• Honam Mathematical Journal
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• v.32 no.4
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• pp.545-561
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• 2010

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.247-252
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• 1999

The purposed of this paper is to introduced some basic concepts of Galois connection between fuzzy ordered sets. And discuss its relations with the property of fuzzy ordered set.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.483-488
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• 2007

Given a set ${\Omega}$, the notion of ${\Omega}-fuzzy$ ideals in a near-ring is introduced, and related properties are investigated. Using fuzzy ideals, ${\Omega}-fuzzy$ ideals are described. Conversely, fuzzy ideals are constructed by using ${\Omega}-fuzzy$ ideals.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.509-524
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• 2020

The notion of fuzzy closure filters is introduced and discussed in an MS-algebra. In particular, we characterize the prime fuzzy closure filters in terms of boosters. Some relationship between the lattice of fuzzy closure filters and the fuzzy ideal lattice of boosters are explored and investigated.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.9-30
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• 2005

The notion of intuitionistic fuzzy convex sublattices is introduced, and its characterization is given. Natural equivalence relations on the set of all intuitionistic fuzzy ideals/filters of a lattice are investigated. Operations on intuitionistic fuzzy sets of a lattice is introduced. Some results of intuitionistic fuzzy ideals/filters under these operations are provided. Using these operations, characterizations of intuitionistic fuzzy ideals/filters are given.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.595-612
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• 2019

In this paper, we introduce the concept of ${\beta}$-fuzzy filters in MS-algebras and ${\beta}$-fuzzy filters are characterized in terms of boosters. It is proved that the lattice of ${\beta}$-fuzzy filters is isomorphic to the fuzzy ideal lattice of boosters.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.465-486
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• 2005

We study the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a distributive lattice. And we prove that the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences on a generalized Boolean algebra.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.1
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• pp.240-263
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• 2021

One of the biggest challenges that the software industry is facing today is to create highly efficient applications without affecting the quality of healthcare system software. The demand for the provision of software with high quality protection has seen a rapid increase in the software business market. Moreover, it is worthless to offer extremely user-friendly software applications with no ideal security. Therefore a need to find optimal solutions and bridge the difference between accessibility and protection by offering accessible software services for defense has become an imminent prerequisite. Several research endeavours on usable security assessments have been performed to fill the gap between functionality and security. In this context, several Multi-Criteria Decision Making (MCDM) approaches have been implemented on different usability and security attributes so as to assess the usable-security of software systems. However, only a few specific studies are based on using the integrated approach of fuzzy Analytic Network Process (FANP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) technique for assessing the significant usable-security of hospital management software. Therefore, in this research study, the authors have employed an integrated methodology of fuzzy logic, ANP and TOPSIS to estimate the usable - security of Hospital Management System Software. For the intended objective, the study has taken into account 5 usable-security factors at first tier and 16 sub-factors at second tier with 6 hospital management system softwares as alternative solutions. To measure the weights of parameters and their relation with each other, Fuzzy ANP is implemented. Thereafter, Fuzzy TOPSIS methodology was employed and the rating of alternatives was calculated on the foundation of the proximity to the positive ideal solution.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.455-464
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• 1998

In this paper, we give another proof of Theorem 2.13 of [4] without using the sup property. For the homomorphic image $f(\mu)$ and preimage $f^{-1}(\nu)$ of fuzzy left (resp. right) ideals $\mu$ and $\nu$ respectively, we establish the chains of level left (resp. right) ideals of $f(\mu)$ and $f^{-1}(\nu)$, respectively. Moreover, we prove that a necessary condition for a fuzzy ideal $\mu$ of a near-ring $R$ to be prime is that $\mu$ is two-valued.

• East Asian mathematical journal
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• v.21 no.2
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• pp.205-217
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• 2005

In this paper we consider the fuzzy ideals of N-group G where N is a near-ring. We introduce the concepts: minimal elements, fuzzy linearly independent elements, and fuzzy basis of an N-group G and obtained fundamental related results.