• Title/Summary/Keyword: set theory

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Extracting Method of Kansei Design Rules Based on Rough Set Analysis

  • Nishino, Tatsuo;Nagamachi, Mitsuo
    • Proceedings of the Korean Society for Emotion and Sensibility Conference
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    • 2002.05a
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    • pp.201-204
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    • 2002
  • Kansei design knowledge acquisition stage is a crucial stage in kansei designing process and kansei engineering (KE) methodology. In kansei engineering methodology, it is essential to extract design knowledge or rules on relationships between customer's kansei and product design element. We attempt to construct a more powerful melted for extracting the design rules from kansei expremental data. We constucted a kansei experiment concerning color kansei evaluation, and analyzed the sane data by both conventional quantification theory type I and rough set theory. Finally, we compared the effectiveness of both methods for extracting rules and examined the extensions of rough set theory in kansei engineering.

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REPRESENTATION OF INTUITIONISTIC FUZZY SOFT SET USING COMPLEX NUMBER

  • KHAN, MOHSIN
    • Journal of applied mathematics & informatics
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    • v.35 no.3_4
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    • pp.331-347
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    • 2017
  • Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.

CORE STABILITY OF DOMINATING SET GAMES

  • Kong, Liang;Fang, Qizhi;Kim, Hye-Kyung
    • Journal of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.871-881
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    • 2008
  • In this paper, we study the core stability of the dominating set game which has arisen from the cost allocation problem related to domination problem on graphs. Let G be a graph whose neighborhood matrix is balanced. Applying duality theory of linear programming and graph theory, we prove that the dominating set game corresponding to G has the stable core if and only if every vertex belongs to a maximum 2-packing in G. We also show that for dominating set games corresponding to G, the core is stable if it is large, the game is extendable, or the game is exact. In fact, the core being large, the game being extendable and the game being exact are shown to be equivalent.

Improvement of ID3 Using Rough Sets (라프셋 이론이 적용에 의한 ID3의 개선)

  • Chung, Hong;Kim, Du-Wan;Chung, Hwan-Mook
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1997.10a
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    • pp.170-174
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    • 1997
  • This paper studies a method for making more efficient classification rules in the ID3 using the rough set theory. Decision tree technique of the ID3 always uses all the attributes in a table of examples for making a new decision tree, but rough set technique can in advance eleminate dispensable attributes. And the former generates only one type of classification rules, but the latter generates all the possibles types of them. The rules generated by the rough set technique are the simplist from as proved by the rough set theory. Therefore, ID3, applying the rough set technique, can reduct the size of the table of examples, generate the simplist form of the classification rules, and also implement an effectie classification system.

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Rough Set-based Incremental Inductive Learning Algorithm Theory and Applications

  • Bang, Won-Chul;Z. Zenn Bien
    • Journal of the Korean Institute of Intelligent Systems
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    • v.11 no.7
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    • pp.666-674
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    • 2001
  • Classical methods to find a minimal set of rules based on the rough set theory are known to be ineffective in dealing with new instances added to the universe. This paper introduces an inductive learning algorithm for incrementally retrieving a minimal set of rules from a given decision table. Then, the algorithm is validated via simulations with two sets of data, in comparison with a classical non-incremental algorithm. The simulation results show that the proposed algorithm is effective in dealing with new instances, especially in practical use.

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The Improvement of Rough- set Theory Histogram in Color- image Segmentation

  • Zheng, Qi;Lee, Hyo Jong
    • Proceedings of the Korea Information Processing Society Conference
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    • 2011.11a
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    • pp.429-430
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    • 2011
  • Roughness set theory is a popular topic to use in color-image segmentation. A new popular color image segmentation algorithm is proposed by scientists with the point using traditional histogram and Histon construct roughness set histogram. But, there is still a problem about that is the correlativity of color vector in roughness set histogram, which take an inactive effect in the process of color-image segmentation. Therefore, this paper represents further research based on this and proposed an improved method proved through lot of experiments. The experimental result reduces the correlativity of color vector in roughness set histogram and calculation time remarkably.

