This paper introduces a new modeling technique of fuzziness in multivariate analysis based on subjective evaluation data. The subjective evaluation data includes diverse perceptions in the evaluators' assessment of the evaluation object. Average data of the evaluators is often used in order to send a generally accurate interpretation of the subjective data. Analyzing of the subjective evaluation data is often called the "Kansei" data analysis. In "Kansei" data analysis, the behavior of the evaluators is often focused on, because of exploring items or objects carrying weight. However, the obtained result by use of the average data does not provide such a character. The proposed modeling technique can provide the tendency of people's opinions and at the same time their diversity. This is achieved by extending the traditional multivariate statistical analysis, by use of the fuzzy-sets-theory
Finite resolution of spacetime at Planck scale gives it a fuzzy structure (the so-called foamy or fractal spacetime). This fuzzy structure of spacetime is a consequence of quantum fluctuation of geometry itself and can be described within non-commutative geometry and some alternative approaches to quantum gravity. In this paper, some consequences of spacetime fuzziness are studied. Due to this fuzzy structure, some basic notions of ordinary quantum mechanics such as position space representation, wave packet broadening during its propagation and coherent states of quantum mechanical systems should be re-examined.
Hyperspectral image classification with a limited number of training samples without loss of accuracy is desirable, as collecting such data is often expensive and time-consuming. However, classifiers trained with limited samples usually end up with a large generalization error. To overcome the said problem, we propose a fuzziness-based active learning framework (FALF), in which we implement the idea of selecting optimal training samples to enhance generalization performance for two different kinds of classifiers, discriminative and generative (e.g. SVM and KNN). The optimal samples are selected by first estimating the boundary of each class and then calculating the fuzziness-based distance between each sample and the estimated class boundaries. Those samples that are at smaller distances from the boundaries and have higher fuzziness are chosen as target candidates for the training set. Through detailed experimentation on three publically available datasets, we showed that when trained with the proposed sample selection framework, both classifiers achieved higher classification accuracy and lower processing time with the small amount of training data as opposed to the case where the training samples were selected randomly. Our experiments demonstrate the effectiveness of our proposed method, which equates favorably with the state-of-the-art methods.
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.
Fuzzy clustering methods identify naturally occurring clusters in a dataset, where the extent to which different clusters are overlapped can differ. Most methods have a parameter to fix the level of fuzziness. However, the appropriate level of fuzziness depends on the application at hand. This paper presents an entropy c-means (ECM), a method of fuzzy clustering that simultaneously optimizes two contradictory objective functions, resulting in the creation of fuzzy clusters with different levels of fuzziness. This allows ECM to identify clusters with different degrees of overlap. ECM optimizes the two objective functions using two multiobjective optimization methods, nondominated sorting genetic algorithm II (NSGA-II) and multiobjective evolutionary algorithm based on decomposition (MOEA/D). We also propose a method to select a suitable tradeoff clustering from the Pareto front. Experiments on challenging synthetic datasets as well as real-world datasets show that ECM leads to better cluster detection compared to the conventional fuzzy clustering methods as well as previously used multiobjective methods for fuzzy clustering.
Building a high quality classifier is one of the key problems in the field of machine learning (ML) and pattern recognition. Many ML algorithms have suffered from high computational power in the presence of large scale data sets. This paper proposes a fuzziness based instance selection technique for the large data sets to increase the efficiency of supervised learning algorithms by improving the shortcomings of designing an effective intrusion detection system (IDS). The proposed methodology is dependent on a new kind of single layer feed-forward neural network (SLFN), called random weight neural network (RWNN). At the first stage, a membership vector corresponding to every training instance is obtained by using RWNN for computing the fuzziness. Secondly, the training instances (along with their fuzziness values) according to the actual class labels are grouped separately. After this, the instances having low fuzziness values in each group are extracted, which are used to build a reduced data set. The instances outputted by the proposed method are used as an input for ML classifiers, which result in reducing the learning time and also increasing the learning capability. The proposed methodology exhibits that the reduced data set can easily learn the boundaries between class labels. The most obvious finding from this study is a considerable increase in the accuracy rate with unseen examples when compared with other instance selection method, i.e., IB2. The proposed method provides the better generalization and fast learning capability. The reasonability of the proposed methodology is theoretically explained and experiments on well known ID data sets support its usefulness.
We propose an extension to the metacommunity (MC) concept and a novel operational methodology that has the potential to refine the analysis of MC structure at different hierarchical levels. We show that assemblages of species can also be seen as assemblages of abstract subregional habitat-related metacommunities (habMCs). This intrinsically fuzzy concept recognizes the existence of habMCs that are typically associated with given habitats, while allowing for the mixing and superposition of different habMCs in all sites and for boundaries among subregions that are neither spatially sharp nor temporally constant. The combination of fuzzy clustering and direct gradient analysis permits us to 1) objectively identify the number of habMCs that are present in a region as well as their spatial distributions and relative weights at different sites; 2) associate different subregions with different biological communities; and 3) quantitatively assess the affinities between habMCs and physical, morphological, biogeochemical, and environmental properties, thereby enabling an analysis of the roles and relative importance of various environmental parameters in shaping the spatial structure of a metacommunity. This concept and methodology offer the possibility of integrating the continuum and community unit concepts and of developing the concept of a habMC ecological niche. This approach also facilitates the practical application of the MC concept, which are not currently in common use. Applying these methods to macrophytobenthic and macrozoobenthic hard-substrate assemblages in the Venetian Lagoon, we identified a hierarchical organization of macrobenthic communities that associated different habMCs with different habitats. Our results demonstrate that different reference terms should be applied to different subregions to assess the ecological status of a waterbody and show that a combination of several environmental parameters describes the spatial heterogeneity of benthic communities much better than any single property can. Our results also emphasize the importance of considering heterogeneity and fuzziness when working in natural systems.
The concept of Semantic Web has introduced an important form of knowledge representation - ontology. As a hierarchical structure of concepts together with their definitions ontology provides means for expressing semantics of data. The ability to build rules with ontology concepts and to perform reasoning increases its attractiveness even further. This paper proposes a framework for expressing fuzzy temporal information using ontology. The framework is built based on ontology suitable for expressing facts and building rules that include fuzzy and temporal terms. This proposed fuzzy temporal ontology can be imported to any domain ontology and used a knowledge base in variety of applications. The paper includes description of build-in predicates needed for constructing fuzzy temporal rules. Simple examples of application of the predicates are presented.