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1
Content available remote Interval-valued Hesitant Fuzzy Soft Sets and their Application in Decision Making
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EN
The soft set theory can be used as a newly mathematical tool to handle uncertainty. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, we propose the interval-valued hesitant fuzzy soft sets which are a combination of the interval-valued hesitant fuzzy sets and soft sets. Then, the complement, AND, OR, union, intersection, restricted union, extended intersection, difference, average, and geometric operations are defined on the interval-valued hesitant fuzzy soft sets, and some basic properties are also discussed in detail. Finally, by means of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and the maximizing deviation method, an algorithm is presented, and a comprehensive sensitivity analysis is employed, and the effectiveness is proved by a numerical example.
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Content available remote Fundamental Properties of Pythagorean Fuzzy Aggregation Operators
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EN
In this paper, some new inequalities of Pythagorean fuzzy weighted averaging (PFWA) operator are explored. Later, we develop some Pythagorean fuzzy point operators and introduce generalized Pythagorean fuzzy weighed averaging (GPFWA) operator. Moreover, combining the Pythagorean fuzzy point operators with GPFWA operator, we present some generalized Pythagorean fuzzy point weighted averaging (GPFPWA) operators, which can adjust the degree of the aggregated arguments with some parameters. Based on GPFPWA operators and normal distribution, an approach to multiple attribute decision making (MADM) problem with completely unknown weight information is proposed under Pythagorean fuzzy environment. Finally, an illustrative example is given to show the feasibility and superiority of the developed method.
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Content available remote A new approach to the analysis of polycrystal plasticity
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EN
When a polycrystal is subjected to inelastic deformation, there inevitably exist residual microstress fields in a polycrystalline material due to its nonhomogeneous morphology. The energy stored in these microstress fields may partly be released and influence the material behavior during subsequent inelastic deformation. Correspondingly, a simple mechanical model is introduced to formulate the constitutive equation for a slip system and the hardening law for single crystal. The corresponding approach for the analysis of polycrystalline materials is obtained based on KBW's self-consistent theory. The proposed approach employs no yield criterion and the corresponding numerical analysis is greatly simplified because it involves no additional process for determination of the activation of slip systems and slip direction. A mixed averaging approach is used in polycrystalline plasticity analysis. The response of 316 stainless steel subjected to typical biaxial nonproportional plastic strain cycling is described and the validity of the proposed approach is demonstrated by the satisfactory agreement between the calculated result and experimental observation.
EN
Soft set theory was originally proposed by Molodtsov in 1999 as a general mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft set model is not appropriate to deal with imprecise and fuzzy problems. In order to handle these types of problems, some fuzzy extensions of soft set theory are presented, yielding fuzzy soft set theory. As a further research, in this work, we first propose concepts of interval fuzzy sets and interval fuzzy soft sets, define some operations on them and study some of their relevant properties, especially, the dual laws are discussed with respect to difference operation in interval fuzzy soft set theory. We then introduce a revised Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method and choice value method for interval fuzzy soft set which the weight information is completely unknown. Meanwhile, an analysis of computation complexity is employed, also the discriminative power of two methods are shown. Finally, two illustrative examples are employed to show that they can be successfully applied to problems that contain uncertainties.
EN
This paper describes the unknown parameter and reliability function of the Weibull distribution based on hierarchical Bayesian model for the progressively Type-II censored data. The scale parameter of the Weibull distribution is considered with a gamma prior under the shape parameter is known. Furthermore, the scale parameter of the gamma prior is assumed to be three different known hyper prior. Under these assumptions, the Weibull parameter and reliability function estimators are derived based on the squared error loss (SEL) function, which can be easily extended to other loss functions situation. The result from hierarchical Bayesian method is used to compare with Bayes and maximum likelihood estimate (MLE) methods. The simulation shown that the results from Bayes is the best, followed by hierarchical Bayesian method, and then MLE in terms of root mean square error (RMSE). Finally, one real dataset has been analyzed for illustrative purposes.
