• Title, Summary, Keyword: interval-valued fuzzy set

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

  • Min, Won-Keun
    • Journal of 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 Intuitionistic Fuzzy Soft Sets (구간치 Intuitionistic Fuzzy Soft sets 관한 연구)

  • Min, Won-Keun
    • Journal of Korean Institute of Intelligent Systems
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    • v.18 no.3
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    • pp.316-322
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    • 2008
  • We introduce the concept of interval-valued intuitionistic fuzzy soft sets, which is an extension of the interval-valued fuzzy soft set. We also introduce the concepts of operations for the interval-valued intuitionistic fuzzy soft sets and study basic some properties.

([r, s], [t, u])-INTERVAL-VALUED INTUITIONISTIC FUZZY GENERALIZED PRECONTINUOUS MAPPINGS

  • Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.25 no.1
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    • pp.1-18
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    • 2017
  • In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

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.

Interval-valued Fuzzy Ideals and Bi-ideals of a Semigroup

  • Cheong, Min-Seok;Hur, Kul
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.4
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    • pp.259-266
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    • 2011
  • We apply the concept of interval-valued fuzzy sets to theory of semigroups. We give some properties of interval-valued fuzzy ideals and interval-valued fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of interval-valued fuzzy ideals and intervalvalued fuzzy bi-ideals.

Lattices of Interval-Valued Fuzzy Subgroups

  • Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.14 no.2
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    • pp.154-161
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    • 2014
  • We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.

Comparison of Interval-valued fuzzy sets, Intuitionistic fuzzy sets, and bipolar-valued fuzzy sets (구간값 퍼지집합, Intuitionistic 퍼지집합, Bipolar-valued 퍼지집합의 비교)

  • Lee, Keon-Myung
    • Journal of Korean Institute of Intelligent Systems
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    • v.14 no.2
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    • pp.125-129
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    • 2004
  • There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic fuzzy sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

INTERVAL-VALUED FUZZY REGULAR LANGUAGE

  • Ravi, K.M.;Alka, Choubey
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.639-649
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    • 2010
  • In this paper, a definition of interval-valued fuzzy regular language (IVFRL) is proposed and their related properties studied. A model of finite automaton (DFA and NDFA) with interval-valued fuzzy transitions is proposed. Acceptance of interval-valued fuzzy regular language by the finite automaton (DFA and NDFA) with interval-valued fuzzy transitions are examined. Moreover, a definition of finite automaton (DFA and NDFA) with interval-valued fuzzy (final) states is proposed. Acceptance of interval-valued fuzzy regular language by the finite automaton (DFA and NDFA) with interval-valued fuzzy (final) states are also discussed. It is observed that, the model finite automaton (DFA and NDFA) with interval-valued fuzzy (final) states is more suitable than the model finite automaton (DFA and NDFA) with interval-valued fuzzy transitions for recognizing the interval-valued fuzzy regular language. In the end, interval-valued fuzzy regular expressions are defined. We can use the proposed interval-valued fuzzy regular expressions in lexical analysis.

Comparison of Interval-valued fuzzy sets, Intuitionistic fuzzy sets, and bipolar-valued fuzzy sets (구간값 퍼지집합, Intuitionistic 퍼지집합, Bipolar-valued 퍼지집합의 비교)

  • 이건명
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.12-15
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    • 2001
  • There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

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INTERVAL-VALUED FUZZY GENERALIZED BI-IDEALS OF A SEMIGROUP

  • Lee, Keon-Chang;Kang, Hee-Won;Hur, Kul
    • Honam Mathematical Journal
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    • v.33 no.4
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    • pp.603-616
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    • 2011
  • We introduce the concept of an interval-valued fuzzy generalized bi-ideal of a semigroup, which is an extension of the concept of an interval-valued fuzzy bi-ideal (and of a noninterval-valued fuzzy bi-ideal and a noninterval-valued fuzzy ideal of a semi-group), and characterize regular semigroups, and both intraregular and left quasiregular semigroup in terms of interval-valued fuzzy generalized bi-ideals.