Complex fuzzy sets

The objective of this paper is to investigate the innovative concept of complex fuzzy sets. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thus, the complex fuzzy set provides a mathematical framework for describing membership in a set in terms of a complex number. The inherent difficulty in acquiring intuition for the concept of complex-valued membership presents a significant obstacle to the realization of its full potential. Consequently, a major part of this work is dedicated to a discussion of the intuitive interpretation of complex-valued grades of membership. Examples of possible applications, which demonstrate the new concept, include a complex fuzzy representation of solar activity (via measurements of the sunspot number), and a signal processing application. A comprehensive study of the mathematical properties of the complex fuzzy set is presented. Basic set theoretic operations on complex fuzzy sets, such as complex fuzzy complement, union, and intersection, are discussed at length. Two novel operations, namely set rotation and set reflection, are introduced. Complex fuzzy relations are also considered. Index Terms-Complex fuzzy intersection, complex fuzzy relations, complex fuzzy sets, complex fuzzy union, complex-valued grades of membership, fuzzy complex numbers     

Elastic distances for time-series classification: Itakura versus Sakoe-Chiba constraints

Knowledge and Information Systems - In the field of time series data mining, the accuracy of the simple, but very successful nearest neighbor (NN) classifier directly depends on the chosen...     

An algorithm for robust image watermarking based on the DCT and Zernike moments

An image watermarking scheme in the 2D DCT domain is proposed by exploring the advantages of using Zernike moments. Zernike transform has been used in image processing applications such as image recognition, authentication, protection, etc. Here, we propose to use the Zernike moments of the DCT transform to provide an efficient watermarking method. Particularly, the novelty of the proposed approach relies on the method for selection of features that will enable both preserving the image quality and robustness to attacks. Also, a criterion for selection of image blocks suitable for watermarking is given. It is based on the ? ₁-norm of Zernike moments. The efficiency of the proposed watermarking algorithm is proved on several examples considering different types of attacks (compression, noise, filtering, geometrical attacks).     

An assessment of in vivo failures of alumina ceramic total hip joint replacements

Several cases of alumina ceramic hip replacement failures are reviewed fractographically. Three main findings are illustrated. Firstly, there is evidence that surgeons can damage the femoral head bore surface during surgery. Secondly, three of the failures described are of extended neck designs which are weaker than those of normal or short length in axial laboratory testing. Under physiological loading, such geometry can lead to levering forces, inappropriate localized contact with the metallic stem and stress concentrations. Delayed failure can ensue, with a fracture pattern quite different from that seen in conventional uniaxial testing. Thirdly, while some failures show head bore surfaces which are clean apart from metallic witness marking, others show brown stains and white deposits suggesting poor conformal contact. We suspect either stems become damaged during surgery before mounting the head or entrapment of debris, pointing to handling care and cleanliness varying between hospitals.     

Detecting anomalous patterns in time-series data using sparse hierarchically parameterized transition matrices

Anomaly detection in time-series data is a relevant problem in many fields such as stochastic data analysis, quality assurance, and predictive modeling. Markov models are an effective tool for time-series data analysis. Previous approaches utilizing Markov models incorporate transition matrices (TMs) at varying dimensionalities and resolutions. Other analysis methods treat TMs as vectors for comparison using search algorithms such as the nearest neighbors comparison algorithm, or use TMs to calculate the probability of discrete subsets of time-series data. We propose an analysis method that treats the elements of a TM as random variables, parameterizing them hierarchically. This approach creates a metric for determining the “normalcy” of a TM generated from a subset of time-series data. The advantages of this novel approach are discussed in terms of computational efficiency, accuracy of anomaly detection, and robustness when analyzing sparse data. Unlike previous approaches, this algorithm is developed with the expectation of sparse TMs. Accounting for this sparseness significantly improves the detection accuracy of the proposed method. Detection rates in a variety of time-series data types range from (97 % TPR, 2.1 % FPR) to (100 % TPR, <0.1 % FPR) with very small sample sizes (20–40 samples) in data with sparse transition probability matrices.     

