• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.543-548
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• 1998

An image of a set that produces a multiset from an ordinary set and its extension to fuzzy multisets is considered. For each input element, its image is added to the output regardless whether or not there already exists the same image in the output. theoretical properties such as commutativity of the image with $\alpha$-cut or multiset addition are proved. Generalization to the image by multivariable functions is moreover defined.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.261-284
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• 2018

In this paper, we recall the definition of soft set, fuzzy soft set, hesitant fuzzy set and hesitant fuzzy soft set and some of their examples. We define the concept of hesitant fuzzy soft multiset which combines hesitant fuzzy soft set and soft multiset theory. We also define basic terms in hesitant fuzzy soft multiset with relevant examples. Some basic operations such as restricted intersection, extended intersection, union, restricted union, AND-product and OR-product and their properties are given, supported with illustrative examples. We finally establish some important results, including De Morgan's inclusions and laws.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1799-1816
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• 2013

Privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union secretly, meaning that any information other than union is not revealed. We propose efficient PPMU protocols, using multiplicative homomorphic cryptosystem. The novelty of our protocol is to directly encrypt a polynomial by representing it by an element of an extension field. The resulting protocols consist of constant rounds and improve communication cost. We also prove the security of our protocol against malicious adversaries, in the random oracle model.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.59-69
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• 2009

The element reduction of a multiset S is to reduce the number of repetitions of an element in S by a predetermined number. Privacy-preserving element reduction of a multiset is an important tool in private computation over multisets. It can be used by itself or by combination with other private set operations. Recently, an efficient privacy-preserving element reduction method was proposed by Kissner and Song [7]. In this paper, we point out a mathematical flaw in their polynomial representation that is used for the element reduction protocol and provide its correction. Also we modify their over-threshold set-operation protocol, using an element reduction with the corrected representation, which is used to output the elements that appear over the predetermined threshold number of times in the multiset resulting from other privacy-preserving set operations.

• The KIPS Transactions:PartB
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• v.9B no.3
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• pp.383-388
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• 2002

We developed a spatial parser generator, SPG, which can automatically create a spatial parser if CMG(Constraint Multiset Grammars) grammars for a visual language are provided by the user with GUI(Graphical User Interface). SPG has the following features. (1) The user uses a visual editor to define the grammars of a virtual language and draw the visual language which should be parsed. (2) The user roughly defines CMG grammars in a visual wan at first. Then the user modifies them and defines final grammars. (3) Because SPG has a constraint solver, it maintains constraints in the parsed virtual language according to the grammars.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.657-668
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• 2016

Given a partition ${\lambda}=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_l)$ of a positive integer n, let Tab(${\lambda}$, k) be the set of all tabloids of shape ${\lambda}$ whose weights range over the set of all k-compositions of n and ${\mathcal{OP}}^k_{\lambda}_{rev}$ the set of all ordered partitions into k blocks of the multiset $\{1^{{\lambda}_l}2^{{\lambda}_{l-1}}{\cdots}l^{{\lambda}_1}\}$. In [2], Butler introduced an inversion-like statistic on Tab(${\lambda}$, k) to show that the rank-selected $M{\ddot{o}}bius$ invariant arising from the subgroup lattice of a finite abelian p-group of type ${\lambda}$ has nonnegative coefficients as a polynomial in p. In this paper, we introduce an inversion-like statistic on the set of ordered partitions of a multiset and construct an inversion-preserving bijection between Tab(${\lambda}$, k) and ${\mathcal{OP}}^k_{\hat{\lambda}}$. When k = 2, we also introduce a major-like statistic on Tab(${\lambda}$, 2) and study its connection to the inversion statistic due to Butler.

• Proceedings of the Korea Information Processing Society Conference
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• 2019.05a
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• pp.36-39
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• 2019

데이터 마이닝에서 클러스터링은 서로 유사한 특징을 갖는 데이터들을 동일한 클래스로 분류하는 방법이다. 클러스터링에는 다양한 방법이 존재하지만 대표적으로 집합으로 표현된 데이터들의 유사도를 측정하기 위해서는 자카드 유사도(Jaccard Similarity)를 이용한다. 자카드 유사도는 서로 다른 집합 간의 공통된 부분을 상대적으로 평가하여 유사도를 측정하는 방법이다. 그러나 최근에는 데이터를 저장할 수 있는 기술과 매체의 발전으로 표현할 수 있는 데이터의 영역과 범위는 발전되고 있기 때문에 많은 연산과 시간의 비용이 발생하게 된다. 이를 해결하기 위해서 두 데이터의 표본의 유사도를 통해 실제 데이터들의 유사도를 추정할 수 있는 Min-Hash 가 제안되었다. 본 논문에서는 이를 활용하여 집합의 영역을 다중 집합(Multiset)으로 확장하여 중복되는 값을 가질 수 있는 두 데이터 간의 유사도를 효율적으로 추정할 수 있는 Min-Max Hash 를 제안한다.

• Communications for Statistical Applications and Methods
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• v.30 no.6
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• pp.561-575
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• 2023

Brain network analysis has attracted the interest of neuroscience researchers in studying brain diseases. Magnetoencephalography (MEG) is especially proper for analyzing functional connectivity due to high temporal and spatial resolution. The application of graph theory for functional connectivity analysis has been studied widely, but research on network modeling for MEG still needs more. Temporal exponential random graph model (TERGM) considers temporal dependencies of networks. We performed the brain network analysis, including static/temporal network statistics, on two groups of epilepsy patients who removed the left (LT) or right (RT) part of the brain and healthy controls. We investigate network differences using Multiset canonical correlation analysis (MCCA) and TERGM between epilepsy patients and healthy controls (HC). The brain network of healthy controls had fewer temporal changes than patient groups. As a result of TERGM, on the simulation networks, LT and RT had less stable state than HC in the network connectivity structure. HC had a stable state of the brain network.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39B no.6
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• pp.370-378
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• 2014

It is well known that data mining plays a crucial role in varities of real-world applications, by which extracts knowledge from large volume of datasets. Among functionalties provided by data mining, frequency mining over given multisets is a basic and essential one. However, most of users would like to obtain the frequency over their multisets without revealing their own multisets. In this work, we come up with a novel way to achive this goal and prove its security rigorously. Our scheme has several advantages over existing work as follows: Firstly, our scheme has the most efficient computational complexity in the cardinality of multisets. Further our security proof is rigorously in the simulation paradigm. Lastly our system assumption is general.