• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.4
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• pp.345-351
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• 2013

In this paper, we investigate the properties of fuzzy Galois (dual Galois, residuated, and dual residuated) connections in a complete residuated lattice L. We give their examples. In particular, we study fuzzy Galois (dual Galois, residuated, dual residuated) connections induced by L-fuzzy relations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.222-230
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• 2014

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang's the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-lower) approximation operators and L-fuzzy preorders. We study various L-fuzzy preorders on $L^X$. They are considered as an important mathematical tool for algebraic structure of fuzzy contexts.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.343-356
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• 2010

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of G-fuzzy congruences on semigroups.

• Korean Journal of Mathematics
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• v.15 no.1
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• pp.59-69
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• 2007

We define an extended fuzzy equivalence relation, discuss some basic properties of extended fuzzy equivalence relations, find the extended fuzzy equivalence relation generated by a fuzzy relation in a set, and give some lattice theoretic properties of extended fuzzy equivalence relations.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.683-691
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• 2014

We redefine a fuzzy congruence, discuss some properties of the fuzzy congruences, find the fuzzy congruence generated by a fuzzy relation on a semigroup, and give some lattice theoretic properties of the fuzzy congruences on semigroups.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.633-641
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• 2005

We investigate the relationship between fuzzy $\sigma$-ideals and fuzzy congruence on a distributive $\sigma$-lattice and obtain some useful results.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.551-572
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• 2005

Recently, there are some empirical Bayes procedures using NA samples. We point out a key equality which may not hold for NA samples. Thus, the results of those empirical Bayes procedures based on NA samples are dubious

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.30-35
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• 2009

We investigate the properties of fuzzy relations, metrics and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, pseudo-(quasi-) metrics induce $\bigodot$-(quasi)-equivalence relations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2762-2777
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• 2017

A fuzzy identity based signature (FIBS) scheme allows a signer with identity ${\omega}$ to generate a signature which could be verified under identity ${\omega}^{\prime}$ if and only if ${\omega}$ and ${\omega}^{\prime}$ are within a certain distance of each other as judged by some metric. In this paper, we propose an efficient FIBS scheme from lattice assumption, which can resist quantum-computer attacks. Without using the Bonsai Tree technique, we utilize the lattice basis delegation technique to generate the private key, which has the advantage of keeping the lattice dimension invariant. We also prove that our proposed scheme is existentially unforgeable under an adaptive chosen message and identity attack in the random oracle model. Compared with existing scheme, our proposed scheme is much more efficient, especially in terms of communication overhead. Since our FIBS scheme possesses similar error-tolerance property, it can be well applied in post-quantum communication biometric authentication environments, where biometric identifiers such as fingerprints, voice, iris and gait are used in human identification.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.65-71
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• 2019

In this paper we give some properties related to fuzzy functions on complete residuated lattices.