• 제목/요약/키워드: Intuitionistic set theory

검색결과 12건 처리시간 0.022초

Generalized Intuitionistic Fuzzy Soft Sets

  • Park, Jin-Han;Kwun, Young-Chel;Hwang, Jin-Soo
    • 한국지능시스템학회논문지
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    • 제21권3호
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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.

Operations on Generalized Intuitionistic Fuzzy Soft Sets

  • Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제11권3호
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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.

REPRESENTATION OF INTUITIONISTIC FUZZY SOFT SET USING COMPLEX NUMBER

  • KHAN, MOHSIN
    • Journal of applied mathematics & informatics
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    • 제35권3_4호
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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.

ROUGH SET THEORY APPLIED TO INTUITIONISTIC FUZZY IDEALS IN RINGS

  • Jun, Young-Bae;Park, Chul-Hwan;Song, Seok-Zun
    • Journal of applied mathematics & informatics
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    • 제25권1_2호
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    • pp.551-562
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    • 2007
  • This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

A NOTE ON WEAK EXCLUDED MIDDLE LAW

  • Chanyoung Sung
    • 충청수학회지
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    • 제36권1호
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    • pp.9-11
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    • 2023
  • Intuitionistic Zermelo-Fraenkel (IZF) set theory is a set theory without the axiom of choice and the law of excluded middle (LEM). The weak excluded middle law (WEM) states that ¬𝜑∨¬¬𝜑 for any formula 𝜑. In IZF we show that LEM is equivalent to WEM plus the condition that any set not equal to the empty set has an element.

INTUITIONISTIC FUZZY IDEALS AND BI-IDEALS

  • HUR, KUL;KIM, KWANG JIN;SONG, HYEONG KEE
    • 호남수학학술지
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    • 제26권3호
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    • pp.309-330
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    • 2004
  • In this paper, we apply the concept of intuitionistic fuzzy sets to theory of semigroups. We give some properties of intuitionistic fuzzy ideals and intuitionistic 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 intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

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A Novel Image Segmentation Method Based on Improved Intuitionistic Fuzzy C-Means Clustering Algorithm

  • Kong, Jun;Hou, Jian;Jiang, Min;Sun, Jinhua
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제13권6호
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    • pp.3121-3143
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    • 2019
  • Segmentation plays an important role in the field of image processing and computer vision. Intuitionistic fuzzy C-means (IFCM) clustering algorithm emerged as an effective technique for image segmentation in recent years. However, standard fuzzy C-means (FCM) and IFCM algorithms are sensitive to noise and initial cluster centers, and they ignore the spatial relationship of pixels. In view of these shortcomings, an improved algorithm based on IFCM is proposed in this paper. Firstly, we propose a modified non-membership function to generate intuitionistic fuzzy set and a method of determining initial clustering centers based on grayscale features, they highlight the effect of uncertainty in intuitionistic fuzzy set and improve the robustness to noise. Secondly, an improved nonlinear kernel function is proposed to map data into kernel space to measure the distance between data and the cluster centers more accurately. Thirdly, the local spatial-gray information measure is introduced, which considers membership degree, gray features and spatial position information at the same time. Finally, we propose a new measure of intuitionistic fuzzy entropy, it takes into account fuzziness and intuition of intuitionistic fuzzy set. The experimental results show that compared with other IFCM based algorithms, the proposed algorithm has better segmentation and clustering performance.

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

  • 이건명
    • 한국지능시스템학회논문지
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    • 제14권2호
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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.

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

  • 이건명
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 2001년도 춘계학술대회 학술발표 논문집
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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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A Generalized Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems

  • Park, Jin-Han;Kwun, Young-Chel;Son, Mi-Jung
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제11권2호
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    • pp.71-76
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    • 2011
  • The problem of decision making under imprecise environments are widely spread in real life decision situations. We present a method of object recognition from imprecise multi observer data, which extends the work of Roy and Maji [J Compu. Appl. Math. 203(2007) 412-418] to generalized intuitionistic fuzzy soft set theory. The method involves the construction of a comparison table from a generalized intuitionistic fuzzy soft set in a parametric sense for decision making.