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.
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.
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.
5] has shown that the intersection of any two fuzzy subgroups is also a fuzzy subgroup and we now show that the intersection of any two anti fuzzy subgroups is also an anti fuzzy subgroup. More over, we state and prove the anti fuzzy version the work of 6] in characterizing union of fuzzy subgroups. Besides, 2] and 7] have worked on the set of all fuzzy symmetric subgroup of the symmetric group F (S_n).
Uncertainty measure can supply a new viewpoint for analyzing knowledge conveyed by an Atanassov's intuitionistic fuzzy set (AIFS). So uncertainty measurement is a key topic in AIFS theory, analogous to the role of entropy in probability theory. After reviewing the existing measures of uncertainty (entropy) for AIFSs, we argue that the existing measures of uncertainty cannot capture all facets of uncertainty associated with an AIFS. Then we point out and justify that there are at least three kinds of uncertainty for an AIFS, namely non-specificity, fuzziness, and intuitionism. We provide formal measures of non-specificity, fuzziness, and intuitionism, together with their properties and proofs. Properties of the proposed non-specificity measure are especially investigated. Finally, a general uncertainty measure consisting of these three uncertainties is presented. Illustrative examples show that the proposed uncertainty measure is consistent with intuitive cognize, and it is more sensitive to changes of AIFSs. Moreover, the proposed uncertainty measure can also discriminate uncertainty hiding in classical sets. Thus, it provides an alternative way to construct unified uncertainty measures.
Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to represent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations represented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.
In this paper, we consider a pricing and remanufacturing decision problem in a fuzzy closed-loop supply chain with one manufacturer, two competitive retailers and one third-party collector. The fuzziness is associated with collecting costs, remanufacturing costs, and customer demands. Two game models are proposed to formulate the pricing and remanufacturing decision problem under different power structures. The channel members' optimal decisions in fuzzy environment are derived from these models. Numerical experiments are also given to explore the impacts of the power structure and fuzziness on the performance of the chain. It is found that the manufacturer has more advantages in pursuing higher expected profit when it performs as a Stackelberg leader. The existence of dominance in the closed-loop supply chain may lead to poor performance of the total system: higher sales prices, lower collecting rate, and lower expected profit of the whole supply chain. The results also show that the fuzziness of costs may have positive influence on the recycling level.
In many cases, fuzziness and randomness simultaneously appear in a system. Hybrid variable is a tool to describe this phenomena. Fuzzy random variable and random fuzzy variable are instances of hybrid variable. In order to measure hybrid event, a concept of chance measure is proposed in this paper. Furthermore, several useful properties about this measure are proved such as self-duality, subadditivity and semicontinuity. Some concepts are also presented such as chance distribution, expected value, variance, moments, critical values, entropy, distance and sequence convergences.