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Interval Valued Intuitionistic(S,T)-fuzzy H_ν-submodules

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Acta Mathematica Sinica,English Series 2006年第4期22卷 963-970页

作者： jian ming zhan W.A. DUDEK Department of Mathematics Hubei Institute for Nationalities Enshi 445000 P. R. China Institute of Mathematics and Computer Science Wroctaw University of Technology Wybrzeze Wyspianskiego 27 50-370 Wroctaw Poland

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.

关键词： Hν-module interval valued intuitionistic (S,T)-fuzzy Hv-submodule interval valued intuitionistic (S T)-fuzzy submodule

An Investigation on Ordered Algebraic Hyperstructures

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Acta Mathematica Sinica,English Series 2017年第8期33卷 1107-1124页

作者： Saber OMIDI Bijan DAVVAZ jian ming zhan Department of Mathematics Yazd University Department of Mathematics Hubei University for Nationalities

In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.

关键词： Algebraic hyperstructure simple ordered semihypergroup regular ordered Krasner hyperring right pure hyperideal purely prime hyperideal

Classification of Krasner Hyperfields of Order 4

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Acta Mathematica Sinica,English Series 2020年第8期36卷 889-902页

作者： Mahdeyeh IRANMANESH Morteza JAFARPOUR Hossien AGHABOZORGI jian ming zhan Department of Mathematics Vali-e-Asr University of RafsanjanRafsanjanIran Department of Mathematics Hubei University for NationalitiesEnshi 445000P.R.China

In this paper,first we introduce n-polygroups and characterize 2-polygroups of order 4 up to *** using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order ***,we propose a hyperfield of order 4 which is not as a quotient hyperfield F/***,some programs written in MATLAB which are based on obtained results compute the number of polygroups,weak polygroups and Krasner hyperfields of order4 up to isomorphism.

关键词： (semi)hypergroup n-polygroup Krasner hyperfield isomorphism

L-fuzzy Roughness of n-ary Polygroups

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Acta Mathematica Sinica,English Series 2011年第1期27卷 97-118页

作者： Yun Qiang YIN jian ming zhan P. CORSINI School of Mathematzcs and Information Sciences East China Institute of Technology Fuzhou 344000 P. R. China Department of Mathematics Hubei University for Nationalities Enshi 445000 P. R. China Department of Biology and Agro-Industrial Economy Via delle Seienze 208 33100 Udine Italy

In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ~）-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called （normal） TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the （strong） homomorphism of θ-lower and T-upper L-fuzzy rough approximation operators is studied.

关键词： n-Ary polygroups (normal) TL-fuzzy n-ary polygroups θ-lower L-fuzzy rough approxi-mation T-upper L-fuzzy rough approximation (strong) homomorphism

A New View on Fuzzy Hypermodules

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1345-1356页

作者： jian ming zhan Bijan DAVVAZ K. P. SHUM Department of Mathematics Hubei Institute for Nationalities Enshi 445000 P. R. China Department of Mathematics Yazd University Yazd Iran Faculty of Science The Chinese University of Hong Kong Shatin Hong Kong (SAR) P. R. China

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy

关键词： hypermodule interval-valued (α,β)-fuzzy sub-hypermodule interval-valued (∈ ∈ Vq)- fuzzy sub-hypermodule fuzzy logic implication operator

Fuzzy Regular Relations on Hyperquasigroups

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Journal of Mathematical Research and Exposition 2010年第6期30卷 1083-1090页

作者： jian ming zhan Department of Mathematics Hubei University for NationalitiesHubei 445000P.R.China

Regular relations play in hyperquasigroups theory a role analogous to congruences in semigroup *** aim of this paper is to introduce the concept of regular relations on hyperquasigroups and to investigate some related ***,the notion of fuzzy regular relations on hyperquasigroups is introduced and some characterizations are discussed.

关键词： hyperquasigroup regular relation fuzzy regular relation.

Interval Valued (∈,∈ ∨q)-Fuzzy Filters of MTL-Algebras

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Journal of Mathematical Research and Exposition 2010年第2期30卷 265-276页

作者： Xue Ling MA jian ming zhan Kar Ping SHUM Department of Mathematics Hubei Institute for Nationalities Hubei 445000 P. R. China Department of Mathematics The University of Hong Kong Hong Kong P. R. China (SAR)

The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships betw... 详细信息

关键词： MTL-algebra filter interval valued (∈,∈ ∨q)-fuzzy (Boolean, MV- and G-) filters.

Self-aligned dual-beam superresolution laser direct writing with a polarization-engineered depletion beam

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Photonics Research 2024年第6期12卷 1194-1200页

作者： GUOLIANG CHEN DEWEI MO jian CHEN QIWEN zhan School of Optical-Electrical and Computer Engineering University of Shanghai for Science and TechnologyShanghai 200093China Shanghai Key Laboratory of Modern Optical System University of Shanghai for Science and TechnologyShanghai 200093China zhangjiang Laboratory Shanghai 201204China

A fiber-based,self-aligned dual-beam laser direct writing system with a polarization-engineered depletion beam is designed,constructed,and *** system employs a vortex fiber to generate a donut-shaped,cylindrically polarized depletion beam while simultaneously allowing the fundamental mode excitation beam to pass *** results in a co-axially self-aligned dual-beam source,enhancing stability and mitigating assembly *** size of the central dark spot of the focused cylindrical vector depletion beam can be easily adjusted using a simple polarization rotation *** a depletion wavelength of 532 nm and an excitation wavelength of800 nm,the dual-beam laser direct writing system has demonstrated a single linewidth of 63 nm and a minimum line spacing of 173 *** optimization of this system may pave the way for practical superresolution photolithography that surpasses the diffraction limit.

关键词： polarization beam depletion

Lower and Upper Fuzzy Topological Subhypergroups

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数学学报(中文版) 2013年第2期 294-294页

作者： Irina CRISTEA jian ming zhan

This paper provides a new connection between algebraic hyperstructures and fuzzy *** specifically,using both properties of fuzzy topological spaces and those of fuzzy subhypergroups, we define the notions of lower(upper) fuzzy topological subhypergroups of a hypergroup endowed with a fuzzy *** results concerning the image and the inverse image of a lower(upper) topological subhypergroup under a very good homomorphism of hypergroups (endowed with fuzzy topologies) are pointed out.

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