Mechanical Properties and Dislocation Structure Evolution in Ti6Al7Nb Alloy Processed by High Pressure Torsion

Ultrafine-grained biocompatible Ti-6Al-7Nb alloy was produced by high pressure torsion (HPT). Lattice defects—vacancies and dislocations—investigated by positron annihilation spectroscopy, observations by scanning electron microscopy, and microhardness evaluation are linked to the strain imposed by different numbers of HPT revolutions and to the distance from the specimen center. Positron annihilation spectroscopy showed significant increase of dislocation density and concentration of vacancy clusters after ½ of the HPT revolution. Microhardness increases by 20 pct with increasing strain, but it is heterogenous due to duplex microstructure. The heterogeneity of the microhardness increases with increasing strain, suggesting that a heavily deformed and fragmented α + β lamellar microstructure is more hardened than primary alpha grains. The defect structure is homogenous after ½ HPT revolution, while the microhardness becomes homogenous after 3 HPT revolutions only.     

Application of ultrasonic methods to determine elastic anisotropy of polycrystalline copper processed by equal-channel angular pressing

Anisotropy of elastic properties of ultrafine-grained polycrystalline copper after one, two and four passes of equal-channel angular pressing (ECAP) is investigated by means of ultrasonic methods. For each material, Young’s and shear moduli in the principal processing directions are evaluated and the symmetry and orientation of the anisotropy are identified. The relation between the determined symmetry and the processing mechanisms is discussed. It is shown that the material after one and two passes of ECAP exhibits a measurable anisotropy, while the material after the fourth pass behaves isotropically. Within the discussion, it is shown that the origin of the observed anisotropy may be attributed to the spatial arrangement of grain boundaries rather than to the crystallographic texture. In the light of this conclusion, the obtained results correspond well with optical and transmission electron microscopy observations of the microstructures of ECAPed materials documented in the literature.     

Effects of civil war: scientific cooperation in the republics of the former Yugoslavia and the province of Kosovo

In this study we investigate the scientific output of Yugoslavia and its successor republics viz. Serbia, Croatia, Slovenia, Bosnia & Herzegovina, Macedonia and Montenegro. Additionally, Kosovo was included as a separate entity, since it recently declared its independence. The publications and cooperation between the republics are analyzed for the years from 1970 until 2007. In contrast to similar studies, we examine a larger time window and take into consideration not only the three big republics (Serbia, Croatia, and Slovenia) but also include the smaller ones, namely Bosnia & Herzegovina, Macedonia and Montenegro. For our analysis we introduce two new indicators: the normalized cooperation score (R^(cs)_iR^{\rm (cs)}_{i}) and the dominance factor (D^(c)_iD^{\rm (c)}_{i}), a measure of dominance within a weighted network. Furthermore, we develop and assess the reliability of various techniques for visualizing our findings. We found that the civil wars had a severe impact on the inner-Yugoslav cooperation network. Additionally it seems, as if with the ending of the conflicts a process of recovery started.     

The formation of hydrophobic and corrosion resistant surfaces on copper and bronze by treatment in myristic acid

The surface of freshly etched copper and bronze samples was modified by immersion in ethanol solutions of myristic (tetradecanoic) acid. Modification resulted in the formation of hydrophobic layers with contact angles up to 141°. Two kinds of surface structure were observed. The modified surface of copper was covered by a uniform layer containing nano-grains or knitted-like structure, whereas the modified surface of bronze was covered by a layer with lamellate patterns and nano-grains. The corrosion properties of bare and modified copper and bronze surfaces were tested by potentiodynamic polarization experiments in 0.014 M Na₂SO₄ + 0.024 M NaHCO₃ solution. The deduced effectiveness of corrosion inhibition by the modified layers on copper and bronze was up to 97 and 68%, respectively. Modification of the surface by immersion in an ethanol solution of myristic acid appears to be a promising treatment for improving the corrosion resistance of copper. The same treatment was not very effective when used on bronze.