A new approach for classification of filters in residuated lattices

Buşneag, Dumitru; Piciu, Dana

doi:10.1016/j.fss.2014.07.022

Cited by 14 publications

(5 citation statements)

References 28 publications

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“…Many of the filters in Example 1 have different names. To avoid confusion, Buşneag and Piciu [18] proposed a new approach for classifying filters and renamed some filters.…”

Section: T-filters and T-int-soft Filtersmentioning

confidence: 99%

“…At present, the filter theories of many fuzzy logical algebras have been extensively studied. On residuated lattices, the relative literature is as follows: [17][18][19][20][21][22][23][24][25][26]. In the literature, many concrete types of filters (implicative filters, fantastic filters, Boolean filters, and so on) have been introduced, their equivalent characterizations studied, and the relations among specific filters were investigated on residuated lattices.…”

Section: Introductionmentioning

confidence: 99%

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The “Generator” of Int-Soft Filters on Residuated Lattices

Zhang

Luo

2019

Mathematics

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In this paper, we give the “generator” of int-soft filters and propose the notion of t-int-soft filters on residuated lattices. We study the properties of t-int-soft filters and obtain some commonalities (e.g., the extension property, quotient characteristics, and a triple of equivalent characteristics). We also use involution-int-soft filters as an example and show some basic properties of involution-int-soft filters. Finally, we investigate the relations among t-int-soft filters and give a simple method for judging their relations.

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“…Many of the filters in Example 1 have different names. To avoid confusion, Buşneag and Piciu [18] proposed a new approach for classifying filters and renamed some filters.…”

Section: T-filters and T-int-soft Filtersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The “Generator” of Int-Soft Filters on Residuated Lattices

Zhang

Luo

2019

Mathematics

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“…Filters can be used to define congruence relations and play an important role in studying logical systems and the related algebraic structures. There are a rich rage of classes of filters so, in [4], we proposed a new approach for the study of filters in residuated lattices.…”

Section: Introductionmentioning

confidence: 99%

Some decompositions of filters in residuated lattices

Piciu

Dan

Chirteş

2019

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this paper we introduce a new class of residuated lattice: residuated lattice with (C∧&→) property and we prove that (C∧&→) ⇔ (C→) + (C∧).Also, we introduce and characterize C→, C∨, C∧ and C∧ & → filters in residuated lattices (i.e., we characterize the filters for which the quotient algebra that is constructed via these filters is a residuated lattice with C→ (C∨ or C∧ or C∧&→ property). We state and prove some results which establish the relationships between these filters and other filters of residuated lattices: BL filters, MTL filters, divisible filters and, by some examples, we show that these filters are different. Starting from the results of algebras, we present for MTL filters, BL filters and C∧&→ filters the decomposition conditions.

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“…It is observed that special filters such as fantastic, implicative and Boolean filters, which can be alternatively described by one identity (Borzooei, Shoar, and Ameri 2012;Busneag and Piciu 2015;Haveshki, Borumand Saeid, and Eslami 2006;Kondo and Dudek 2008;Ma and Hu 2014;Zhu and Xu 2010) on commutative residuated lattices, can be generalized to non-commutative cases by two identities, and their properties are preserved without any additional condition (Kondo 2012;Liu and Li 2007). Associated with the work in Ma and Yang (2015), a natural question is how to define the notions of generalized Bosbach states on non-commutative residuated lattices to inherit the properties from commutative case without any additional condition?…”

Section: Introductionmentioning

confidence: 99%

Hybrid generalized Bosbach and Rie c̆ an states on non-commutative residuated lattices

Yang²

2016

International Journal of General Systems

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Generalized Bosbach and Riecan states, which are useful for the development of an algebraic theory of probabilistic models for commutative or non-commutative fuzzy logics, have been investigated in the literature. In this paper, a new way arising from generalizing residuated lattice-based filters from commutative case to non-commutative one is applied to introduce new notions of generalized Bosbach and Riecan states, which are called hybrid ones, on non-commutative residuated lattices is provided, and the relationships between hybrid generalized states and those existing ones are studied, examples show that they are different. In particular, two problems from L.C. Ciungu, G. Georgescu, and C. Mure, "Generalized Bosbach States: Part I" (Archive for Mathematical Logic 52 (2013): 335-376) are solved, and properties of hybrid generalized states, which are similar to those on commutative residuated lattices, are obtained without the condition "strong". ARTICLE HISTORY

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A new approach for classification of filters in residuated lattices

Cited by 14 publications

References 28 publications

The “Generator” of Int-Soft Filters on Residuated Lattices

The “Generator” of Int-Soft Filters on Residuated Lattices

Some decompositions of filters in residuated lattices

Hybrid generalized Bosbach and Rie c̆ an states on non-commutative residuated lattices

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