In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many aggregation and defuzzification operators produce results independent to the decision makers strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take into account the level weights and the decision makers optimism strategy. This gives flexibility to the WABL operator and, through machine learning, can be trained in the direction of the decision makers strategy, producing more satisfactory results for the decision maker. However, in order to determine the WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers have been studied. Computational examples explaining the theoretical results have been performed.

Simulation workflow is a top-level model for the design and control of simulation process. It connects multiple simulation components with time and interaction restrictions to form a complete simulation system. Before the construction and evaluation of the component models, the validation of upper-layer simulation workflow is of the most importance in a simulation system. However, the methods especially for validating simulation workflow is very limit. Many of the existing validation techniques are domain-dependent with cumbersome questionnaire design and expert scoring. Therefore, this paper present an empirical learning-based validation procedure to implement a semi-automated evaluation for simulation workflow. First, representative features of general simulation workflow and their relations with validation indices are proposed. The calculation process of workflow credibility based on Analytic Hierarchy Process (AHP) is then introduced. In order to make full use of the historical data and implement more efficient validation, four learning algorithms, including back propagation neural network (BPNN), extreme learning machine (ELM), evolving new-neuron (eNFN) and fast incremental gaussian mixture model (FIGMN), are introduced for constructing the empirical relation between the workflow credibility and its features. A case study on a landing-process simulation workflow is established to test the feasibility of the proposed procedure. The experimental results also provide some useful overview of the state-of-the-art learning algorithms on the credibility evaluation of simulation models.

Owing to the expeditious growth in the information and communication technologies, smart cities have raised the expectations in terms of efficient functioning and management. One key aspect of residents' daily comfort is assured through affording reliable traffic management and route planning. Comprehensively, the majority of the present trip planning applications and service providers are enabling their trip planning recommendations relying on shortest paths and/or fastest routes. However, such suggestions may discount drivers' preferences with respect to safe and less disturbing trips. Road anomalies such as cracks, potholes, and manholes induce risky driving scenarios and can lead to vehicles damages and costly repairs. Accordingly, in this paper, we propose a crowdsensing based dynamic route planning system. Leveraging both the vehicle motion sensors and the inertial sensors within the smart devices, road surface types and anomalies have been detected and categorized. In addition, the monitored events are geo-referenced utilizing GPS receivers on both vehicles and smart devices. Consequently, road segments assessments are conducted using fuzzy system models based on aspects such as the number of anomalies and their severity levels in each road segment. Afterward, another fuzzy model is adopted to recommend the best trip routes based on the road segments quality in each potential route. Extensive road experiments are held to build and show the potential of the proposed system.

The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers' choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the RIM quantifier. Motivated by the idea of normal distribution-based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.

Firstly in this paper we propose a new criterion function for evaluation of the reductive property about the fuzzy reasoning result for fuzzy modus ponens and fuzzy modus tollens. Secondly unlike fuzzy reasoning methods based on the similarity measure, we propose a new fuzzy reasoning method based on distance measure. Thirdly the reductive property for 5 fuzzy reasoning methods are checked with respect to fuzzy modus ponens and fuzzy modus tollens. Through the experiment, we show that proposed method is better than the previous methods in accordance with human thinking.

The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they generally suffer from this problem of lacking prior knowledge to pre-define the exact failure thresholds for a machinery operating in a dynamic environment with a high level of uncertainty. In this case, dynamic thresholds depicted by the discrete states is a very attractive way to estimate the RUL of a dynamic machinery. Currently, there are only very few works considering the dynamic thresholds, and these studies adopted different algorithms to determine the discrete states and predict the continuous states separately, which largely increases the complexity of the learning process. In this paper, we propose a novel prognostics approach for RUL estimation of aero-engines with self-joint prediction of continuous and discrete states, wherein the prediction of continuous and discrete states are conducted simultaneously and dynamically within one learning framework.

Existing fuzzy neural networks (FNNs) are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep fuzzy neural network, namely deep evolving fuzzy neural networks (DEVFNN). Fuzzy rules can be automatically extracted from data streams or removed if they play little role during their lifespan. The structure of the network can be deepened on demand by stacking additional layers using a drift detection method which not only detects the covariate drift, variations of input space, but also accurately identifies the real drift, dynamic changes of both feature space and target space. DEVFNN is developed under the stacked generalization principle via the feature augmentation concept where a recently developed algorithm, namely Generic Classifier (gClass), drives the hidden layer. It is equipped by an automatic feature selection method which controls activation and deactivation of input attributes to induce varying subsets of input features. A deep network simplification procedure is put forward using the concept of hidden layer merging to prevent uncontrollable growth of input space dimension due to the nature of feature augmentation approach in building a deep network structure. DEVFNN works in the sample-wise fashion and is compatible for data stream applications. The efficacy of DEVFNN has been thoroughly evaluated using six datasets with non-stationary properties under the prequential test-then-train protocol. It has been compared with four state-of the art data stream methods and its shallow counterpart where DEVFNN demonstrates improvement of classification accuracy.

In this book we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics), plithogenic probability (as generalization of classical, imprecise, and neutrosophic probabilities), and plithogenic statistics (as generalization of classical, and neutrosophic statistics). Plithogenic Set is a set whose elements are characterized by one or more attributes, and each attribute may have many values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, logic, probability and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion, equality are influenced by the attribute values contradiction (dissimilarity) degrees. Formal definitions of plithogenic set, logic, probability, statistics are presented into the book, followed by plithogenic aggregation operators, various theorems related to them, and afterwards examples and applications of these new concepts in our everyday life.

Extracting characteristics from the training datasets of classification problems has proven effective in a number of meta-analyses. Among them, measures of classification complexity can estimate the difficulty in separating the data points into their expected classes. Descriptors of the spatial distribution of the data and estimates of the shape and size of the decision boundary are among the existent measures for this characterization. This information can support the formulation of new data-driven pre-processing and pattern recognition techniques, which can in turn be focused on challenging characteristics of the problems. This paper surveys and analyzes measures which can be extracted from the training datasets in order to characterize the complexity of the respective classification problems. Their use in recent literature is also reviewed and discussed, allowing to prospect opportunities for future work in the area. Finally, descriptions are given on an R package named Extended Complexity Library (ECoL) that implements a set of complexity measures and is made publicly available.

The concept of stochastic configuration networks (SCNs) others a solid framework for fast implementation of feedforward neural networks through randomized learning. Unlike conventional randomized approaches, SCNs provide an avenue to select appropriate scope of random parameters to ensure the universal approximation property. In this paper, a deep version of stochastic configuration networks, namely deep stacked stochastic configuration network (DSSCN), is proposed for modeling non-stationary data streams. As an extension of evolving stochastic connfiguration networks (eSCNs), this work contributes a way to grow and shrink the structure of deep stochastic configuration networks autonomously from data streams. The performance of DSSCN is evaluated by six benchmark datasets. Simulation results, compared with prominent data stream algorithms, show that the proposed method is capable of achieving comparable accuracy and evolving compact and parsimonious deep stacked network architecture.