• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.328-331
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• 2001

In Cretu [Fuzzy Sets and Systems 120(2001) 371-383], triangular norms and their hierarchy are investigated. In this paper, we give new proofs which are significantly shorter than those given in Cretu, applying a known result which involves only one argument of one-place rather than two place arguments by Klement et al. [FSS 86(1997) 189-195]

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.139-145
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• 2002

In Cretu (2001), triangular norms and their hierarchy are investigated. In this paper, we give new proofs which are significantly shorter than those given in Cretu, applying a known result which involves only one argument of one-place rather than two-place argument s by Klement et al.(1997).

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.353-359
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• 2017

Starting from a t-norm T, it is possible to construct a class of new t-norms, so-called T-generalized t-norm. The purpose of this paper is to describe some properties of this class of generalized t-norms. An algebraic structure as well as a binary relation among t-norms are also investigated. Some open problems are discussed as well.

• Journal of Software Assessment and Valuation
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• v.16 no.2
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• pp.153-162
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• 2020

Digital image forgery detection is one of very important fields in the field of digital forensics. As the forged images change naturally through the advancement of technology, it has made it difficult to detect forged images. In this paper, we use passive forgery detection for copy paste forgery in digital images. In addition, it detects copy-paste forgery using the L₀ Norm-based LE operator, and compares the detection accuracy with the forgery detection using the existing L₂, L₁ Norm-based LE operator. In comparison of detection rates, the proposed lower triangular(Ayalneh and Choi) window was more robust to BAG mismatch detection than the conventional window filter. In addition, in the case of using the lower triangular window, the performance of image forgery detection was measured increasingly higher as the L₂, L₁ and L₀ Norm LE operator was performed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.7
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• pp.2420-2433
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• 2014

Fusing the scores of multibiometrics is a very promising approach to improve the overall system's accuracy and the verification performance. In recent years, there are several approaches towards studying score level fusion of several biometric systems. However, most of them does not consider the genuine and imposter score distributions and result in a higher equal error rate usually. In this paper, a novel score level fusion approach of different biometric systems (dual iris, thermal and visible face traits) based on $Acz{\acute{e}}l$-Alsina triangular norm is proposed. It achieves higher identification performance as well as acquires a closer genuine distance and larger imposter distance. The experimental tests are conducted on a virtual multibiometrics database, which merges the challenging CASIA-Iris-Thousand database with noisy samples and the NVIE face database with visible and thermal face images. The rigorous results suggest that significant performance improvement can be achieved after the implementation of multibiometrics. The comparative experiments also ascertain that the proposed fusion approach outperforms the state-of-art verification performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.99-106
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• 2005

We present a relation between the orthogonality of the constrained Legendre polynomials over the triangular domain and the BB ($B{\acute{e}zier}\;-Bernstein$) coefficients of the polynomials using the equivalence of orthogonal complements. Using it we also show that the best constrained degree reduction of polynomials in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.565-579
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• 2009

In this paper, we give some new fixed point theorems for contractive type mappings in intuitionistic fuzzy metric spaces. We improve and generalize the well-known fixed point theorems of Banach [4] and Edelstein [8] in intuitionistic fuzzy metric spaces. Our main results are intuitionistic fuzzy version of Fang's results [10]. Further, we obtain some applications to validate our main results to product spaces.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.411-424
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• 2006

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck's common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem ([21]).

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.11-23
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• 2013

In this paper, we obtain a common fixed point theorem for multivalued mappings in a complete Menger $\mathcal{L}$-fuzzy metric space. $\mathcal{L}$-fuzzy metric space is a generalization of fuzzy metric spaces and intuitionistic fuzzy metric spaces. We extend and generalize the results of Kubiaczyk and Sharma [24], Sharma, Kutukcu and Rathore [34].

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1287-1303
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• 2015

The Hausdorff topology induced by a fuzzy metric space under more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy metric space based on a natural concept of Cauchy sequence in fuzzy metric space.