Review of Some Promising Fractional Physical Models

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of non-integer order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.Comment: 38 pages, LaTe

Trust Based Consensus Model for Social Network in an Incomplete Linguistic Information Context

A theoretical framework to consensus building within a networked social group is put forward. This article investigates a trust based estimation and aggregation methods as part of a visual consensus model for multiple criteria group decision making with incomplete linguistic information. A novel trust propagation method is proposed to derive trust relationship from an incomplete connected trust network and the trust score induced order weighted averaging operator is presented to aggregate the orthopairs of trust/distrust values obtained from different trust paths. Then, the concept of relative trust score is defined, whose use is twofold: (1) to estimate the unknown preference values and (2) as a reliable source to determine experts' weights. A visual feedback process is developed to provide experts with graphical representations of their consensus status within the group as well as to identify the alternatives and preference values that should be reconsidered for changing in the subsequent consensus round. The feedback process also includes a recommendation mechanism to provide advice to those experts that are identified as contributing less to consensus on how to change their identified preference values. It is proved that the implementation of the visual feedback mechanism guarantees the convergence of the consensus reaching process

Failure Diagnosis and Prognosis of Safety Critical Systems: Applications in Aerospace Industries

Many safety-critical systems such as aircraft, space crafts, and large power plants are required to operate in a reliable and efficient working condition without any performance degradation. As a result, fault diagnosis and prognosis (FDP) is a research topic of great interest in these systems. FDP systems attempt to use historical and current data of a system, which are collected from various measurements to detect faults, diagnose the types of possible failures, predict and manage failures in advance. This thesis deals with FDP of safety-critical systems. For this purpose, two critical systems including a multifunctional spoiler (MFS) and hydro-control value system are considered, and some challenging issues from the FDP are investigated. This research work consists of three general directions, i.e., monitoring, failure diagnosis, and prognosis. The proposed FDP methods are based on data-driven and model-based approaches. The main aim of the data-driven methods is to utilize measurement data from the system and forecast the remaining useful life (RUL) of the faulty components accurately and efficiently. In this regard, two dierent methods are developed. A modular FDP method based on a divide and conquer strategy is presented for the MFS system. The modular structure contains three components:1) fault diagnosis unit, 2) failure parameter estimation unit and 3) RUL unit. The fault diagnosis unit identifies types of faults based on an integration of neural network (NN) method and discrete wavelet transform (DWT) technique. Failure parameter estimation unit observes the failure parameter via a distributed neural network. Afterward, the RUL of the system is predicted by an adaptive Bayesian method. In another work, an innovative data-driven FDP method is developed for hydro-control valve systems. The idea is to use redundancy in multi-sensor data information and enhance the performance of the FDP system. Therefore, a combination of a feature selection method and support vector machine (SVM) method is applied to select proper sensors for monitoring of the hydro-valve system and isolate types of fault. Then, adaptive neuro-fuzzy inference systems (ANFIS) method is used to estimate the failure path. Similarly, an online Bayesian algorithm is implemented for forecasting RUL. Model-based methods employ high-delity physics-based model of a system for prognosis task. In this thesis, a novel model-based approach based on an integrated extended Kalman lter (EKF) and Bayesian method is introduced for the MFS system. To monitor the MFS system, a residual estimation method using EKF is performed to capture the progress of the failure. Later, a transformation is utilized to obtain a new measure to estimate the degradation path (DP). Moreover, the recursive Bayesian algorithm is invoked to predict the RUL. Finally, relative accuracy (RA) measure is utilized to assess the performance of the proposed methods

Trust networks for recommender systems

Recommender systems use information about their user’s profiles and relationships to suggest items that might be of interest to them. Recommenders that incorporate a social trust network among their users have the potential to make more personalized recommendations compared to traditional systems, provided they succeed in utilizing the additional (dis)trust information to their advantage. Such trust-enhanced recommenders consist of two main components: recommendation technologies and trust metrics (techniques which aim to estimate the trust between two unknown users.) We introduce a new bilattice-based model that considers trust and distrust as two different but dependent components, and study the accompanying trust metrics. Two of their key building blocks are trust propagation and aggregation. If user a wants to form an opinion about an unknown user x, a can contact one of his acquaintances, who can contact another one, etc., until a user is reached who is connected with x (propagation). Since a will often contact several persons, one also needs a mechanism to combine the trust scores that result from several propagation paths (aggregation). We introduce new fuzzy logic propagation operators and focus on the potential of OWA strategies and the effect of knowledge defects. Our experiments demonstrate that propagators that actively incorporate distrust are more accurate than standard approaches, and that new aggregators result in better predictions than purely bilattice-based operators. In the second part of the dissertation, we focus on the application of trust networks in recommender systems. After the introduction of a new detection measure for controversial items, we show that trust-based approaches are more effective than baselines. We also propose a new algorithm that achieves an immediate high coverage while the accuracy remains adequate. Furthermore, we also provide the first experimental study on the potential of distrust in a memory-based collaborative filtering recommendation process. Finally, we also study the user cold start problem; we propose to identify key figures in the network, and to suggest them as possible connection points for newcomers. Our experiments show that it is much more beneficial for a new user to connect to an identified key figure instead of making random connections

