Fuzzy sets: Abstraction Axiom, Statistical Interpretation, Observations of Fuzzy Sets

The issues relating fuzzy sets definition are under consideration including the analogue for separation axiom, statistical interpretation and membership function representation by the conditional Probabilities.

A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

On Blocking Sets in Affine Hjelmslev Planes

ACM Computing Classification System (1998): G.2.1.

On Pareto Sets in Multi-Criteria Optimization

Здравко Д. Славов - В тази работа се разглеждат Паретовските решения в непрекъсната многокритериална оптимизация. Обсъжда се ролята на някои предположения, които влияят на характеристиките на Паретовските множества. Авторът се е опитал да премахне предположенията за вдлъбнатост на целевите функции и изпъкналост на допустимата област, които обикновено се използват в многокритериалната оптимизация. Резултатите са на базата на конструирането на ретракция от допустимата област върху Парето-оптималното множество.

Evolution of Sets Systems and Homotopy Groups of Spheres

Симеон Т. Стефанов, Велика И. Драгиева - В работата е изследвана еволюцията на системи от множества върху n-мерната евклидова сфера S^n. Установена е връзката на такива системи с хомотопичните групи на сферите. Получени са някои комбинаторни приложения за многостени.

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Stable sets in one-seller assignment games

We consider von Neumann -- Morgenstern stable sets in assignment games with one seller and many buyers. We prove that a set of imputations is a stable set if and only if it is the graph of a certain type of continuous and monotone function. This characterization enables us to interpret the standards of behavior encompassed by the various stable sets as possible outcomes of well-known auction procedures when groups of buyers may form bidder rings. We also show that the union of all stable sets can be described as the union of convex polytopes all of whose vertices are marginal contribution payoff vectors. Consequently, each stable set is contained in the Weber set. The Shapley value, however, typically falls outside the union of all stable sets.

The application of reduced-size short tandem repeat primer sets in the analysis of human DNA from degraded and compromised samples

The purpose of this research was to demonstrate the applicability of reduced-size STR (Miniplex) primer sets to challenging samples and to provide the forensic community with new information regarding the analysis of degraded and inhibited DNA. The Miniplex primer sets were validated in accordance with guidelines set forth by the Scientific Working Group on DNA Analysis Methods (SWGDAM) in order to demonstrate the scientific validity of the kits. The Miniplex sets were also used in the analysis of DNA extracted from human skeletal remains and telogen hair. In addition, a method for evaluating the mechanism of PCR inhibition was developed using qPCR. The Miniplexes were demonstrated to be a robust and sensitive tool for the analysis of DNA with as low as 100 pg of template DNA. They also proved to be better than commercial kits in the analysis of DNA from human skeletal remains, with 64% of samples tested producing full profiles, compared to 16% for a commercial kit. The Miniplexes also produced amplification of nuclear DNA from human telogen hairs, with partial profiles obtained from as low as 60 pg of template DNA. These data suggest smaller PCR amplicons may provide a useful alternative to mitochondrial DNA for forensic analysis of degraded DNA from human skeletal remains, telogen hairs, and other challenging samples. In the evaluation of inhibition by qPCR, the effect of amplicon length and primer melting temperature was evaluated in order to determine the binding mechanisms of different PCR inhibitors. Several mechanisms were indicated by the inhibitors tested, including binding of the polymerase, binding to the DNA, and effects on the processivity of the polymerase during primer extension. The data obtained from qPCR illustrated a method by which the type of inhibitor could be inferred in forensic samples, and some methods of reducing inhibition for specific inhibitors were demonstrated. An understanding of the mechanism of the inhibitors found in forensic samples will allow analysts to select the proper methods for inhibition removal or the type of analysis that can be performed, and will increase the information that can be obtained from inhibited samples.

Surprises and Insights from Long-Term Aquatic Data Sets and Experiments

long-term research on freshwater ecosystems provides insights that can be difficult to obtain from other approaches. Widespread monitoring of ecologically relevant water-quality parameters spanning decades can facilitate important tests of ecological principles. Unique long-term data sets and analytical tools are increasingly available, allowing for powerful and synthetic analyses across sites. long-term measurements or experiments in aquatic systems can catch rare events, changes in highly variable systems, time-lagged responses, cumulative effects of stressors, and biotic responses that encompass multiple generations. Data are available from formal networks, local to international agencies, private organizations, various institutions, and paleontological and historic records; brief literature surveys suggest much existing data are not synthesized. Ecological sciences will benefit from careful maintenance and analyses of existing long-term programs, and subsequent insights can aid in the design of effective future long-term experimental and observational efforts. long-term research on freshwaters is particularly important because of their value to humanity.