PL
W prezentowanej pracy opisano metodę estymacji nieznanego parametru oraz funkcji niezawodności rozkładu Weibulla w oparciu o hierarchiczny model Bayesa dla danych uciętych (cenzurowanych) progresywnie typu II. Rozważano parametr skali rozkładu Weibulla o rozkładzie prawdopodobieństwa apriorycznego gamma w sytuacji, gdzie wartość parametru kształtu była znana. Ponadto, przyjęto, że (hiper)parametr skali rozkładu apriorycznego gamma może mieć trzy różne, znane hiper-rozkłady aprioryczne (ang. hyper priors). Przy tych założeniach, estymatory parametru i funkcji niezawodności rozkładu Weibulla wyprowadzono na podstawie kwadratowej funkcji straty (ang. squared error loss, SEL), którą można łatwo rozszerzyć na inne funkcje straty. Wyniki otrzymane z wykorzystaniem hierarchicznej metody Bayesowskiej porównano z wynikami klasycznej estymacji Bayesowskiej oraz estymacji metodą największego prawdopodobieństwa (ang. maximum likelihood estimate, MLE). Symulacja wykazała, że najlepsze wyniki, jeśli chodzi o średnią kwadratową błędów (ang. root mean squared error, RMSE), daje metoda Bayesa, a w dalszej kolejności hierarchiczna metoda Bayesa oraz MLE. W końcowej części pracy rozważane problemy zilustrowano analizując zbiór danych rzeczywistych.
EN
Interval-valued fuzzy soft decision making problems have obtained great popularity recently. Most of the current methods depend on level soft set that provide choice value of alternatives to be ranked. Such choice value always encounter the equal condition that the optimal alternative can't be gained. Most important of all, the current decision making procedure is not in accordance with the way that the decision makers think about the decision making problems. In this paper, we initiate a new axiomatic definition of interval-valued fuzzy distance measure and similarity measure, which is expressed by interval-valued fuzzy number (IVFN) that will reduce the information loss and keep more original information. Later, the objective weights of various parameters are determined via grey system theory, meanwhile, we develop the combined weights, which can show both the subjective information and the objective information. Then, we present three algorithms to solve interval-valued fuzzy soft decision making problems by Multi- Attributive Border Approximation area Comparison (MABAC), Evaluation based on Distance from Average Solution (EDAS) and new similarity measure. Three approaches solve some unreasonable conditions and promote the development of decision making methods. Finally, the effectiveness and feasibility of approaches are demonstrated by some numerical examples.
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Content available remote A note on ω-limit set of a tree map
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EN
Let T be a tree and f : T →T be continuous. Denote by P(f) and ω(x, f) the set of periodic points of f and w-limit set of x under f respectively. Write ᴧ(f) = UxϵTω(x,f). In this paper, we show that if ...[wzór], then ω(x, f) is an infinite minimal set.
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EN
Biochar amendment may improve crop growth through its nutrients and indirect fertility. However, this improvement varies in a wide range of biochars, crops, and soils. Our objectives were to determine the response of crop growth to biochar amendment and to assess the N use efficiency relative to the biochar and the soil types. In this pot experiment, we investi-gated five typical agricultural soils in China amended with two biochars. Four treatments were designed: the soil itself as a control, the soil amended with 1% biochar, the soil with fertilizer NPK, and the soil with added biochar and fertilizer. Biochar amendment increased the maize biomass and the N use efficiency in the red soil (p<0.05) but not in the other four soils (p>0.05). In the red soil, the biomass under biochar+NPK was 2.67-3.49 times higher than that of only NPK, and 1.48-1.62 times higher than that of only biochar amendment, 21-36 and 35-42% of which were contributed from biochar fertility and indirect fertility, respectively. This study indicates that biochar amendment is very plausible for the red soil but has a minor or even negative effect on the other four soils in China.
EN
Tetrabromobisphenol-A (TBBPA) and its analogue compounds (bisphenol-A (BPA) and 2,6-dibromophenol (2, 6-DBP)) sorption on CTMAB-clays was investigated in this paper through bath experiments. Montmorillonite and kaolinite modified by CTAMB, as the adsorbent, were firstly characterized by XRD, FTIR and SEManalysis. The surface areas was determined using N2 (77K) sorption-desorption analysis. Kinetic studies showed that sorption reached equilibrium in 5 hours and followed the pseudosecond order kinetic model. The intra-particle diffusion model for sorption was also investigated and compared to identify the sorption mechanism. The sorption isotherms, well fitted by Freundlich model, were changed from being non-linear to being linear with intercalating CTMAB into clays, which indicated that CTMAB increased the partition interaction. A combination of partition and specific sorption might be contributed to TBBPA and its composition products sorption mechanism. The Freundlich coefficients (kF) and distribution coefficients (kd) for both two adsorbents were primarily increased by increasing amount of adsorbed CTMAB, while the organic carbon normalized sorption coefficients (koc) did not follow this trend. Meanwhile, 100%CEC-CTMAB-Montmorillonite showed an advantage of removal of the selected compounds than 100%CEC-CTAMB-Kaolinite. The sorption capacity of BPA was bigger than that of 2,6-DBP in spite of their similar hydrophobicity, which indicated some molecule properties might influence the sorption on CTMAB-clays. Moreover, the negative ΔG0 and ΔH0 indicated the spontaneous and exothermal process. The TBBPA sorption on CTMAB-clays was considerably enhanced in the acid condition.
