• Kyungpook Mathematical Journal
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• 제32권1호
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• pp.21-30
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• 1992

• Communications of the Korean Mathematical Society
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• 제30권3호
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• pp.277-282
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• 2015

We obtain some conditions for disconnectedness of a topological space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interrelations between them. In particular, we show that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected. We also obtain a result concerning a minimal open set on a subspace.

• Honam Mathematical Journal
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• 제32권2호
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• pp.307-331
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• 2010

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy ${\gamma}$-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy ${\gamma}$-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy ${\gamma}$-open set is discussed.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.743-749
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• 2021

The purpose of this article is to study few properties of fuzzy mean open and fuzzy mean closed sets in fuzzy topological spaces. Further, the idea of fuzzy mean clopen set is introduced. It is observed that a fuzzy mean clopen set is both fuzzy mean open and fuzzy mean closed but the converse is not true.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권5호
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• pp.1755-1777
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• 2022

The development of wireless communication technology has led to the underutilization of radio spectra. To address this limitation, an intelligent cognitive radio network was developed. Specific emitter identification (SEI) is a key technology in this network. However, in realistic non-cooperative scenarios, the system may detect signal classes beyond those in the training database, and only a few labeled signal samples are available for network training, both of which deteriorate identification performance. To overcome these challenges, a meta-learning-based open-set identification system is proposed for SEI. First, the received signals were pre-processed using bi-spectral analysis and a Radon transform to obtain signal representation vectors, which were then fed into an open-set SEI network. This network consisted of a deep feature extractor and an intrinsic feature memorizer that can detect signals of unknown classes and classify signals of different known classes. The training loss functions and the procedures of the open-set SEI network were then designed for parameter optimization. Considering the few-shot problems of open-set SEI, meta-training loss functions and meta-training procedures that require only a few labeled signal samples were further developed for open-set SEI network training. The experimental results demonstrate that this approach outperforms other state-of-the-art SEI methods in open-set scenarios. In addition, excellent open-set SEI performance was achieved using at least 50 training signal samples, and effective operation in low signal-to-noise ratio (SNR) environments was demonstrated.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제17권6호
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• pp.1743-1758
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• 2023

Automatic modulation classification is a critical algorithm for non-cooperative communication systems. This paper addresses the challenging problem of closed-set and open-set signal modulation classification in complex channels. We propose a novel approach that incorporates a self-learning filter and center-loss in Deep Residual Shrinking Networks (DRSN) for closed-set modulation classification, and the Opendistance method for open-set modulation classification. Our approach achieves better performance than existing methods in both closed-set and open-set recognition. In closed-set recognition, the self-learning filter and center-loss combination improves recognition performance, with a maximum accuracy of over 92.18%. In open-set recognition, the use of a self-learning filter and center-loss provide an effective feature vector for open-set recognition, and the Opendistance method outperforms SoftMax and OpenMax in F1 scores and mean average accuracy under high openness. Overall, our proposed approach demonstrates promising results for automatic modulation classification, providing better performance in non-cooperative communication systems.

• Journal of Applied and Pure Mathematics
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• 제4권1_2호
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• pp.79-84
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• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological spaces.

• Journal of the Chungcheong Mathematical Society
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• 제30권2호
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• pp.165-175
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• 2017

This paper gives an extensive study of ideal topological space and introduce two new types of set with the help of local function. Several characterizations of these sets will also be discussed through this paper and finally gives new representation of ${\alpha}$-sets and semi-open sets.

• Communications of the Korean Mathematical Society
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• 제32권1호
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• pp.175-181
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• 2017

In this paper, we introduce a notion of cleanly covered topological spaces along with two strong separation axioms. Some properties of cleanly covered topological spaces are obtained in term of maximal open sets including some similar properties of a topological space in term of maximal closed sets. Two strong separation axioms are also investigated in terms of minimal open and maximal closed sets.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.251-257
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• 2021

This article is devoted to introduce the notion of fuzzy cleanly covered fuzzy topological spaces; in addition two strong fuzzy separation axioms are studied. By means of fuzzy maximal open sets some properties of fuzzy cleanly covered fuzzy topological spaces are obtained and also by means of fuzzy maximal closed sets few identical results of a fuzzy topological spaces are investigated. Through fuzzy minimal open and fuzzy maximal closed sets, two strong fuzzy separation axioms are discussed.