• Title, Summary, Keyword: Fuzzy Set Theory

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Generalized Intuitionistic Fuzzy Soft Sets

  • Park, Jin-Han;Kwun, Young-Chel;Hwang, Jin-Soo
    • Journal of 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.

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.

A study of hesitant fuzzy soft multiset theory

  • Onyeozili, I.A.;Balami, Holyheavy;Peter, C.M.
    • Annals of Fuzzy Mathematics and Informatics
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    • v.16 no.3
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    • pp.261-284
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    • 2018
  • In this paper, we recall the definition of soft set, fuzzy soft set, hesitant fuzzy set and hesitant fuzzy soft set and some of their examples. We define the concept of hesitant fuzzy soft multiset which combines hesitant fuzzy soft set and soft multiset theory. We also define basic terms in hesitant fuzzy soft multiset with relevant examples. Some basic operations such as restricted intersection, extended intersection, union, restricted union, AND-product and OR-product and their properties are given, supported with illustrative examples. We finally establish some important results, including De Morgan's inclusions and laws.

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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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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Inference of RMR Value Using Fuzzy Set Theory and Neuro-Fuzzy Techniques (퍼지집합이론 및 뉴로-퍼지기법을 이용한 RMR 값의 추론)

  • 배규진;조만섭
    • Tunnel and Underground Space
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    • v.11 no.4
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    • pp.289-300
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    • 2001
  • In the design of tunnel, it contains inaccuracy of data, fuzziness of evaluation, observer error and so on. The face observation during tunnel excavation, therefore, plays an important role to raise stability and to reduce supporting cost. This study is carried out to minimize the subjectiveness of observer and to exactly evaluate the natural properties of ground during the face observation. For these purpose, fuzzy set theory and neuro-fuzzy techniques in artificial intelligent techniques are applied to the inference of the RMR value from the observation data. The correlation between original RMR vague and inferred RM $R_{_FU}$ and RM $R_{_NF}$ values from fuzzy set theory and neuro-fuzzy techniques is investigated using 46 data. The results show that good correlation between original RMR value and infected RM $R_{_FU}$ and RM $R_{_NF}$ value is observed when the correlation coefficients are |R|=0.96 and |R|=0.95 respectively. From these results, applicability of fuzzy set theory and neuro-fuzzy techniques to rock mats classification is proved to be sufficiently high enough. enough.

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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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An Experimental Study on Fuzzy Document Retrieval System (퍼지개념을 적용한 질의식의 분석과 문헌정보 검색에 관한 연구)

  • Lee Seung Chai
    • Journal of the Korean Society for Library and Information Science
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    • v.21
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    • pp.249-290
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    • 1991
  • Theoretical developments in the information retrieval have offered a number of alternatives to traditional Boolean retrieval. Probability theory and fuzzy set theory have played prominent roles here. Fuzzy set theory is an attempt to generalize traditional set theory by permitting partial membership in a set and this means recognizing different degrees to which a document can match a request. In this study, an experimentation of a document retrieval system using the fuzzy relation matrix of the keywords is described and the results are offered. The queries composed of keywords and Boolean operaters AND, OR, NOT were processed in the retrieval method, and the method was implemented on the PC of 32bit level (30 MHz) in an experimental system. The measurement of the recall ratio and precision ratio verified the effectiveness of the proposed fuzzy relation matrix of keywords and retrieval method. Compared to traditional crisp method in the same document database, the recall ratio increased $10\%$ high although the precision ratio decreased slightly. The problems, in this experiment, to be resolved are first, the design of the automatic data input and fuzzy indexing modules, through which the system . can have the ability of competition and usefulness. Second, devising a systematic procedure for assigning fuzzy weights to keywords in documents and in queries.

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T-FUZZY INTEGRALS OF SET-VALUED MAPPINGS

  • CHO, SUNG JIN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.1
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    • pp.39-48
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    • 2000
  • In this paper we define T-fuzzy integrals of set-valued mappings, which are extensions of fuzzy integrals of the single-valued functions defined by Sugeno. And we discuss their properties.

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Operations on Generalized Intuitionistic Fuzzy Soft Sets

  • Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.3
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    • pp.184-189
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    • 2011
  • Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan's law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on generalized intuitionistic fuzzy soft sets. We discuss the basic properties of operations on generalized intuitionistic fuzzy soft sets such as necessity and possibility. Moreover, we illustrate their interconnections between each other.