• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.579-591
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• 2015

Properties of prime filters are studied in BE-algebras as well as in commutative BE-algebras. An equivalent condition is derived for a BE-algebra to become a totally ordered set. A condition L is introduced in a commutative BE-algebra in ordered to study some more properties of prime filters in commutative BE-algebras. A set of equivalent conditions is derived for a commutative BE-algebra to become a chain. Some topological properties of the space of all prime filters of BE-algebras are studied.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.525-535
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• 2016

We define a fuzzy lattice as a fuzzy relation, prove the distributive inequalities and the modular inequality of fuzzy lattices, and show that the fuzzy totally ordered set is a distributive fuzzy lattice and that the distributive fuzzy lattice is modular.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.361-374
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• 2009

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its level set, show that a fuzzy totally ordered set is a distributive fuzzy lattice, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

• The Transactions of the Korea Information Processing Society
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• v.4 no.10
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• pp.2493-2500
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• 1997

We propose a new key management scheme for multiuser group which is classified as hierarchical structure (sometimes it is called a multilevel security hierarchy) in the symmetric key cryptosystem. The proposed scheme is based on the trapdoor one-way permutations which are generated by the pseudo-random permutation algorithm, and it is avaliable for multilevel hierarchical structure composed of a totally ordered set and a partially ordered set, since it has advantage for time and storage from an implemental point of view. Moreover, we obtain a performance analysis by comparing with the other scheme, and show that the proposed scheme is very efficient for computing time of key generation and memory size of key storage.

• ETRI Journal
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• v.33 no.3
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• pp.344-354
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• 2011

In this paper, a model is introduced named double relation chains (DRC) based on ordered sets. It is proved that using DRC and special relationships among the members of an alphabet, vectors of this alphabet can be stored and searched in a tree. This idea is general; however, one special application of DRC is the longest prefix matching (LPM) problem in an IP network. Applying the idea of DRC to the LPM problem makes the prefixes comparable like numbers using a pair of w-bit vectors to store at least one and at most w prefixes, where w is the IP address length. This leads to good compression performance. Based on this, two recently introduced structures called coded prefix trees and scalar prefix trees are shown to be specific applications of DRC. They are implementable on balanced trees which cause the node access complexity for prefix search and update procedures to be O(log n) where n is the number of prefixes. As another advantage, the number of node accesses for these procedures does not depend on w. Additionally, they need fewer number of node accesses compared to recent range-based solutions. These structures are applicable on both IPv4 and IPv6, and can be implemented in software or hardware.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.473-480
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• 2007

In this paper we define prime right ideals of semirings and prove that if every right ideal of a semiring R is prime then R is weakly regular. We also prove that if the set of right ideals of R is totally ordered then every right ideal of R is prime if and only if R is right weakly regular. Moreover in this paper we also define prime subsemimodule (generalizing the concept of prime right ideals) of an R-semimodule. We prove that if a subsemimodule K of an R-semimodule M is prime then $A_K(M)$ is also a prime ideal of R.

• Journal of KIISE:Databases
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• v.35 no.5
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• pp.447-458
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• 2008

In this paper, we address an efficient processing scheme for k-nearest neighbor queries to retrieve k static objects in road network databases. Existing methods cannot expect a query processing speed-up by index structures in road network databases, since it is impossible to build an index by the network distance, which cannot meet the triangular inequality requirement, essential for index creation, but only possible in a totally ordered set. Thus, these previous methods suffer from a serious performance degradation in query processing. Another method using pre-computed network distances also suffers from a serious storage overhead to maintain a huge amount of pre-computed network distances. To solve these performance and storage problems at the same time, this paper proposes a novel approach that creates an index for moving objects by approximating their network distances and efficiently processes k-nearest neighbor queries by means of the approximate index. For this approach, we proposed a systematic way of mapping each moving object on a road network into the corresponding absolute position in the m-dimensional space. To meet the triangular inequality this paper proposes a new notion of average network distance, and uses FastMap to map moving objects to their corresponding points in the m-dimensional space. After then, we present an approximate indexing algorithm to build an R*-tree, a multidimensional index, on the m-dimensional points of moving objects. The proposed scheme presents a query processing algorithm capable of efficiently evaluating k-nearest neighbor queries by finding k-nearest points (i.e., k-nearest moving objects) from the m-dimensional index. Finally, a variety of extensive experiments verifies the performance enhancement of the proposed approach by performing especially for the real-life road network databases.

• SUVANNABHUMI
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• v.3 no.1
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• pp.47-66
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• 2011

Malay society is rooted on the Islamic concept. That Islam influenced every corner of that Malay society which had ever been an edge of the civilizations of the Indus and Ganges. Once the letters of that Hindu religion namely Sanscrit was adopted to this Malay society for the purpose of getting the Malay language, that is, Bahasa Melayu down to the practical literation but in vain. The Sanscrit was too complicated for Malay society to imitate and put it into practice in everyday life because it was totally different type of letters which has many of the similar allographs for a sound. In the end Malay society gave it up and just used the Malay language without using any letters for herself. After a few centuries Islam entered this Malay society with taking Arabic letters. It was not merely influencing Malay cultures, but to the religious life according to wide spread of that Islam. Finally Arabic letters was to the very means that Malay language was written by. It means that Arabic letters had been used for Arabic language in former times, but it became a similar form of letters for a new language which was named as Malay language. This Arabic letters for Arabic language has no problems whereas Arabic letters for Malay language has some of it. Naturally speaking, arabic letters was not designed for any other language but just for Arabic language itself. On account of this, there occurred a few problems in writing Malay consonants, just like p, ng, g, c, ny and v. These 6 letters could never be written down in Arabic letters. Those 6 ones were never known before in trying to pronounce by Arab people. Therefore, Malay society had only to modify a few new forms of letters for these 6 letters which had frequently been found in their own Malay sounds. As a result, pa was derived from fa, nga was derived from ain, ga was derived from kaf, ca was derived from jim, nya was derived from tha or ba, and va was derived from wau itself. Where must these 6 newly modified letters be put on this Arabic keyboard? This is the very core of this working paper. As a matter of course, these 6 letters were put on the place where 6 Arabic signs which were scarecely written in Malay language. Those 6 are found when they are used only in the 'shift-key-using-letters.' These newly designed 6 letters were put instead of the original places of fatha, kasra, damma, sukun, tanween and so on. The main differences between the 2 set of 6 letters are this: 6 in Arabic orginal keyboard are only signs for Arabic letters, on the other hand 6 Malay's are real letters. In others words, 6 newly modified Malay letters were substituted for unused 6 Arabic signs in Malay keyboard. This type of newly designed Malay Jawi Script keyboard is still used in Malaysia, Brunei and some other Malay countries. But this sort of keyboard also needs to go forward to find out another way of keyboard system which is in accordance with the alphabetically ordered keyboard system. It means that alif is going to be typed for A key, and zai shall be typed when Z key is pressed. This keyboard system is called 'Malay Jawi-English Rumi matching keyboard system', even though this system should probably be inconvenient for Malay Jawi experts who are good at Arabic 'alif-ba-ta'order.