Global compilation of benthic data sets I

Approaches to quantify the organic carbon accumulation on a global scale generally do not consider the small-scale variability of sedimentary and oceanographic boundary conditions along continental margins. In this study, we present a new approach to regionalize the total organic carbon (TOC) content in surface sediments (<5 cm sediment depth). It is based on a compilation of more than 5500 single measurements from various sources. Global TOC distribution was determined by the application of a combined qualitative and quantitative-geostatistical method. Overall, 33 benthic TOC-based provinces were defined and used to process the global distribution pattern of the TOC content in surface sediments in a 1°x1° grid resolution. Regional dependencies of data points within each single province are expressed by modeled semi-variograms. Measured and estimated TOC values show good correlation, emphasizing the reasonable applicability of the method. The accumulation of organic carbon in marine surface sediments is a key parameter in the control of mineralization processes and the material exchange between the sediment and the ocean water. Our approach will help to improve global budgets of nutrient and carbon cycles.

Data compilation on the biological response to ocean acidification: environmental and experimental context of data sets and related literature

The exponential growth of studies on the biological response to ocean acidification over the last few decades has generated a large amount of data. To facilitate data comparison, a data compilation hosted at the data publisher PANGAEA was initiated in 2008 and is updated on a regular basis (doi:10.1594/PANGAEA.149999). By January 2015, a total of 581 data sets (over 4 000 000 data points) from 539 papers had been archived. Here we present the developments of this data compilation five years since its first description by Nisumaa et al. (2010). Most of study sites from which data archived are still in the Northern Hemisphere and the number of archived data from studies from the Southern Hemisphere and polar oceans are still relatively low. Data from 60 studies that investigated the response of a mix of organisms or natural communities were all added after 2010, indicating a welcomed shift from the study of individual organisms to communities and ecosystems. The initial imbalance of considerably more data archived on calcification and primary production than on other processes has improved. There is also a clear tendency towards more data archived from multifactorial studies after 2010. For easier and more effective access to ocean acidification data, the ocean acidification community is strongly encouraged to contribute to the data archiving effort, and help develop standard vocabularies describing the variables and define best practices for archiving ocean acidification data.

Designing Choice Sets to Exploit Focusing Illusion

Focusing illusion describes how, when making choices, people may put disproportionate attention on certain attributes of the options and hence, causing those options to be overvalued. For instance, in deciding whether or not to take out a loan, people may focus more on getting the loan than on its small and dispersed costs. Building on recent literature on focusing illusion in economic choice, we theoretically propose and empirically test that focusing illusion can be advantageously exploited such that attention is put back on the ignored attributes. To demonstrate this, we use hypothetical loan decisions where people choose between loans with different repayment plans to finance a purchase. We show that when adding a steeply decreasing-installments plan to the original choice set of not borrowing or borrowing under a fixed-installments plan, the preference for the fixed-installments plan is lessened. This is because preference for the fixed-installments plan shifted towards not borrowing. We discuss potential applications of our results in designing choice sets of intertemporal sequences.

Primary data sets of the hydrographic atlas of the Southern Ocean

The general knowledge of the hydrographic structure of the Southern Ocean is still rather incomplete since observations particularly in the ice covered regions are cumbersome to be carried out. But we know from the available information that thermohaline processes have large amplitudes and cover a wide range of scales in this part of the world ocean. The modification of water masses around Antarctica have indeed a worldwide impact, these processes ultimately determine the cold state of the present climate in the world ocean. We have converted efforts of the German and Russian polar research institutions to collect and validate the presently available temperature, salinity and oxygen data of the ocean south of 30°S latitude. We have carried out this work in spite of the fact that the hydrographic programme of the World Ocean Circulation Experiment (WOCE) will provide more new information in due time, but its contribution to the high latitudes of the Southern Ocean is quite sparse. The modified picture of the hydrographic structure of the Southern Ocean presented in this atlas may serve the oceanographic community in many ways and help to unravel the role of this ocean in the global climate system. This atlas could only be prepared with the altruistic assistance of many colleagues from various institutions worldwide who have provided us with their data and their advice. Their generous help is gratefully acknowledged. During two years scientists from the Arctic and Antarctic Research Institute in St. Petersburg and the Alfred Wegener Institute for Polar and Marine Research in Bremerhaven have cooperated in a fruitful way to establish the atlas and the archive of about 38749 validated hydrographic stations. We hope that both sources of information will be widely applied for future ocean studies and will serve as a reference state for global change considerations.