• Title/Summary/Keyword: Interval

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ON INTERVAL-VALUED FUZZY LATTICES

  • LEE, JEONG GON;HUR, KUL;LIM, PYUNG KI
    • Honam Mathematical Journal
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    • v.37 no.2
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    • pp.187-205
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    • 2015
  • We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

Non-stochastic interval factor method-based FEA for structural stress responses with uncertainty

  • Lee, Dongkyu;Shin, Soomi
    • Structural Engineering and Mechanics
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    • v.62 no.6
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    • pp.703-708
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    • 2017
  • The goal of this study is to evaluate behavior uncertainties of structures by using interval finite element analysis based on interval factor method as a specific non-stochastic tool. The interval finite element method, i.e., interval FEM, is a finite element method that uses interval parameters in situations where it is not possible to get reliable probabilistic characteristics of the structure. The present method solves the uncertainty problems of a 2D solid structure, in which structural characteristics are assumed to be represented as interval parameters. An interval analysis method using interval factors is applied to obtain the solution. Numerical applications verify the intuitive effectiveness of the present method to investigate structural uncertainties such as displacement and stress without the application of probability theory.

An improved interval analysis method for uncertain structures

  • Wu, Jie;Zhao, You Qun;Chen, Su Huan
    • Structural Engineering and Mechanics
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    • v.20 no.6
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    • pp.713-726
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    • 2005
  • Based on the improved first order Taylor interval expansion, a new interval analysis method for the static or dynamic response of the structures with interval parameters is presented. In the improved first order Taylor interval expansion, the first order derivative terms of the function are also considered to be intervals. Combining the improved first order Taylor series expansion and the interval extension of function, the new interval analysis method is derived. The present method is implemented for a continuous beam and a frame structure. The numerical results show that the method is more accurate than the one based on the conventional first order Taylor expansion.

Confidence Intervals for a Proportion in Finite Population Sampling

  • Lee, Seung-Chun
    • Communications for Statistical Applications and Methods
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    • v.16 no.3
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    • pp.501-509
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    • 2009
  • Recently the interval estimation of binomial proportions is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the well-known Wald confidence interval. Various alternatives have been proposed. Among them, the Agresti-Coull confidence interval, the Wilson confidence interval and the Bayes confidence interval resulting from the noninformative Jefferys prior were recommended by Brown et al. (2001). However, unlike the binomial distribution case, little is known about the properties of the confidence intervals in finite population sampling. In this note, the property of confidence intervals is investigated in anile population sampling.

THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

  • Jang, Lee-Chae
    • Honam Mathematical Journal
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    • v.30 no.1
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    • pp.171-183
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    • 2008
  • In a previous work [18], the authors investigated autocontinuity, converse-autocontinuity, uniformly autocontinuity, uniformly converse-autocontinuity, and fuzzy multiplicativity of monotone set function defined by Choquet integral([3,4,13,14,15]) instead of fuzzy integral([16,17]). We consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [18]. These integrals, which can be regarded as interval-valued aggregation operators, have been used in [10,11,12,19,20]. In this paper, we investigate some characterizations of monotone interval-valued set functions defined by the interval-valued Choquet integral such as autocontinuity, converse-autocontinuity, uniform autocontinuity, uniform converse-autocontinuity, and fuzzy multiplicativity.

NEW CONCEPTS OF REGULAR INTERVAL-VALUED FUZZY GRAPHS

  • TALEBI, A.A.;RASHMANLOU, HOSSEIN;DAVVAZ, BIJAN
    • Journal of applied mathematics & informatics
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    • v.35 no.1_2
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    • pp.95-111
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    • 2017
  • Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

Interval-Valued Fuzzy Cosets

  • Lee, Keon-Chang;Hur, Kul;Lim, Pyung-Ki
    • Journal of the Korean Institute of Intelligent Systems
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    • v.22 no.5
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    • pp.646-655
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    • 2012
  • First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

A Note on Interval-Valued Fuzzy Soft Sets (Interval-Valued Fuzzy Soft sets 관한 연구)

  • Min, Won-Keun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.3
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    • pp.412-415
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    • 2008
  • In this paper, we show that the concepts of null interval-valued fuzzy and absolute interval-valued fuzzy soft sets are not reasonable. Thus we introduce the modified concepts for them and study some properties. Also we introduce an operation for the interval-valued fuzzy soft set theory and study basic properties.

INTERVAL-VALUED FUZZY SEMI-PREOPEN SETS AND INTERVAL-VALUED FUZZY SEMI-PRECONTINUOUS MAPPINGS

  • Jun, Young-Bae;Kim, Sung-Sook;Kim, Chang-Su
    • Honam Mathematical Journal
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    • v.29 no.2
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    • pp.223-244
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    • 2007
  • We introduce the notions of interval-valued fuzzy semipreopen sets (mappings), interval-valued fuzzy semi-pre interior and interval-valued fuzzy semi-pre-continuous mappings by using the notion of interval-valued fuzzy sets. We also investigate related properties and characterize interval-valued fuzzy semi-preopen sets (mappings) and interval-valued fuzzy semi-precontinuous mappings.

A NOTE ON THE MONOTONE INTERVAL-VALUED SET FUNCTION DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

  • Jang, Lee-Chae
    • Communications of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.227-234
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    • 2007
  • At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.