• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.61-79
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• 2012

In this paper, we investigate soft hemirings by fuzzy theory. Some characterizations of hemirings are introduced by means of soft sets. In particular, the $h$-hemiregular hemirings and $h$-intra-hemiregular hemirings are also characterized.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.521-538
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• 2024

In this paper, using the notion of the imprecise set, the idea of an imprecise group is introduced including some examples. The two key rules of classical set theory are obeyed by this extended version of fuzzy sets, which the existing complement definition of a fuzzy set failed to do. With the support from general group theory, the paper also provides some fundamental properties of an imprecise group here. Additionally, it includes a few characteristics of imprecise subgroups, and abelian imprecise group.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.221-236
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• 2023

In this paper, we define the notions of (3, 2)-fuzzy ideal of subtraction semigroup and near subtraction semigroup. Also, we discuss some of its properties with examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.6-9
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• 2006

A generalized net is used to construct a model which describes the process of evaluation of the problems solved by students. The model utilizes the theory of intuitionistic fuzzy sets. The model can be used to simulate some processes, related to estimation of students' background.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.187-205
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• 2020

In this article, we prove coincidence point theorems for comparable 𝜓-contractive mappings in ordered non-Archimedean fuzzy metric spaces utilizing the recently established concept of 𝓣-comparability and relatively weaker order theoretic variants. With a view to show the usefulness and applicability of this work, we solve the system of ordered Fredholm integral equations as an application. In the process, this presentation generalize and improve some prominent recent results obtained in Mihet [Fuzzy Sets Syst., 159 (6), 739-744, (2008)], Altun and Mihet [ Fixed Point Theory Appl. 2010, 782680, (2010)], Alam and Imdad [Fixed Point Theory, 18(2), 415-432, (2017)] and several others in the settings of partially ordered non-Archimedean fuzzy metric spaces.

• Journal of the Korea institute for structural maintenance and inspection
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• v.2 no.3
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• pp.223-234
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• 1998

In this study, an attempt is made to apply the concept of fuzzy-bayesian theory to the integrity assessment of structure system, and uncertainty states are represented in terms of fuzzy sets which define several linguistic variables such as "very good", "good", "average", "poor", "very poor", etc. Especially, the concept of fuzzy conditional probability aids to derive a new reliability analysis which includes the subjective assessment of engineers without introducing any additional correction factors. The fuzzy concept are also used as reliability indexes for the condition assessment based on the proposed models, the proposed fuzzy theory-based approach with the results of PEM and AFOSM are applied to retaining wall.

• Economic and Environmental Geology
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• v.41 no.6
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• pp.763-771
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• 2008

Uncertainties are pervasive in engineering geological problems. Therefore, the presence of uncertainties and their significance in analysis and design of slopes have been recognized. Since the uncertainties cannot be taken into account by the conventional deterministic approaches in slope stability analysis, the probabilistic analysis has been considered as the primary tool for representing uncertainties in mathematical models. However, some uncertainties are caused by incomplete information due to lack of information, and those uncertainties cannot be handled appropriately by the probabilistic approach. For those uncertainties, the theory of fuzzy sets is more appropriate. Therefore, in this study, fuzzy reliability analysis has been proposed in order to deal with the uncertainties which cannot be quantified in the probabilistic analysis due to the limited information. For the practical example, a slope is selected in this study and both the probabilistic analysis and the fuzzy reliability analysis have been carried out for planar failure. In the fuzzy reliability analysis, the dip angle and internal friction angle of discontinuity are considered as triangular fuzzy numbers since the random properties of the variables cannot be obtained completely under the conditions of limited information. In the study, the fuzzy reliability index and the probabilities of failure are evaluated from fuzzy arithmetic and compared to those from the probabilistic approach using Monte Carlo simulation and point estimate method. The analysis results show that the fuzzy reliability analysis is more appropriate for the condition that the uncertainties arise due to incomplete information.

• Journal of the Korean Society of Safety
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• v.36 no.2
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• pp.49-57
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• 2021

In the case of military supplies, any potential failure and causes of failures must be considered. This study is aimed at examining the failure modes of a rotorcraft landing system to identify the priority items. Failure mode and effects analysis (FMEA) is applied to the rotorcraft landing system. In general, the FMEA is used to evaluate the reliability in engineering fields. Three elements, specifically, the severity, occurrence, and detectability are used to evaluate the failure modes. The risk priority number (RPN) can be obtained by multiplying the scores or the risk levels pertaining to severity, occurrence, and detectability. In this study, different weights of the three elements are considered for the RPN assessment to implement the FMEA. Furthermore, the FMEA is implemented using a fuzzy rule base, similarity aggregation model (SAM), and grey theory model (GTM) to perform a comparative analysis. The same input data are used for all models to enable a fair comparison. The FMEA is applied to military supplies by considering methodological issues. In general, the fuzzy theory is based on a hypothesis regarding the likelihood of the conversion of the crisp value to the fuzzy input. Fuzzy FMEA is the basic method to obtain the fuzzy RPN. The three elements of the FMEA are used as five linguistic terms. The membership functions as triangular fuzzy sets are the simplest models defined by the three elements. In addition, a fuzzy set is described using a membership function mapping the elements to the intervals 0 and 1. The fuzzy rule base is designed to identify the failure modes according to the expert knowledge. The IF-THEN criterion of the fuzzy rule base is formulated to convert a fuzzy input into a fuzzy output. The total number of rules is 125 in the fuzzy rule base. The SAM expresses the judgment corresponding to the individual experiences of the experts performing FMEA as weights. Implementing the SAM is of significance when operating fuzzy sets regarding the expert opinion and can confirm the concurrence of expert opinion. The GTM can perform defuzzification to obtain a crisp value from a fuzzy membership function and determine the priorities by considering the degree of relation and the form of a matrix and weights for the severity, occurrence, and detectability. The proposed models prioritize the failure modes of the rotorcraft landing system. The conventional FMEA and fuzzy rule base can set the same priorities. SAM and GTM can set different priorities with objectivity through weight setting.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.451-460
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• 2016

The notion of a rough fuzzy filter in a BE-algebra is introduced and some properties of such a filter are investigated. The relations between the upper (lower) rough filters and the upper (lower) approximations of their homomorphism images are discussed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.39
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• pp.75-80
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• 1996

Fuzzy approaches used to solve MONLP(Multiobjective Nonlinear Programming Problem) are based on the max-min method of fuzzy sets theory However, since the min operator noncompensatory, these approaches can not guarentee an efficient solution to the problem. In this paper, we presents an algorithm for finding the aggregation operator to find efficient solution. In particular, our presented algorithm is guarentee an efficient solution. On the basis of proposed algorithm, an illustrative numerical example is presented.