• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.121-135
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• 1999

This paper studies the problem of inverting minimal path sets to obtain minimal cut sets for complex system. We describe efficiency of inversion algorithm by the use of boolean algebra and we develop inclusion-exclusion algorithm and pivotal decomposition algorithm for reliability calculation of complex system. Several examples are illustrated and the computation speeds between the two algorithms are undertaken.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.63-66
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• 2002

As a generalization of fuzzy sets, the concept of interval-valued fuzzy sets was introduced by Gorzalczany(GO). In this paper, we shall extend the concept of "fuzzy inclusion", introduced by Sostak[SO1], to the interval-valued fuzzy setting and study its fundamental properties for some extent.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.263-281
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• 2022

The main aim of this paper is to discuss two different types of soft hemirings, soft intersection and soft union. We discuss applications and results related to soft intersection hemirings or soft intersection k-ideals and soft union hemirings or soft union k-ideals. The deep concept of k-closure, intersection and union of soft sets, ∧-product and ∨-product among soft sets, upper 𝛽-inclusion and lower 𝛽-inclusion of soft sets is discussed here. Many applications related to soft intersection-union sum and soft intersection-union product of sets are investigated in this paper. We characterize k-hemiregular hemirings by the soft intersection k-ideals and soft union k-ideals.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.69-83
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• 2022

We investigate the concept of lacunary statistical convergence and lacunary strongly convergence for sequence of sets in intuitionistic fuzzy metric space (IFMS) and examine their characterization. We obtain some inclusion relation relating to these concepts. Further some necessary and sufficient conditions for equality of the sets of statistical convergence and lacunary statistical convergence for sequence of sets in IFMS have been established. The concept of strong Cesàro summability in IFMS has been defined and some results are established.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.515-530
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• 2011

This paper deals with the existence result of solutions of a second order functional differential inclusion, governed by a class of nonconvex sweeping process, with a nonconvex perturbation.

• Nuclear Engineering and Technology
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• v.24 no.1
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• pp.14-29
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• 1992

COMCAF, a computer code for the common-cause failure analysis, is developed to treat the common-cause failures in nuclear power plants. In the treatment of common-cause failures, the minimal cut sets of the system are obtained first without changing the fault-tree structure. The occurrence probabilities of the minimal cut sets are then calculated accounting for the common-cause failures among components in the same minimal cut set or in different minimal cut sets. The basic parameter model is used to model the common-cause failures between similar or identical components. For dissimilar components, the assumption of symmetry used in the basic parameter model is applied to the basic events affecting two or more components. The top event probability is evaluated using the inclusion-exclusion method. In addition to the common-cause failures of components in the same minimal cut sets, failures of components in the different minimal cut sets are also easily accounted for by this method. This study applied this common-cause failure analysis to the PWR auxiliary feedwater system. The results in the top event probability for the system are compared with those of no common-cause failures.

• Environmental Engineering Research
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• v.25 no.3
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• pp.418-425
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• 2020

In this study soft computing techniques including, Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were investigated for the prediction of Cr(VI) transport efficiency by novel Polymer Inclusion Membranes (PIMs). Transport experiments carried out by varying parameters such as time, film thickness, carrier type, carier rate, plasticizer type, and plasticizer rate. The predictive performance of ANN and ANFIS model was evaluated by using statistical performance criteria such as Root Mean Standard Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R²). Moreover, Sensitivity Analysis (SA) was carried out to investigate the effect of each input on PIMs Cr(VI) removal efficiency. The proposed ANN model presented reliable and valid results, followed by ANFIS model results. RMSE and MAE values were 0.00556, 0.00163 for ANN and 0.00924, 0.00493 for ANFIS model in the prediction of Cr(VI) removal efficiency on testing data sets. The R² values were 0.973 and 0.867 on testing data sets by ANN and ANFIS, respectively. Results show that the ANN-based prediction model performed better than ANFIS. SA demonstrated that time; film thickness; carrier type and plasticizer type are major operating parameters having 33.61%, 26.85%, 21.07% and 8.917% contribution, respectively.

• Journal of the Korean Society of Safety
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• v.11 no.1
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• pp.16-26
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• 1996

In a series of original papers, [1-17] efficient methods and algorithms have been presented, for the exact solution of many reliability problems represented by binary networks. A starting point of these methods was the concept of domination, firstly introduced in ,elation with reliability problems in [2]. It's application to directed networks resulted in the development of a topological formula for the classical problem of the two terminal reliability. This result was extended later to the all-terminal and the k-terminal reliability problems. All papers mentioned above use a path oriented representation for the network topology. In practical applications, however, it is common and often advantageous to work with cut sets. This article considers the Domination theory for reliability problem of a network. Some topological formula are derived and the power and the application of this formula are shown through the alternative proof of topological formula of A. Satyanarayana [2].

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.573-578
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• 1998

In this paper, we propose a new technique of codification. The purpose of this method is to take in consideration the natural language nuances and the fuzziness that characterizes the human reasoning. So, we warranted a means of more flexible encoding that translates as well the linguistic descriptions. Its principle is simple and intuitive. It consists simply in replacing in ambiguous cases, a unique number by an interval. The introduction of the new codification necessitates the elaboration of metric or similarity in order to compare two intervals. This comparison must take in consideration the difference of their size, the remoteness of their center and the width of their intersection. In consequence, we defined three new fuzzy concepts : "fuzzy inclusion degree", "fuzzy resemblance degree," and " fuzzy curve".

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.589-597
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• 2018

For $A,B{\in}M_2(\mathbb{C})$, let the Jordan product be AB + BA and G(A) the eigenvalue inclusion set, the Gershgorin set of A. Characterization is obtained for maps ${\phi}:M_2(\mathbb{C}){\rightarrow}M_2(\mathbb{C})$ satisfying $$G[{\phi}(A){\phi}(B)+{\phi}(B){\phi}(A)]=G(AB+BA)$$ for all matrices A and B. In fact, it is shown that such a map has the form ${\phi}(A)={\pm}(PD)A(PD)^{-1}$, where P is a permutation matrix and D is a unitary diagonal matrix in $M_2(\mathbb{C})$.