• Honam Mathematical Journal
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• v.29 no.2
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• pp.279-288
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• 2007

The notion of fuzzy n-fold implicative ordered filters in implicative semigroups is introduced, and related properties are investigated. Relations between fuzzy ordered filters and fuzzy n-fold implicative ordered filters are provided. Characterizations of a fuzzy n-fold implicative ordered filter are given, and an extension property for a fuzzy n-fold implicative ordered filter is obtained.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.47-55
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• 1999

This paper continues the investigations of implicative semigroups and of their ordered filters which were started in general case by M.W. Chan and K. P. Shum [3]. In particular, the notion of an implicative ordered filter of an implicative semigroup is introduced. We state some equivalent conditions for an ordered filter to be an implicative ordered filter and obtain the so called extension property for implicative ordered filters.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.81-85
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• 1996

We introduce fuzzy ordered filter, fuzzy weakly implicative ordered filter and fuzzy implicative ordered filter of implicative commutative semigroups and prove and some results.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.185-191
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• 1997

The notions of implicative semigroup and ordered filter were introduced by M. W. Chan and K. pp. Shum [3]. The first is a generalization of implicative semilattice (see W. C. Nemitz [6] and T. S. Blyth [2]) and has a close relation with the implication in mathematical logic and set theoretic difference (see G. Birkhoff [1] and H. B. Curry [4]). For the general development of implicative semilattice theory the ordered filters play an important role, which is shown by W. C. Nemitz [6].

• Honam Mathematical Journal
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• v.39 no.2
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• pp.199-216
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• 2017

In the paper [Y. B. Jun, B. Davvaz and A. Khan, Filters of ordered semigroups based on the fuzzy points, JIFS 24 (2013) 619-630]. Jun et al. discussed the notion of (${\in},{\in}{\vee}q_k$)-fuzzy left (resp., right) filters as a generalization of the notion of (${\in},{\in}{\vee}q$)-fuzzy left (resp., right) filters of ordered semigroups. In this article, we try to obtain a more general form that (${\in},{\in}{\vee}q_k$)-fuzzy left (resp., right) filters in ordered semigroups. The notion of (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filters is discussed, and several properties are investigated. Characterizations of an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filter are established. A condition for an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filter to be a fuzzy left (resp., right) filter is provided. The important achievement of the study with an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (right) filter is that the notion of an (${\in},{\in}{\vee}q_k$)-fuzzy left ( right) filter and hence an (${\in},{\in}{\vee}q$)-fuzzy left (resp. right) filter are special cases of an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp. right) filter, and thus several results in published papers are becoming corollaries of our results obtained in this paper.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.9-14
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• 2007

In this paper, we introduce more extended special sets in implicative semigroups, and obtain some relations with ordered filters.

• Korean Journal of Remote Sensing
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• v.25 no.1
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• pp.21-30
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• 2009

The purposes of this paper are to present a selection method of neighboring pixels whose local statistics are similar to the center pixel and combine the selection result with mean curvature diffusion filter to reduce noises in remote sensed imagery. The order of selection of neighboring pixels is critical, especially for finding a pixel belonging to the homogeneous region, since the statistics of the homogeneous region vary according to the selection order. An effective strategy for selecting neighboring pixels, which uses rank-order differences vector obtained by computing the intensity differences between the center pixel and neighboring pixels and arranging them in ascending order, is proposed in this paper. By using region growing method, we divide the elements of the rank-ordered differences vector into two groups, homogeneous rank-ordered differences vector and outlier rank-ordered differences vector. The mean curvature diffusion filter is combined with a line process, which chooses selectively diffusion coefficient of the neighboring pixels belonging into homogeneous rank-ordered differences vector. Experimental results using an aerial image and a TerraSAR-X satellite image showed that the proposed method reduced more efficiently noises than some conventional adaptive filters using all neighboring pixels in updating the center pixel.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.5
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• pp.1638-1653
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• 2014

A sequential optimization algorithm (SOA) for resource allocation in a cyclic-prefixed single-carrier cognitive relay system is proposed in this study. Both subcarrier pairing (SP) and power allocation are performed subject to a primary user interference constraint to minimize the mean squared error of frequency-domain equalization at the secondary destination receiver. Under uniform power allocation at the secondary source and optimal power allocation at the secondary relay, the ordered SP is proven to be asymptotically optimal in maximizing the matched filter bound on the signal-to-interference-plus-noise ratio. SOA implements the ordered SP before power allocation optimization by decoupling the ordered SP from the power allocation. Simulation results show that SOA can optimize resource allocation efficiently by significantly reducing complexity.

• Journal of Radiopharmaceuticals and Molecular Probes
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• v.3 no.2
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• pp.65-71
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• 2017

To assess the effects of filter and reconstruction of Cu-64 PET data on Siemens scanner, the various reconstruction algorithm with various filters were assessed in terms of spatial resolution, non-uniformity (NU), recovery coefficient (RC), and spillover ratio (SOR). Image reconstruction was performed using filtered backprojection (FBP), 2D ordered subset expectation maximization (OSEM), 3D reprojection algorithm (3DRP), and maximum a posteriori algorithms (MAP). For the FBP reconstruction, ramp, butterworth, hamming, hanning, or parzen filters were used. Attenuation or scatter correction were performed to assess the effect of attenuation and scatter correction. Regarding spatial resolution, highest achievable volumetric resolution was $3.08mm^3$ at the center of FOV when MAP (${\beta}=0.1$) reconstruction method was used. SOR was below 4% for FBP when ramp, Hamming, Hanning, or Shepp-logan filter were used. The lowest NU (highest uniform) after attenuation & scatter correction was 5.39% when FBP (parzen filter) was used. Regarding RC, 0.9 < RC < 1.1 was obtained when OSEM (iteration: 10) was used when attenuation and scatter correction were applied. In this study, image quality of Cu-64 on Siemens Inveon PET was investigated. This data will helpful for the quantification of Cu-64 PET data.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.59-68
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• 2009

We introduce the notion of GT-algebras as a generalization of the concept of Tarski algebras. We introduce the notion of GT-filters in GT-algebras, and we prove some properties of GT-filters.