• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권4호
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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.

• 대한수학회논문집
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• 제18권4호
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• pp.635-641
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• 2003

The notion of negative difference on a poset is introduced, and the interrelations between FI-algebras and posets with negative difference are discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권3호
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권2호
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• pp.129-134
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• 2011

We investigate the properties of Galois, dual Galois, residuated, and dual residuated connections on posets. In particular, we show that their connections are related to relations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권1호
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• pp.59-64
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• 2011

In 2001, the notion of a fuzzy poset defined on a set X via a triplet (L, G, I) of functions with domain X ${\times}$ X and range [0, 1] satisfying a special condition L+G+I = 1 is introduced by J. Negger and Hee Sik Kim, where L is the 'less than' function, G is the 'greater than' function, and I is the 'incomparable to' function. Using this approach, we are able to define a special class of fuzzy posets, and define the 'skeleton' of a fuzzy poset in view of major relation. In this sense, we define the linear discrepancy of a fuzzy poset of size n as the minimum value of all maximum of I(x, y)${\mid}$f(x)-f(y)${\mid}$ for f ${\in}$ F and x, y ${\in}$ X with I(x, y) > $\frac{1}{2}$, where F is the set of all injective order-preserving maps from the fuzzy poset to the set of positive integers. We first show that the definition is well-defined. Then, it is shown that the optimality appears at the same injective order-preserving maps in both cases of a fuzzy poset and its skeleton if the linear discrepancy of a skeleton of a fuzzy poset is 1.