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Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets
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作者 Donglei Tang Rui Hu Chunwei Pan 《Analysis in Theory and Applications》 2014年第3期296-305,共10页
In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same p... In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered. 展开更多
关键词 p.c.f self-similar sets Hoelder estimates harmonic function.
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The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets
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作者 Donglei Tang Rui Hu 《Analysis in Theory and Applications》 CSCD 2017年第2期149-156,共8页
In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite (p.c.f.) self-similar sets.
关键词 p.c.f. self-similar sets oscillation inequality H61der estimate harmonic functions.
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A Local Property of Hausdorff Centered Measure of Self-Similar Sets
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作者 Zhiwei Zhu Zuoling Zhou 《Analysis in Theory and Applications》 2014年第2期164-172,共9页
We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s(E∩B(x,r))≤(2r)^sfor all x ∈ E and r〉 0, where Cs ... We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s(E∩B(x,r))≤(2r)^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure. 展开更多
关键词 Hausdorff centered measure Hausdorff measure self-similar sets.
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A NEGATIVE ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS WITH OPEN SET CONDITION 被引量:5
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作者 Jiandong Yin 《Analysis in Theory and Applications》 2009年第2期182-200,共19页
Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answ... Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture. 展开更多
关键词 self-similar set best covering natural covering Hausdorff measure
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AN ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS 被引量:4
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作者 Baoguo Jia Shaoyuan Xu 《Analysis in Theory and Applications》 2007年第1期9-15,共7页
In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.
关键词 self-similar set best covering natural covering Hausdorff measure
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THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS 被引量:2
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作者 ZhangXiaoqun LiuYanyan 《Acta Mathematica Scientia》 SCIE CSCD 2004年第3期485-492,共8页
A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..
关键词 Random graph-directed self-similar set Hausdorff dimension box-counting dimension REGULAR
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ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION 被引量:2
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作者 Shaoyuan Xu Weiyi Su Zuoling Zhou 《Analysis in Theory and Applications》 2008年第1期93-100,共8页
In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition (OSC). As applications, we discuss a self-simila... In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition (OSC). As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure. 展开更多
关键词 self-similar set Hausdorff measure and Hausdorff dimension open set condition
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The Structure and the Sufficent and Necessary Conditions for Generalized Statistically Self-Similar Sets 被引量:1
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作者 DENG Ai-jiao HU Di-he (College of Mathematics and Computer Science,Wuhan University,Wuhan 430072,China) 《Wuhan University Journal of Natural Sciences》 CAS 2000年第1期13-21,共9页
We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statist... We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours. 展开更多
关键词 statistically recursive set generalized statistically self-similar set Hausdorff metric
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ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION 被引量:1
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作者 Shaoyuan Xu Weiyi Su 《Analysis in Theory and Applications》 2007年第4期334-342,共9页
Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we ... Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition (OSC), and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds. 展开更多
关键词 self-similar s-set upper convex density upper spherical density Hausdorff measure elementary density bound
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FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS
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作者 余旌胡 范文涛 《Acta Mathematica Scientia》 SCIE CSCD 2000年第2期256-260,共5页
In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
关键词 statistically self-similar set statistically self-similar measure dimension distribution contractive map
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THE EXACT MEASURES OF A CLASS OF SELF-SIMILAR SETS ON THE PLANE
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作者 Zhiwei Zhu Zuoling Zhou 《Analysis in Theory and Applications》 2008年第2期160-182,共23页
Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi(x) =λix + bi, i = 1,2, 3, x =(x1, x2), b1=(0, 0), b3=(1-λ3 /2,√3... Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi(x) =λix + bi, i = 1,2, 3, x =(x1, x2), b1=(0, 0), b3=(1-λ3 /2,√3/2 (1-λ3)) This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter. 展开更多
关键词 self-similar set Hausdorff measure centred covering measure packing measure
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Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points
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作者 Shaoyuan Xu Wangbin Xu Zuoling Zhou 《Analysis in Theory and Applications》 CSCD 2015年第1期92-100,共9页
In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets a... In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered. 展开更多
关键词 self-similar set upper convex density Hausdorff measure and Hausdorff dimension contracting-similarity fixed point.