A Linguistic Study on the Writing of Section 'Sets' in Middle School Mathematics Textbooks of 7-ga (중학교 수학교과서 7-가의 집합 단원 기술에 관한 언어학적 고찰)

  • Jeong Kwang-Taek
    • School Mathematics
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    • v.8 no.2
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    • pp.177-213
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    • 2006
  • It is well known that the set theory is very fundamental and important in modern mathematics. So, the middle school mathematics begins with section 'Sets' which is introduced from the 2nd curriculum change. Therefore, it is natural to arrange the set theory at the beginning of middle school mathematics curriculum. But most of text-books develop the set theory section very rigorously and tightly under less considering the student's language level. The purpose of this study is to have effective learning of set theory section for every middle school students, we analysis the definitions and writing contents of section 'Sets' in each textbooks as a linguistic viewpoint, and investigate its further uses in each textbooks.

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Inference System Fusing Rough Set Theory and Neuro-Fuzzy Network (Rough Set Theory와 Neuro-Fuzzy Network를 이용한 추론시스템)

  • Jung, Il-Hun;Seo, Jae-Yong;Yon, Jung-Heum;Cho, Hyun-Chan;Jeon, Hong-Tae
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.36S no.9
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    • pp.49-57
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    • 1999
  • The fusion of fuzzy set theory and neural networks technologies have concentrated on applying neural networks to obtain the optimal rule bases of fuzzy logic system. Unfortunately, this is very hard to achieve due to limited learning capabilities of neural networks. To overcome this difficulty, we propose a new approach in which rough set theory and neuro-fuzzy fusion are combined to obtain the optimal rule base from input/output data. Compared with conventional FNN, the proposed algorithm is considerably more realistic because it reduces overlapped data when construction a rule base. This results are applied to the construction of inference rules for controlling the temperature at specified points in a refrigerator.

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A Study for Process Planning of Progressive Working by the using of Fuzzy Set Theory (Fuzzy set 이론을 이용한 프로그레시브 가공의 공정설계에 관한 연구)

  • Kim, Y. M.;Kim, J. H.;Kim, C.;Choi, J. C.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2001.04a
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    • pp.735-739
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    • 2001
  • This paper describes a research work of developing computer-aided design of a product with bending and piercing for progressive working. An approach to the system for progressive working os based on the knowledge-based rules. Knowledge for the system is formulated from plasticity theorise, experimental results and the empirical knowledge of field experts. the system has been written in AutoLISP on the AutoCAD with a personal computer and is composed of three main modules, which are input and shape treatment, flat pattern layout and strip layout modules. Strip layout of the system is designed by using fuzzy set theory. Process planning is determinated by fuzzy value according to several rules. Strip layout drawing generated in strip layout module is presented in 3-D graphic forms, including bending sequences and piercing processes with punch profiles divided into for external area. Results obtained using the modules enable the manufacturer for progressive working of electric products to be more efficient in this field.

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Concept Structures, Functional Equivalence and the East Asian Welfare State Discussion: An Application of Set Theory in Comparative Social Policy (개념구조, 기능적 등가물 그리고 동아시아복지국가론: 비교사회정책연구에서 집합이론의 활용)

  • Lee, Sophia Seung-yoon
    • 한국사회정책
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    • v.19 no.3
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    • pp.185-214
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    • 2012
  • After the introduction of the three welfare regimes by Esping-Andersen, discussion on 'other' types of welfare regimes was facilitated and the scholarly focus on East Asian economic development gradually shifted to the East Asian welfare states discussion from the late 1990s. Literature on East Asian welfare states increased our understanding on the characteristics of not only the East Asian welfare state as a whole but also of each country in the region. However, compared the attention given to developing variables and empirical studies on the East Asian welfare state, less attention has been given to the concept of East Asian welfare states. Recognizing the limitation in developing comparable variables without a concept analysis of the East Asian welfare states, this study highlights the importance of conceptualization and concept analysis in comparative social policy studies. This paper first discusses on the concepts, conceptualization and on the use of set theory in comparative social policy research. Next, the study argues the validity of 'functional equivalence' in the East Asian welfare state studies and critically reviews the existing literature. Lastly, this paper suggests how the concept of functional equivalence can be successfully employed for the East Asian welfare states studies with a concept analysis and by applying a set theory including the fuzzy set theory.