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EN
Mg-0.5Si-xSn (x=0.95, 2.9, 5.02wt.%) alloys were cast and extruded at 593K (320 ºC) with an extrusion ratio of 25. The microstructure and mechanical properties of as-cast and extruded test alloys were investigated by OM, SEM, XRD and tensile tests. The experimental results indicate that the microstructure of the Mg-0.5Si-xSn alloys consists of primary α-Mg dendrites and an interdendritic eutectic containing α-Mg, Mg2Si and Mg2Sn. There is no coarse primary Mg2Si phase in the test alloys due to low Si content. With the increase in the Sn content, the Mg2Si phase was refined. The shape of Mg2Si phase was changed from branch to short bar, and the size of them were reduced. The ultimate tensile strength and yield strength of Mg-0.52Si-2.9Sn alloy at the temperature of 473K (200 ºC) reach 133MPa and 112MPa respectively. Refined eutectic Mg2Si phase and dispersed Mg2Sn phase with good elevated temperature stability are beneficial to improve the elevated temperature performance of the alloys. However, with the excess addition of Sn, large block-like Mg2Sn appears around the grain boundary leading to lower mechanical properties.
EN
As-cast Mg-6Li-0.3Zn-0.6Y and Mg-6Li-1.2Zn-1.2Y (wt%) alloys were prepared and extruded at 260 ºC with an extrusion ratio of 25. The microstructure and mechanical behavior of as-cast and extruded alloys are reported and discussed. The results show that Mg-6Li-1.2Zn- 1.2Y alloy is composed of α-Mg, β-Li, and W-Mg3Zn3Y2 phases while Mg-6Li-0.3Zn-0.6Y alloy contains α-Mg, β-Li, W-Mg3Zn3Y2 phase and X-Mg12ZnY. After hot extrusion, the microstructure of specimens is refined and the average grains size of extruded alloys is 15 μm. Dynamic recrystallization occurs during the extrusion, leading to grain refinement of test alloys. Both the strength and elongation of test alloys are improved by extrusion. The extruded Mg-6Li-0.3Zn-0.6Y alloy possesses an ultimate strength of 225 MPa with an elongation of 18% while the strength and elongation of Mg-6Li-1.2Zn-1.2Y alloy are 206 MPa and 28%, respectively. The X-phase in Mg-6Li-0.3Zn- 0.6Y is beneficial to the improvement of strength, but will lead to the decrease of ductility.
EN
Eupatilin, mainly derived from Artemisia asiatica (Asteraceae), is an O-methylated flavone with various bioactivities. In the present study, a validated ultra-performance liquid chromatography–tandem mass spectrometry (UPLC–MS/MS) method was established for the quantification of eupatilin in rat plasma with the internal standard (IS) of tussilagone and the protein precipitation of plasma samples was performed using acetonitrile–methanol (9:1, v/v). The eupatilin and IS were eluted separately on a UPLC BEH C18 column (2.1 mm × 100 mm, 1.7 μm) with the gradient mobile phase consisted of 0.1% formic acid and acetonitrile. The protonated analytes were quantified by multiple reactions monitoring (MRM) mode with an electrospray ionization (ESI) source operated in positive ion mode. The calibration plots were found to be linear over the range from 2 to 1000 ng/mL for eupatilin in rat plasma. Both of the intra-day and inter-day precision variations (RSDs) were ≤13%. The recoveries of eupatilin in rat plasma were between 83.7% and 94.6%, and the accuracy of the method ranged from 95.8% to 107.6%. In addition, the validated method was applied to pharmacokinetic study of eupatilin after an intravenous dose of 2 mg/kg to rats.
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