• Title, Summary, Keyword: set theory

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Soft sets in fuzzy setting

  • Chen, Xueyou
    • Annals of Fuzzy Mathematics and Informatics
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    • v.16 no.2
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    • pp.223-237
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    • 2018
  • Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. In 1982, Pawlak initiated the rough set theory, Dubois and Prade combined fuzzy sets and rough sets all together. In 1999, Molodtsov introduced the concept of soft sets to solve complicated problems and various types of uncertainties. Maji et al. studied the (Zadeh's) fuzzification of the soft set theory. As a generalization, I define the notion of a soft set in L-set theory, introduce several operators for L-soft set theory, and investigate the rough operators on $L^X$ induced by an L-soft set.

Generalized Intuitionistic Fuzzy Soft Sets

  • Park, Jin-Han;Kwun, Young-Chel;Hwang, Jin-Soo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.21 no.3
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    • pp.389-394
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    • 2011
  • The notion of generalized intuitionistic fuzzy soft set theory is proposed. Our generalized intuitionistic fuzzy soft set theory is a combination of the generalized intuitionistic fuzzy set theory and the soft set theory. In other words, our generalized intuitionistic fuzzy soft set theory is an extension of the intuitionistic fuzzy soft set theory. The complement, "and" and "or" operations are defined on the generalized intuitionistic fuzzy soft sets. Their basic properties for the generalized intuitionistic fuzzy soft sets are also presented and discussed.

A Philosophical Implication of Rough Set Theory (러프집합론의 철학적 함의)

  • Park, Chang Kyun
    • Korean Journal of Logic
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    • v.17 no.2
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    • pp.349-358
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    • 2014
  • Human being has attempted to solve the problem of imperfect knowledge for a long time. In 1982 Pawlak proposed the rough set theory to manipulate the problem in the area of artificial intelligence. The rough set theory has two interesting properties: one is that a rough set is considered as distinct sets according to distinct knowledge bases, and the other is that distinct rough sets are considered as one same set in a certain knowledge base. This leads to a significant philosophical interpretation: a concept (or an event) may be understood as different ones from different perspectives, while different concepts (or events) may be understood as a same one in a certain perspective. This paper claims that such properties of rough set theory produce a mathematical model to support critical realism and theory ladenness of observation in the philosophy of science.

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Proposals on Teaching the Set Theory in Secondary School (집합교육의 개선에 대한 몇 가지 제언)

  • 이만근
    • Journal of Educational Research in Mathematics
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    • v.11 no.1
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    • pp.103-111
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    • 2001
  • The set concept has long been recognized as important for organizing traditional mathematics. Although 'to understand mathematical structure' is an important educational purpose, we think that leaching the abstract set theory in the 7th grade is too early. In this paper, we reviewed the set theory in the secondary school and we made some proposals such like that we must accept the term 'set' as 'collection' in 7th grade.

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On the applications of fuzzy approaches in medical diagnosis and bioinformatics (의학 진단 및 생물 정보학 분야에서 퍼지 접근법의 적용에 관한 연구)

  • Jung, Hye-Young
    • Journal of the Korean Data and Information Science Society
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    • v.29 no.6
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    • pp.1445-1456
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    • 2018
  • The relationships, properties, and objects in the data generated from medical diagnosis and bioinformatics are fundamentally fuzzy. Fuzzy set theory is an ideal framework to deal with such data. Fuzzy set theory is considered to be an extended set theory to deal with uncertainty of boundary and classification. In this paper, we illustrate how fuzzy approaches based on fuzzy set theory can be applied to data in medical diagnostics and bioinformatics with various examples.

Inductive Learning Algorithm using Rough Set Theory (Rough Set 이론을 이용한 연역학습 알고리즘)

  • 방원철;변증남
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.331-337
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    • 1997
  • In this paper we will discuss a type of inductive learning called learning from examples, whose task is to induce general descriptions of concepts from specific instances of these concepts. In many real life situations however new instances can be added to the set of instances. It is first proposed within the framework of rough set theory, for such cases, an algorithm to find minimal set of rules for decision tables without recalculation for overall set of instances. The method of learning presented here is based on a rough set concept proposed by Pawlak[2]. It is shown an algorithm to fund minimal set of rules using reduct change theorems giving criteria for minimum recalculation and an illustrative example.

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Determination of the Input/Output Relations and Rule Generation for Fuzzy Combustion Control System of Refuse Incinerator using Rough Set Theory (Rough Set 이론을 이용한 쓰레기 소각로의 퍼지제어 시스템을 위한 입출력 관계 설정 및 규칙 생성)

  • 방원철;변증남
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.81-86
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    • 1997
  • It is proposed, for fuzzy combustion control system of refuse incinerator to find the relationship between inputs and outputs and to generate rules to control by using rough set theory. It is not easy to find out the corresponding inputs for each output and the control rules with incomplete or imprecise information consisting expert knowledge, process and manipulator values in the field, and operation manual for the given system. Most decision problems can be formulated employing decision table formalism. A decision table on fuzzy combustion control system for refuse incinerator is simplified and produces control(rules). The I/O realtions and the control rules found by rough set theory are compared with the previous result.

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A Study on the Development of Regional Innovative Capability Indices Using Fuzzy Multi-Criteria Decision Making (퍼지다기준 의사결정기법을 이용한 지역혁신역량지수의 도출)

  • Heo, Jae-Yong
    • Journal of Technology Innovation
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    • v.16 no.1
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    • pp.1-21
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    • 2008
  • We attempt to make regional innovative capability indices for overall understanding of regional innovation. We'll analyze various indicators on it using fuzzy set theory and compare regional innovative capabilities of 16 regions in Korea. The fuzzy set theory can reflect more normally the uncertainty of the stakeholder's responses than other decision making analysis methods. The overall results suggest that experts on regional innovation rank GRDP most important and Daejeon is the most innovative region. Building up regional innovative capabilities should be made for more balanced national land development.

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A study on a design of developed-ERES/WCS using the ASR and fuzzy set theory as a part of human interface technique (Human interface 기술의 일환으로서 ASR과 fuzzy set theory를 이용한 developed-ERES/WCS 설계에 관한 연구)

  • 이순요;이창민;박세권
    • 제어로봇시스템학회:학술대회논문집
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    • pp.76-81
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    • 1988
  • As a means of human interface, this study designs Developed-ERES/WCS with voice recognition capability and fuzzy set theory. In the advanced teleoperator system, when an error occurs on the automatic mode, the error is recovered after the automatic mode is changed into the manual mode intervened by a human. The purpose of this study is to reduce human work load and to shorten error recovery time during error recovery.

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