the immunologists, or empirically derived weights from the training dataset. Neither of these is sufficiently flexible to work with different datasets to produce optimum classification result. To address such limitation, this work proposes an approach for computing the three output context values of the DCA by employing the recently proposed TSK+ fuzzy inference system, such that the weights are always optimal for the provided data set regarding a specific application. The proposed approach was validated and evaluated by applying it to the two popular datasets KDD99 and UNSW NB15. The results from the experiments demonstrate that, the proposed approach outperforms the conventional DCA in terms of classification accuracy.

Type-2 fuzzy sets and systems can better handle uncertainties compared to its type-1 counterpart, and the widely applied Mamdani and TSK fuzzy inference approaches have been both extended to support interval type-2 fuzzy sets. Fuzzy interpolation enhances the conventional Mamdani and TKS fuzzy inference systems, which not only enables inferences when inputs are not covered by an incomplete or sparse rule base but also helps in system simplification for very complex problems. This paper extends the recently proposed fuzzy interpolation approach TSK+ to allow the utilization of interval type-2 TSK fuzzy rule bases. One illustrative case based on an example problem from the literature demonstrates the working of the proposed system, and the application on the cart centering problem reveals the power of the proposed system. The experimental investigation confirmed that the proposed approach is able to perform fuzzy inferences using either dense or sparse interval type-2 TSK rule bases with promising results generated.

The Quality of Services (QoS) is the measure of data transmission quality and service availability of a network, aiming to maintain the data, especially delay-sensitive data such as VoIP, to be transmitted over the network with the required quality. Major network device manufacturers have each developed their own smart dynamic QoS solutions, such as AutoQoS supported by Cisco, CoS (Class of Service) by Netgear devices, and QoS Maps on SROS (Secure Router Operating System) provided by HP, to maintain the service level of network traffic. Such smart QoS solutions usually only work for manufacture qualified devices and otherwise only a pre-defined static policy mapping can be applied. This paper presents a dynamic QoS solution based on the differentiated services (DiffServ) approach for enterprise networks, which is able to modify the priority level of a packet in real time by adjusting the value of Differentiated Services Code Point (DSCP) in Internet Protocol (IP) header of network packets. This is implemented by a 0-order TSK fuzzy model with a sparse rule base which is developed by considering the current network delay, application desired priority level and user current priority group. DSCP values are dynamically generated by the TSK fuzzy model and updated in real time. The proposed system has been evaluated in a real network environment with promising results generated.

Fuzzy modelling has been widely and successfully applied to control problems. Traditional fuzzy modelling requires 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.

Fuzzy rule interpolation enables fuzzy inference with sparse rule bases by interpolating inference results, and may help to reduce system complexity by removing similar (often redundant) neighbouring rules. In particular, the recently proposed closed form fuzzy interpolation offers a unique approach which guarantees convex interpolated results in a closed form. However, the difficulty in defining the required precise-valued membership functions still poses significant restrictions over the applicability of this approach. Such limitations can be alleviated by employing type-2 fuzzy sets as their membership functions are themselves fuzzy. This paper extends the closed form fuzzy rule interpolation using interval type-2 fuzzy sets. In this way, as illustrated in the experiments, closed form fuzzy interpolation is able to deal with uncertainty in data and knowledge with more flexibility.

There is a growing interest in applying computational intelligence in the predictive toxicology (PT) domain, where a large number of predictive models are becoming available. Evaluation of such models is therefore considered to be a crucial part of their development and potential use, especially for regulatory purposes. The current evaluation approaches mainly focus on statistical measures of model performance, and few of them have taken data quality into consideration. However, it has been well recognised that datasets and models should not be considered in isolation. This paper proposes a new confidence index for evaluating PT models. A fuzzy complex number (FCN) framework is expanded in an effort to represent and evaluate dataset and regression-based model quality in a two-dimensional manner, thereby ensuring the linguistic evaluation is transparent and explainable. The utility and applicability of this research is illustrated by an experiment which evaluates 17 regression-based PT models. The experimental results have been compared and analysed against existing methods, and show that the FCN-based approach provides a consistent and interpretable means of model assessment. The proposed indexing mechanism can be used, together with customised statistical measures, in assisting PT model selection. This approach also helps to capture the relationships between datasets and models, and contributes to the development of data and model governance in PT.

Automated modeling refers to automatic (re-)formulation of alternative system models that embody the simplification, abstraction, and approximation of knowledge and data for a given task. This technique is highly desirable for effective problem solving in many application domains. Over the past two decades, compositional modeling (CM) has established itself as a leading approach in automated modeling. CM is a framework to construct system models by composing generic and reusable model fragments (MFs) selected from a knowledge base. However, the existing work mainly concerns the knowledge and data that are represented by crisp and precise information. Little work has been carried out to explore its potential to deal with uncertain environments. This paper presents an innovative framework of fuzzy compositional modeling (FCM) to develop such work. The proposed approach is capable of representing and reasoning with a wide range of inexact information. An innovative notion of fuzzy complex numbers (FCNs) is developed in an effort to enable synthesis of consistent scenario descriptions from imprecise MFs. This paper also introduces the modulus of FCNs to constrain the resulting scenario descriptions. The usefulness of this study is illustrated by means of an example to construct possible scenario descriptions from given evidence, which is in support of crime investigation.

Dealing with various inexact pieces of information has become an intrinsically important issue in knowledge-based reasoning, because many problem domains involve imprecise, incomplete and uncertain information. Indeed, different approaches exist for reasoning with inexact knowledge and data. However, the common strategy they adopt is to integrate various types of inexact information into a global measure. This may destroy the underlying semantics associated with different information components. This paper presents an innovative notion of fuzzy complex numbers (FCNs), which extends real complex numbers to representing two-dimensional uncertainties conjunctively without necessarily integrating them. This new framework is applied to supporting compositional modelling (CM). In particular, calculus of FCNs over arithmetic and propositional relations is developed to entail scenario model synthesis from model fragments, and modulus of FCNs is introduced to constrain the scenario descriptions. The utility and usefulness of this work are illustrated by means of an example for constructing possible scenario descriptions from given evidence in the crime investigation domain.

Given a set of collected evidence and a knowledge base, fuzzy compositional modelling (FCM) begins by retrieving model fragments which are the most likely to be relevant to the available data. Since FCM often involves imprecise and uncertain information, a match between the available data and the knowledge base cannot in general be done precisely, partial matching may suffice. This paper proposes a more flexible fuzzy model fragment retrieval mechanism to match data items with broader, including possibly subjective information in the knowledge base. It is capable of retrieving those model fragments that can approximately match the collected evidence, when no exact match occurs. The retrieval process and its capability is illustrated by means of an application example.

Compositional modelling (CM) has been applied to synthesize automatically plausible scenarios in many problem domains with promising results. However, it is assumed that the generic and reusable model fragments within the knowledge base can all be expressed by precise and crisp information. This paper presents an initial attempt to extend the existing CM work to allow the generation of scenario spaces which are capable of representing, storing and supporting inference about imprecise or ill-defined data, by the use of fuzzy sets. A knowledge representation formalism for both fuzzy parameters and fuzzy constraints is incorporated into the representation of conventional model fragments. The applicability of the proposed method is illustrated by means of a simple worked example for supporting crime investigation.