Blind restoration of images with penalty-based decision making : a consensus approach

In this thesis we show a relationship between fuzzy decision making and image processing . Various applications for image noise reduction with consensus methodology are introduced. A new approach is introduced to deal with non-stationary Gaussian noise and spatial non-stationary noise in MRI

Uninorm trust propagation and aggregation methods for group decision making in social network with four tuples information

The file attached to this record is the authors accepted version. The publisher's final version of record can be found by following the DOI link below.A novel social network based group decision making (SN-GDM) model with experts' weights not provided beforehand and with the following four tuple information: trust; distrust; hesitancy; and inconsistency, is introduced. The concepts of trust score (TS) and knowledge degree (KD) are de ned and combined into a trust order space. Then, a strict trust ranking order relation of trust function values (TFs) is built in which TS and KD play a similar role to the mean and the variance in Statistics. After the operational laws of TFs for uninorm operators are built, the uninorm propagation operator is investigated. It can propagate through a network both trust and distrust information simultaneously and therefore it prevents the loss of trust information in the propagating process. When an indirect trust relationship is built, the uninorm trust weighted average (UTWA) operator and the uninorm trust ordered weighted average (UTOWA) operator are de ned and used to aggregate individual trust relationship and to obtain their associated ranking order relation. Hence, the most trusted expert is distinguished from the group, and the weights of experts are determined in a reasonable way: the higher an expert is trusted the more importance value is assigned to the expert. Therefore, the novelty of the proposed SN-GDM is that it can use indirect trust relationship via trusted third partners (TTPs) as a reliable resource to determine experts' weights. Finally, the individual trust decision making matrices are aggregated into a collective one and the alternative with the highest trust order relation is selected as the best one

Fuzzy Operator Trees for Modeling Utility Functions

In this thesis, we propose a method for modeling utility (rating) functions based on a novel concept called textbf{Fuzzy Operator Tree} (FOT for short). As the notion suggests, this method makes use of techniques from fuzzy set theory and implements a fuzzy rating function, that is, a utility function that maps to the unit interval, where $0$ corresponds to the lowest and $1$ to the highest evaluation. Even though the original motivation comes from quality control, FOTs are completely general and widely applicable. Our approach allows a human expert to specify a model in the form of an FOT in a quite convenient and intuitive way. To this end, he simply has to split evaluation criteria into sub-criteria in a recursive manner, and to determine in which way these sub-criteria ought to be combined: conjunctively, disjunctively, or by means of an averaging operator. The result of this process is the qualitative structure of the model. A second step, then, it is to parameterize the model. To support or even free the expert form this step, we develop a method for calibrating the model on the basis of exemplary ratings, that is, in a purely data-driven way. This method, which makes use of optimization techniques from the field of evolutionary algorithms, constitutes the second major contribution of the thesis. The third contribution of the thesis is a method for evaluating an FOT in a cost-efficient way. Roughly speaking, an FOT can be seen as an aggregation function that combines the evaluations of a number of basic criteria into an overall rating of an object. Essentially, the cost of computing this rating is hence given by sum of the evaluation costs of the basic criteria. In practice, however, the precise utility degree is often not needed. Instead, it is enough to know whether it lies above or below an important threshold value. In such cases, the evaluation process, understood as a sequential evaluation of basic criteria, can be stopped as soon as this question can be answered in a unique way. Of course, the (expected) number of basic criteria and, therefore, the (expected) evaluation cost will then strongly depend on the order of the evaluations, and this is what is optimized by the methods that we have developed

Machine Learning Methods for Fuzzy Pattern Tree Induction

This thesis elaborates on a novel approach to fuzzy machine learning, that is, the combination of machine learning methods with mathematical tools for modeling and information processing based on fuzzy logic. More specifically, the thesis is devoted to so-called fuzzy pattern trees, a model class that has recently been introduced for representing dependencies between input and output variables in supervised learning tasks, such as classification and regression. Due to its hierarchical, modular structure and the use of different types of (nonlinear) aggregation operators, a fuzzy pattern tree has the ability to represent such dependencies in a very exible and compact way, thereby offering a reasonable balance between accuracy and model transparency. The focus of the thesis is on novel algorithms for pattern tree induction, i.e., for learning fuzzy pattern trees from observed data. In total, three new algorithms are introduced and compared to an existing method for the data-driven construction of pattern trees. While the first two algorithms are mainly geared toward an improvement of predictive accuracy, the last one focuses on eficiency aspects and seeks to make the learning process faster. The description and discussion of each algorithm is complemented with theoretical analyses and empirical studies in order to show the effectiveness of the proposed solutions