Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

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A Short Review on One Dimensional Wigner Crystallization

10.20944/preprints202012.0495.v1 ◽

2020 ◽

Author(s):

Niccolo Traverso Ziani ◽

Fabio Cavaliere ◽

Karina Guerrero Becerra ◽

Maura Sassetti

Keyword(s):

Carbon Nanotubes ◽

Structural Transition ◽

Luttinger Liquid ◽

Electronic System ◽

Short Review ◽

One Dimensional ◽

Basic Properties ◽

Wigner Crystallization ◽

Liquid Theory ◽

The One

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions will be shortly addressed, together with the basic properties of carbon nanotubes that are require. Then, the most relevant properties of Wigner molecules will be addressed, and finally the experiments will be described.

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Aximatics for Rough Set Model Based on Vague Relations

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.282-283.283 ◽

2011 ◽

Vol 282-283 ◽

pp. 283-286

Author(s):

Hai Dong Zhang ◽

Yan Ping He

Keyword(s):

Rough Set ◽

Rough Sets ◽

General Framework ◽

Axiomatic Approach ◽

Constructive Approach ◽

Approximation Operators ◽

Rough Approximation ◽

Axiomatic Approaches ◽

Set Approximation

This paper presents a general framework for the study of rough set approximation operators in vague environment in which both constructive and axiomatic approaches are used. In constructive approach, by means of a vague relation defined by us, a new pair of vague rough approximation operators is ﬁrst deﬁned. Also some properties about the approximation operators are then discussed. In axiomatic approach, an operator-oriented characterization of vague rough sets is proposed, that is, vague rough approximation operators are defined by axioms.

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Soft Covering Based Rough Sets and Their Application

The Scientific World JOURNAL ◽

10.1155/2014/970893 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 11

Author(s):

Şaziye Yüksel ◽

Zehra Güzel Ergül ◽

Naime Tozlu

Keyword(s):

Rough Set ◽

Rough Sets ◽

Prostate Cancer Risk ◽

Approximation Operator ◽

Soft Sets ◽

Upper Approximation ◽

Approximation Operators ◽

Model Combining ◽

Rough Approximation ◽

Generalized Rough Set

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty.

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Soft Rough Approximation Operators and Related Results

Journal of Applied Mathematics ◽

10.1155/2013/241485 ◽

2013 ◽

Vol 2013 ◽

pp. 1-15 ◽

Cited By ~ 2

Author(s):

Zhaowen Li ◽

Bin Qin ◽

Zhangyong Cai

Keyword(s):

Topological Space ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Soft Set ◽

Soft Sets ◽

Approximation Operators ◽

Rough Approximation ◽

Generalized Rough Set ◽

Special Case

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.

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A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

The Scientific World JOURNAL ◽

10.1155/2014/783940 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Tianyu Xue ◽

Zhan’ao Xue ◽

Huiru Cheng ◽

Jie Liu ◽

Tailong Zhu

Keyword(s):

Rough Sets ◽

Rough Set Theory ◽

Binary Relations ◽

Approximation Space ◽

Upper Approximation ◽

Approximation Operators ◽

Rough Approximation ◽

Fuzzy Binary Relation ◽

Novel Method ◽

Interval Valued

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.

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N-soft rough sets and its applications

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-200338 ◽

2021 ◽

Vol 40 (1) ◽

pp. 565-573

Author(s):

Di Zhang ◽

Pi-Yu Li ◽

Shuang An

Keyword(s):

Decision Making ◽

Hybrid Model ◽

Rough Sets ◽

Real Life ◽

Decision Problems ◽

Multi Criteria Decision Making ◽

Approximation Space ◽

Soft Sets ◽

Approximation Operators ◽

Rough Approximation

In this paper, we propose a new hybrid model called N-soft rough sets, which can be seen as a combination of rough sets and N-soft sets. Moreover, approximation operators and some useful properties with respect to N-soft rough approximation space are introduced. Furthermore, we propose decision making procedures for N-soft rough sets, the approximation sets are utilized to handle problems involving multi-criteria decision-making(MCDM), aiming at electing the optional objects and the possible optional objects based on their attribute set. The algorithm addresses some limitations of the extended rough sets models in dealing with inconsistent decision problems. Finally, an application of N-soft rough sets in multi-criteria decision making is illustrated with a real life example.

