Aggregation for Atanassov's intuitionistic and interval valued fuzzy sets: the median operator

Atanassov's intuitionistic fuzzy sets (AIFS) and interval valued fuzzy sets (IVFS) are two generalizations of a fuzzy set, which are equivalent mathematically although different semantically. We analyze the median aggregation operator for AIFS and IVFS. Different mathematical theories have lead to different definitions of the median operator. We look at the median from various perspectives: as an instance of the intuitionistic ordered weighted averaging operator, as a Fermat point in a plane, as a minimizer of input disagreement, and as an operation on distributive lattices. We underline several connections between these approaches and summarize essential properties of the median in different representations.

Compression and probing C−H···I hydrogen bonds of iodoform under high pressure by x-ray diffraction and raman scattering

High-pressure methods were applied to investigate the structural stability and hydrogen bonding of polar molecules of iodoform by synchrotron radiation X-ray diffraction and Raman spectra measurements, respectively. Up to a pressure of 40 GPa, no phase transitions were observed. The discontinuous frequency shift of the C−H stretching band is believed to be related to the enhancement of the C−H···I weak hydrogen bonds under high pressures. Ab initio calculations were performed, and the results predict the frequency shift of the C−H stretching vibration as C−H···I interacts via hydrogen bonding. The bulk modulus is 17.3 ± 0.8 GPa, with a pressure derivative of 5.2.

A penalty-based aggregation operator for non-convex intervals

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.

Behavioural effects of tourism on oceanic common dolphins, Delphinus sp., in New Zealand: the effects of Markov analysis variations and current tour operator compliance with regulations

Common dolphins, Delphinus sp., are one of the marine mammal species tourism operations in New Zealand focus on. While effects of cetacean-watching activities have previously been examined in coastal regions in New Zealand, this study is the first to investigate effects of commercial tourism and recreational vessels on common dolphins in an open oceanic habitat. Observations from both an independent research vessel and aboard commercial tour vessels operating off the central and east coast Bay of Plenty, North Island, New Zealand were used to assess dolphin behaviour and record the level of compliance by permitted commercial tour operators and private recreational vessels with New Zealand regulations. Dolphin behaviour was assessed using two different approaches to Markov chain analysis in order to examine variation of responses of dolphins to vessels. Results showed that, regardless of the variance in Markov methods, dolphin foraging behaviour was significantly altered by boat interactions. Dolphins spent less time foraging during interactions and took significantly longer to return to foraging once disrupted by vessel presence. This research raises concerns about the potential disruption to feeding, a biologically critical behaviour. This may be particularly important in an open oceanic habitat, where prey resources are typically widely dispersed and unpredictable in abundance. Furthermore, because tourism in this region focuses on common dolphins transiting between adjacent coastal locations, the potential for cumulative effects could exacerbate the local effects demonstrated in this study. While the overall level of compliance by commercial operators was relatively high, non-compliance to the regulations was observed with time restriction, number or speed of vessels interacting with dolphins not being respected. Additionally, prohibited swimming with calves did occur. The effects shown in this study should be carefully considered within conservation management plans, in order to reduce the risk of detrimental effects on common dolphins within the region.

A new insight into growth mechanism and kinetics of mesoporous silica nanoparticles by in situ small angle x-ray scattering

The growth mechanism and kinetics of mesoporous silica nanoparticles (MSNs) were investigated for the first time by using a synchrotron time-resolved small-angle X-ray scattering (SAXS) analysis. The synchrotron SAXS offers unsurpassed time resolution and the ability to detect structural changes of nanometer sized objects, which are beneficial for the understanding of the growth mechanism of small MSNs (∼20 nm). The Porod invariant was used to quantify the conversion of tetraethyl orthosilicate (TEOS) in silica during MSN formation, and the growth kinetics were investigated at different solution pH and temperature through calculating the scattering invariant as a function of reaction time. The growth of MSNs was found to be accelerated at high temperature and high pH, resulting in a higher rate of silica formation. Modeling SAXS data of micelles, where a well-defined electrostatic interaction is assumed, determines the size and shape of hexadecyltrimethylammonium bromide (CTAB) micelles before and after the addition of TEOS. The results suggested that the micelle size increases and the micelle shape changes from ellipsoid to spherical, which might be attributed to the solubilization of TEOS in the hydrophobic core of CTAB micelles. A new "swelling-shrinking" mechanism is proposed. The mechanism provides new insights into understanding MSN growth for the formation of functional mesoporous materials exhibiting controlled morphologies. The SAXS analyses were correlated to the structure of CTAB micelles and chemical reaction of TEOS. This study has provided critical information to an understanding of the growth kinetics and mechanism of MSNs.