• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.4
• /
• pp.556-561
• /
• 2009

In this paper, we propose new method to calculate the distance between intuitionistic fuzzy sets(IFSs) based on the three dimensional representation of IFSs and analyze the relations of similarity measure and distance measure of IFSs. Finally, we apply the proposed measures to pattern recognitions.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.1
• /
• pp.8-11
• /
• 2011

Atanassov [1,2] and Szmidt and Kacprzyk[7,8] studied various methods for measuring distances between intuitionistic fuzzy sets. In this paper, we consider interval-valued intuitionistic fuzzy sets and discuss these methods for measuring distances between interval-valued intuitionistic fuzzy sets.

• Communications of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.23-34
• /
• 2015

We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.12a
• /
• pp.9-12
• /
• 2002

Representation and quantification of fuzziness are required for the uncertain system modelling and controller design. Conventional results show that entropy of fuzzy sets represent the fuzziness of fuzzy sets. In this literature, the relations of fuzzy enropy, distance measure and similarity measure are discussed, and distance measure is proposed. With the help of relations of fuzzy enropy, distance measure and similarity measure, fuzzy entropy is represented by the newly proposed distance measure. With simple fuzzy set, example is illustrated.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.4
• /
• pp.455-459
• /
• 2007

Interval-valued fuzzy sets were suggested for the first time by Gorzafczany(1983) and Turksen(1986). Based on this, Zeng and Li(2006) introduced concepts of similarity measure and entropy on interval-valued fuzzy sets which are different from Bustince and Burillo(1996). In this paper, by using Choquet integral with respect to a fuzzy measure, we introduce distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets and discuss some properties of them. Choquet integral is a generalization concept of Lebesgue inetgral, because the two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure.

• Communications of the Korean Mathematical Society
• /
• v.28 no.4
• /
• pp.833-850
• /
• 2013

We present an algorithm for computing the Hausdorff distance between two parametric curves in $\mathbb{R}^n$, or more generally between two sets of parametric curves in $\mathbb{R}^n$. During repeated subdivision of the parameter space, we prune subintervals that cannot contain an optimal point. Typically, our algorithm costs O(logM) operations, compared with O(M) operations for a direct, brute-force method, to achieve an accuracy of $O(M^{-1})$.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.12 no.6
• /
• pp.583-588
• /
• 2002

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. Tt is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of $F\bigcapF^c and F\bigcupF^c$, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of $F\bigcapF^c and F\bigcupF^c$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.12a
• /
• pp.13-16
• /
• 2002

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] Proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. It is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.30 no.9C
• /
• pp.854-859
• /
• 2005

We construct the fuzzy entropy for measuring of uncertainty with the help of relation between distance measure and similarity measure. Proposed fuzzy entropy is constructed through distance measure. In this study, the distance measure is used Hamming distance measure. Also for the measure of similarity between fuzzy sets or crisp sets, we construct similarity measure through distance measure, and the proposed 려zzy entropies and similarity measures are proved.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.5
• /
• pp.521-526
• /
• 2005

The fuzzy entropy is proposed for measuring of uncertainty with the help of relation between distance measure and similarity measure. The proposed fuzzy entropy is constructed through a distance measure. In this study, Hamming distance measure is employed for a distance measure. Also a similarity measure is constructed through a distance measure for the measure of similarity between fuzzy sets or crisp sets and the proposed fuzzy entropies and similarity measures are proved.