• Title/Summary/Keyword: Well-ordered set

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Topology on Semi-Well Ordered Sets

  • Angela Sunny;P. Sini
    • Kyungpook Mathematical Journal
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    • v.64 no.1
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    • pp.161-169
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    • 2024
  • A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

A CHARACTERIZATION OF FINITE FACTORIZATION POSITIVE MONOIDS

  • Polo, Harold
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.669-679
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    • 2022
  • We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

PRIME FILTERS OF COMMUTATIVE BE-ALGEBRAS

  • RAO, M. SAMBASIVA
    • 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.

ON FUZZY QUOTIENT RINGS AND CHAIN CONDITIONS

  • Lee, Kyoung-Hee
    • The Pure and Applied Mathematics
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    • v.7 no.1
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    • pp.33-40
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    • 2000
  • We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.

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GENERALIZED ALTERNATING SIGN MATRICES AND SIGNED PERMUTATION MATRICES

  • Brualdi, Richard A.;Kim, Hwa Kyung
    • Journal of the Korean Mathematical Society
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    • v.58 no.4
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    • pp.921-948
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    • 2021
  • We continue the investigations in [6] extending the Bruhat order on n × n alternating sign matrices to our more general setting. We show that the resulting partially ordered set is a graded lattice with a well-define rank function. Many illustrative examples are given.

A RESOLVENT APPROACH FOR SOLVING A SET-VALUED VARIATIONAL INCLUSION PROBLEM USING WEAK-RRD SET-VALUED MAPPING

  • Ahmad, Iqbal;Ahmad, Rais;Iqbal, Javid
    • Korean Journal of Mathematics
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    • v.24 no.2
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    • pp.199-213
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    • 2016
  • The resolvent operator approach of [2] is applied to solve a set-valued variational inclusion problem in ordered Hilbert spaces. The resolvent operator under consideration is called relaxed resolvent operator and we demonstrate some of its properties. To obtain the solution of a set-valued variational inclusion problem, an iterative algorithm is developed and weak-RRD set-valued mapping is used. The problem as well as main result of this paper are more general than many previous problems and results available in the literature.

ON FUZZY IDBALS OF LIE ALGEBRAS

  • Jun, Young-Bae;Kim, Kyung-Ho;Roh, Eun-Hwan
    • Journal of applied mathematics & informatics
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    • v.10 no.1_2
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    • pp.251-259
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    • 2002
  • The fuzzification of an ideal in a Lie algebra is considered. Using a level subset of a fuzzy subset of a Lie algebra, we give a characterization of a fuzzy ideal, and using a family of ideals of a Lie algebra, we establish a fuzzy ideal. With relation to the ascending chain of ideals, a characterization for the set of values of any fuzzy ideal to be a well-ordered subset of the closed unit interval [0,1] is stated.

A note on Box-Cox transformation and application in microarray data

  • Rahman, Mezbahur;Lee, Nam-Yong
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.5
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    • pp.967-976
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    • 2011
  • The Box-Cox transformation is a well known family of power transformations that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. Normalization (studentization) of the regressors is a common practice in analyzing microarray data. Here, we implement Box-Cox transformation in normalizing regressors in microarray data. Pridictabilty of the model can be improved using data transformation compared to studentization.

The Linear Discrepancy of a Fuzzy Poset

  • Cheong, Min-Seok;Chae, Gab-Byung;Kim, Sang-Mok
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.1
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    • pp.59-64
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    • 2011
  • In 2001, the notion of a fuzzy poset defined on a set X via a triplet (L, G, I) of functions with domain X ${\times}$ X and range [0, 1] satisfying a special condition L+G+I = 1 is introduced by J. Negger and Hee Sik Kim, where L is the 'less than' function, G is the 'greater than' function, and I is the 'incomparable to' function. Using this approach, we are able to define a special class of fuzzy posets, and define the 'skeleton' of a fuzzy poset in view of major relation. In this sense, we define the linear discrepancy of a fuzzy poset of size n as the minimum value of all maximum of I(x, y)${\mid}$f(x)-f(y)${\mid}$ for f ${\in}$ F and x, y ${\in}$ X with I(x, y) > $\frac{1}{2}$, where F is the set of all injective order-preserving maps from the fuzzy poset to the set of positive integers. We first show that the definition is well-defined. Then, it is shown that the optimality appears at the same injective order-preserving maps in both cases of a fuzzy poset and its skeleton if the linear discrepancy of a skeleton of a fuzzy poset is 1.

Numerical measures of Indicating Placement of Posets on Scale from Chains to Antichains

  • Bae, Kyoung-Yul
    • The Journal of Information Technology and Database
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    • v.3 no.1
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    • pp.97-108
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    • 1996
  • In this paper we obtain several function defined on finite partially ordered sets(posets) which may indicate constraints of comparability on sets of teams(tasks, etc.) for which evaluation is computationally simple, a relatively rare condition in graph-based algorithms. Using these functions a set of numerical coefficients and associated distributions obtained from a computer simulation of certain families of random graphs is determined. From this information estimates may be made as to the actual linearity of complicated posets. Applications of these ideas is to all areas where obtaining rankings from partial information in rational ways is relevant as in, e.g., team_, scaling_, and scheduling theory as well as in theoretical computer science. Theoretical consideration of special and desirable properties of various functions is provided permitting judgment concerning sensitivity of these functions to changes in parameters describing (finite) posets.

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