The possibility theory as a mathematical model of randomness and fuzziness phenomena is considered in a variant that enables the modeling of both probabilistic randomness, including that inherent in unpredictably evolving stochastic objects whose probabilistic models cannot be empirically reconstructed and nonprobabilistic randomness (fuzziness) inherent in real physical, technical, and economical objects, human-machine and expert systems, etc. Some principal distinctions between the considered variant and the known possibility theory variants, in particular, in mathematical formalism and its relationship with probability theory, substantive interpretation, and applications exemplified by solving the problems of identification and estimation optimization, empirical reconstruction of a fuzzy model for a studied object, measurement data analysis and interpretation, etc. (in the paper "Mathematical Modeling of Randomness and Fuzziness Phenomena in Scientific Studies. II. Applications") are shown.
The qualities of new data used in the sequential learning phase of the online sequential extreme learning machine algorithm (OS-ELM) have a significant impact on the performance of OS-ELM. This paper proposes a novel data filter mechanism for OS-ELM from the perspective of fuzziness and a fuzziness-based online sequential extreme learning machine algorithm (FOS-ELM). In FOS-ELM, when new data arrive, a fuzzy classifier first picks out the meaningful data according to the fuzziness of each sample. Specifically, the new samples with high-output fuzziness are selected and then used in sequential learning. The experimental results on eight binary classification problems and three multiclass classification problems have shown that FOS-ELM updated by the new samples with high-output fuzziness has better generalization performance than OS-ELM. Since the unimportant data are discarded before sequential learning, FOS-ELM can save more memory and have higher computational efficiency. In addition, FOS-ELM can handle data one-by-one or chunk-by-chunk with fixed or varying sizes. The relationship between the fuzziness of new samples and the model performance is also studied in this paper, which is expected to provide some useful guidelines for improving the generalization ability of online sequential learning algorithms.
This paper investigates the stress-strength reliability in the presence of fuzziness. The fuzzy membership function is defined as a function of the difference between stress and strength values, and the fuzzy reliability of single unit and multicomponent systems are calculated. The inclusion of fuzziness in the stress-strength interference enables the user to make more sensitive analysis. Illustrations are presented for various stress and strength distributions, (C) 2015 Elsevier B.V. All rights reserved.
We investigate a connection between recent results in three-dimensional (3D) quantum gravity, providing an effective noncommutative-spacetime description, and some earlier heuristic descriptions of a quantum-gravity contribution to the fuzziness of the worldlines of particles. We show that 3D-gravity-inspired spacetime noncommutativity reflects some of the features suggested by previous heuristic arguments. Most notably, gravity-induced worldline fuzziness, while irrelevantly small on terrestrial scales, could be observably large for propagation of particles over cosmological distances.
Nitrate is the primary form of nitrogen in natural waters and it can easily pass through soil to groundwater. Some levels of nitrate concentration in groundwater can cause some health problems such as methemoglobinemia in infants and several cancers. Since geological structures are not homogeneous, investigation of spatial variability of nitrate concentrations in groundwater is characterized by particularly high uncertainties. In this paper, a novel methodology for measure of uncertainty in groundwater nitrate variability is presented. To appraise the fuzziness, which is a type of uncertainty in spatial models, point cumulative semimadogram (PCSM) measure and a metric distance were employed. Measures of fuzziness have been carried out for each location using the experimental and model PCSMs. Finally an uncertainty map, which defines the regional variation of the uncertainty in different categories, has been composed.
In this paper, we propose a method to construct a polygonal rough-fuzzy set from a set of polygonal fuzzy sets representing the aggregation of multiple experts' opinions and propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the ratio of fuzziness of the constructed polygonal rough-fuzzy sets, where the values of the antecedent variables and the consequence variable appearing in the fuzzy rules are represented by the constructed polygonal rough-fuzzy sets. The proposed fuzzy interpolative reasoning method can overcome the drawbacks of the existing method due to the fact that it can deal with fuzzy interpolative reasoning using polygonal rough-fuzzy sets and it gets more reasonable fuzzy interpolative reasoning results than the existing method. (C) 2014 Elsevier Inc. All rights reserved.
This paper studies the pricing and retail service decisions of a product in a supply chain with one manufacturer and two retailers. It is assumed that the supply chain is operated in fuzzy uncertainty environments. The fuzziness is associated with the customer demands, manufacturing costs and service cost coefficients. Three different game structures are considered, i.e., Manufacturer-leader Stackelberg, Retailer-leader Stackelberg, and Vertical Nash. Expected value models are developed to determine the optimal pricing and retail service strategies. The corresponding analytical equilibrium solutions are obtained by solving the models. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results, and to gain various marketing strategies employed under different situations. (C) 2014 Elsevier Inc. All rights reserved.
This paper considers some elements of the optimal fuzzy decision theory that are similar to the optimal statistical decision theory, in particular, the theory of optimal fuzzy identification and optimal fuzzy hypothesis testing, such as Neyman-Pearson statistical hypothesis testing and optimal fuzzy estimation along with a sequential fuzzy identification algorithm similar to the Wald sequential statistical criterion. Some elements of the fuzzy measuring and computing transducer theory and its applications in the problems of the analysis and interpretation of measurement experiment data are given.
Countering cyber threats, especially attack detection, is a challenging area of research in the field of information assurance. Intruders use polymorphic mechanisms to masquerade the attack payload and evade the detection techniques Many supervised and unsupervised learning approaches from the field of machine learning and pattern recognition have been used to increase the efficacy of intrusion detection systems (IDSs). Supervised learning approaches use only labeled samples to train a classifier, but obtaining sufficient labeled samples is cumbersome, and requires the efforts of domain experts. However, unlabeled samples can easily be obtained in many real world problems. Compared to supervised learning approaches, semi-supervised learning (SSL) addresses this issue by considering large amount of unlabeled samples together with the labeled samples to build a better classifier. This paper proposes a novel fuzziness based semi-supervised learning approach by utilizing unlabeled samples assisted with supervised learning algorithm to improve the classifier's performance for the IDSs. A single hidden layer feed-forward neural network (SLFN) is trained to output a fuzzy membership vector, and the sample categorization (low, mid, and high fuzziness categories) on unlabeled samples is performed using the fuzzy quantity. The classifier is retrained after incorporating each category separately into the original training set. The experimental results using this technique of intrusion detection on the NSL-KDD dataset show that unlabeled samples belonging to low and high fuzziness groups make major contributions to improve the classifier's performance compared to existing classifiers e.g., naive bayes, support vector machine, random forests, etc. (C) 2016 Elsevier Inc. All rights reserved.