• Communications of the Korean Mathematical Society
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• v.30 no.1
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• pp.23-34
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• 2015

We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.251-259
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• 2015

Let $\mathbb{F}^d_q$ be a d-dimensional vector space over a finite field $\mathbb{F}^d_q$ with q elements. We endow the space $\mathbb{F}^d_q$ with a normalized counting measure dx. Let ${\sigma}$ be a normalized surface measure on an algebraic variety V contained in the space ($\mathbb{F}^d_q$, dx). We define the restricted averaging operator AV by $A_Vf(X)=f*{\sigma}(x)$ for $x{\in}V$, where $f:(\mathbb{F}^d_q,dx){\rightarrow}\mathbb{C}$: In this paper, we initially investigate $L^p{\rightarrow}L^r$ estimates of the restricted averaging operator AV. As a main result, we obtain the optimal results on this problem in the case when the varieties V are any nondegenerate algebraic curves in two dimensional vector spaces over finite fields. The Fourier restriction estimates for curves on $\mathbb{F}^2_q$ play a crucial role in proving our results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.4952-4975
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• 2018

An induced hesitant linguistic aggregation operator is investigated in the paper, in which, hesitant fuzzy linguistic evaluation values are associated with probabilistic information. To deal with these hesitant fuzzy linguistic information, an induced hesitant fuzzy linguistic probabilistic ordered weighted averaging (IHFLPOWA) operator is proposed, monotonicity, boundary and idempotency of IHFLPOWA are proved. Then andness, orness and the entropy of dispersion of IHFLPOWA are analyzed, which are used to characterize the weighting vector of the operator, these properties show that IHFLPOWA is extensions of the induced linguistic ordered weighted averaging operator and linguistic probabilistic aggregation operator. In this paper, IHFLPOWA is utilized to gather linguistic information and create fuzzy ontologies, and a movie fuzzy ontology as an illustrative case study is used to show the elaboration of the proposed method and comparison with the existing linguistic aggregation operators, it seems that the IHFLPOWA operator is an useful and alternative operator for dealing with hesitant fuzzy linguistic information with probabilistic information.

• Asia pacific journal of information systems
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• v.16 no.1
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• pp.85-101
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• 2006

Actual type of aggregation performed by an ordered weighted averaging (OWA) operator heavily depends upon the weighting vector. A number of approaches have been suggested for obtaining the associated weights. In this paper, we present analytic forms of OWA operator weighting functions, each of which has such properties as rank-based weights and constant value of orness, irrespective of number of objectives aggregated. Specifically, we propose four analytic forms of OWA weighting functions that can be positioned at 0.25, 0.334, 0.667, and 0.75 on the orness scale. The merits for using these weights over other weighting schemes can be mentioned in a couple of ways. Firstiy, we can efficiently utilize the analytic forms of weighting functions without solving complicated mathematical programs once the degree of orness is specified a priori by decision maker. Secondly, combined with well-known OWA operator weights such as max, min, and average, any weighting vectors, having a desired value of orness and being independent of the number of objectives, can be generated. This can be accomplished by convex combinations of predetermined weighting functions having constant values of orness. Finally, in terms of a measure of dispersion, newly generated weighting vectors show just a few discrepancies with weights generated by maximum entropy OWA.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.259-272
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• 2017

In this paper we study the mapping properties of the finite field restricted averaging operators to various algebraic varieties. We derive necessary conditions for the boundedness of the generalized restricted averaging operator related to arbitrary algebraic varieties. It is shown that the necessary conditions are in fact sufficient in the specific case when the Fourier transform on varieties has enough decay estimates. Our work extends the known optimal result on regular varieties such as paraboloids and spheres to certain lower dimensional varieties.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.265-272
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• 2009

Fuzzy number intuitionistic fuzzy sets (FNIFSs), each of which is characterized by a membership function and a non-membership function whose values are trigonometric fuzzy number rather than exact numbers, are a very useful means to describe the decision information in the process of decision making. Wang [10] developed some arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator. In this paper, based on the FIFHA operator and the FIFWA operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as fuzzy number intuitionistic fuzzy decision matrices where each of the elements is characterized by fuzzy number intuitionistic fuzzy numbers, and the information about attribute weights is partially known. An example is used to illustrate the applicability of the proposed approach.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.31-37
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• 2002

In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.

• Atmosphere
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• v.24 no.2
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• pp.197-206
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• 2014

The effects of different averaging operators and atmospheric stability on the turbulent fluxes are investigated using the vertical velocity, air temperature, carbon dioxide concentration, and absolute humidity data measured at 10 Hz by a 3-dimensional sonic anemometer and an open-path $CO_2/H_2O$ infrared gas analyzer installed at a height of 18.5 m on the rooftop of the Jungnang KT building located at a typical residential area in Seoul, Korea. For this purpose, 7 different averaging operators including block average, linear regression, and moving averages during 100 s, 300 s, 600 s, 900 s, and 1800 s are considered and the data quality control procedure such as physical limit check and spike removal is also applied. It is found that as the averaging interval becomes shorter, turbulent fluxes computed by the moving average become smaller and the ratios of turbulent fluxes computed by the 100 s moving average to the fluxes by the 1800 s moving average under unstable stability are smaller than those under neutral stability. The turbulent fluxes computed by the linear regression are 85~92% of those computed by the 1800 s moving average and nearly the same as those computed by 900 s moving average, implying that the adequate selection of an averaging operator and its interval will be very important to estimate more accurate turbulent fluxes at urban area.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1788-1792
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• 2006

The ordered weighted averaging (OWA) operator by Yager has received more and more attention since its appearance. One key point in the OWA operator is to determine its associated weights. Among numerous methods that have appeared in the literature, we notice the maximum entropy OWA (MEOWA) weights that are determined by taking into account two appealing measures characterizing the OWA weights. Instead of maximizing the entropy in the formulation for determining the MEOWA weights, the new method in the article tries to obtain the OWA weights which are evenly spread out around equal weights as much as possible while strictly satisfying the orness value provided in the program. This consideration leads to the least squared OWA (LSOWA) weighting method in which the program tries to obtain the weights that minimize the sum of deviations from the equal weights since entropy is maximized when the weights are equal. Above all, the LSOWA weights display symmetric allocations of weights on the basis of equal weights. The positive or negative allocations of weights from the median as a basis depend on the magnitude of orness specified. Further interval LSOWA weights are constructed when a decision-maker specifies his or her value of orness in uncertain numerical bounds.