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On Simplified Axiomatic Characterizations of (υ σ)-Fuzzy Rough Approximation Operators

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488517500192 ◽

2017 ◽

Vol 25 (03) ◽

pp. 457-476 ◽

Cited By ~ 1

Author(s):

Hongying Zhang ◽

Haijuan Song

Keyword(s):

Rough Sets ◽

Axiomatic Approach ◽

Fuzzy Relation ◽

Fuzzy Relations ◽

Constructive Approach ◽

Axiomatic Characterizations ◽

Approximation Operators ◽

Rough Approximation ◽

Potential Applications ◽

Two Universes

The axiomatic approach is more appropriate than constructive approach for studying the algebraic structure of rough sets. In this paper, the more simple axiomatic characterizations of (υ σ)-fuzzy rough approximation operators are explored where υ is a residuated implicator and σis its dual implicator. Firstly, we review the existing independent axiomatic sets to characterize various types of υ-lower and σ-upper fuzzy rough approximation operators. Secondly, we present one-axiom characterizations of (υ σ)-fuzzy rough approximation operators constructed by a serial fuzzy relation on two universes. Furthermore, we show that (υ σ)-fuzzy rough approximation operators, corresponding to reexive, symmetric and T-transitive fuzzy relations, can be presented by only two axioms respectively. We conclude the paper by introducing some potential applications and future works.

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SELF-ASSEMBLED METAL QUANTUM DOTS

International Journal of Nanoscience ◽

10.1142/s0219581x04002784 ◽

2004 ◽

Vol 03 (06) ◽

pp. 877-889 ◽

Cited By ~ 2

Author(s):

L. J. CHEN ◽

P. Y. SU ◽

J. M. LIANG ◽

J. C. HU ◽

W. W. WU ◽

...

Keyword(s):

Shape Control ◽

Room Temperature ◽

Lattice Structure ◽

Hexagonal Structure ◽

Displacement Reaction ◽

Ordered Structure ◽

One Dimensional ◽

Uniform Dispersion ◽

Self Assembled ◽

The One

Long-range order of uniform in size and regular in shape 2D arrays of Au@TOAB-DT nanoparticles (4.9 nm) were formed by a displacement reaction of the outer-shells from tetraoctylammonium bromide (TOAB) to dodecanethiol (DT) molecules at room temperature. The displacement reaction has utilized both superior size and shape control of Au@TOAB nanoparticles and uniform dispersion capability of Au@DT nanoparticles to achieve an extraordinarily large in extent (3 μ m × 3 μ m ) regular nanoparticle lattice structure. Self-assembled NiSi quantum dot arrays have been grown on relaxed epitaxial Si 0.7 Ge 0.3 on (001) Si . The formation of the one-dimensional ordered structure is attributed to the nucleation of NiSi nanodots on the surface undulations induced by step bunching on the surface of SiGe film owing to the miscut of the wafers from normal to the (001) Si direction. The two-dimensional, pseudo-hexagonal structure was achieved under the influence of repulsive stress between nanodots.

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A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model

Symmetry ◽

10.3390/sym10120711 ◽

2018 ◽

Vol 10 (12) ◽

pp. 711 ◽

Cited By ~ 2

Author(s):

Kholood Alsager ◽

Noura Alshehri ◽

Muhammad Akram

Keyword(s):

Decision Making ◽

Fault Detection ◽

Hybrid Model ◽

Rough Set ◽

Rough Sets ◽

General Framework ◽

Fuzzy Soft Set ◽

Rough Model ◽

Approximation Operators ◽

Rough Approximation

In this paper, we propose a new hybrid model, multi Q-hesitant fuzzy soft multi-granulation rough set model, by combining a multi Q-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi Q-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi Q-hesitant fuzzy soft ( M k Q H F S ) rough approximation operators in terms of M k Q H F S relations and M k Q H F S multi-granulation rough approximation operators in terms of M k Q H F S relations. We study the main properties of lower and upper M k Q H F S rough approximation operators and lower and upper M k Q H F S multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi Q-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology.

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