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NOTE ON THE PAPER “ AN NEGATIVE ANSWER TO A CONJECTURE ON THE SELF-SIMILAR SETS SATISFYING THE OPEN SET CONDITION”
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作者 Shaoyuan Xu Wangbin Xu 《Analysis in Theory and Applications》 2012年第1期49-57,共9页
In this paper, we present a more simple and much shorter proof for the main result in the paper " An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition", which was published... In this paper, we present a more simple and much shorter proof for the main result in the paper " An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition", which was published in the journal Analysis in Theory and Applications in 2009. 展开更多
关键词 self-similar set best covering natural covering Hausdorff measure andHausdorff dimension
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Evaluation of Industrial IoT Service Providers with TOPSIS Based on Circular Intuitionistic Fuzzy Sets
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作者 Elif Çalo˘glu Büyükselçuk 《Computers, Materials & Continua》 SCIE EI 2024年第7期715-746,共32页
Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling man... Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling manufacturers to improve operational efficiency,reduce costs,and enhance product quality.These platforms provide manufacturers with real-time visibility into their production processes and supply chains,allowing them to optimize operations and make informed decisions.In addition,IIoT service providers can help manufacturers create new revenue streams through the development of innovative products and services and enable them to leverage the benefits of emerging technologies such as Artificial Intelligence(AI)and machine learning.Overall,the implementation of IIoT platforms in the manufacturing industry is crucial for companies seeking to remain competitive and meet the ever-increasing demands of customers in the digital age.In this study,the evaluation criteria to be considered in the selection of IIoT service provider in small andmedium-sized(SME)manufacturing enterprises will be determined and IIoT service providers alternatives will be evaluated using the technique for order preference by similarity to an ideal solution(TOPSIS)method based on circular intuitionistic fuzzy sets.Based on the assessments conducted in accordance with the literature review and expert consultations,a set of 8 selection criteria has been established.These criteria encompass industry expertise,customer support,flexibility and scalability,security,cost-effectiveness,reliability,data analytics,as well as compatibility and usability.Upon evaluating these criteria,it was observed that the security criterion holds the highest significance,succeeded by cost-effectiveness,data analytics,flexibility and scalability,reliability,and customer support criteria,in descending order of importance.Following the evaluation of seven distinct alternatives against these criteria,it was deduced that the A6 alternative,a German service provider,emerged as the most favorable option.The identical issue was addressed utilizing sensitivity analysis alongside various multi-criteria decision-making(MCDM)methods,and after comprehensive evaluation,the outcomes were assessed.Spearman’s correlation coefficient was computed to ascertain the association between the rankings derived from solving the problem using diverse MCDM methods. 展开更多
关键词 IIoT MANUFACTURING TOPSIS circular intuitionistic fuzzy sets
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Fuzzy Multi-Criteria Decision Support System for the Best Anti-Aging Treatment Selection Process through Normal Wiggly Hesitant Fuzzy Sets
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作者 Daekook Kang Ramya Lakshmanaraj +5 位作者 Samayan Narayanamoorthy Navaneethakrishnan Suganthi Keerthana Devi Samayan Kalaiselvan Ranganathan Saraswathy Dragan Pamucar Vladimir Simic 《Computers, Materials & Continua》 SCIE EI 2024年第9期4947-4972,共26页
This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment met... This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine. 展开更多
关键词 Normal wiggly hesitant pythagorean fuzzy set hesitant pythagorean fuzzy set anti-aging treatment entropy VIse Kriterijumska Optimizacija I Kompromisno Resenje
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Novelty of Different Distance Approach for Multi-Criteria Decision-Making Challenges Using q-Rung Vague Sets
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作者 Murugan Palanikumar Nasreen Kausar +3 位作者 Dragan Pamucar Seifedine Kadry Chomyong Kim Yunyoung Nam 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第6期3353-3385,共33页
In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung n... In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung normal vague weighted averaging(log q-rung NVWA),a log q-rung normal vague weighted geometric(log q-rung NVWG),a log generalized q-rung normal vague weighted averaging(log Gq-rung NVWA),and a log generalized q-rungnormal vagueweightedgeometric(logGq-rungNVWG)operator are discussed in this article.Adescription is provided of the scoring function,accuracy function and operational laws of the log q-rung VS.The algorithms underlying these functions are also described.A numerical example is provided to extend the Euclidean distance and the Humming distance.Additionally,idempotency,boundedness,commutativity,and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization.We chose five anemia patients with four types of symptoms including seizures,emotional shock or hysteria,brain cause,and high fever,who had either retrograde amnesia,anterograde amnesia,transient global amnesia,post-traumatic amnesia,or infantile amnesia.Natural numbers q are used to express the results of the models.To demonstrate the effectiveness and accuracy of the models we are investigating,we compare several existing models with those that have been developed. 展开更多
关键词 Vague set aggregating operators euclidean distance hamming distance decision making
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An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets
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作者 Rana Muhammad Zulqarnain Wen-Xiu Ma +2 位作者 Imran Siddique Hijaz Ahmad Sameh Askar 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1829-1862,共34页
Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and stra... Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented. 展开更多
关键词 Interval-valued Pythagorean fuzzy soft set IVPFSIWA operator IVPFSIWG operator MCGDM SCM
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On Multi-Granulation Rough Sets with Its Applications
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作者 Radwan Abu-Gdairi R.Mareay M.Badr 《Computers, Materials & Continua》 SCIE EI 2024年第4期1025-1038,共14页
Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificati... Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS. 展开更多
关键词 Multi-granulation rough sets data classifications information systems interior operators closure operators approximation structures
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All-electron basis sets for H to Xe specific for ZORA calculations:Applications in atoms and molecules
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作者 C.S.Gomes F.E.Jorge A.Canal Neto 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第8期238-246,共9页
A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions ... A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately.Using the ZORA-CCSD(T)/QZP-ZORA theoretical model,atomic ionization energies and bond lengths,harmonic vibrational frequencies,and atomization energies of some molecules were calculated.The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties.For atomization energies,a similar observation emerges when considering spin-orbit couplings.With the augmented QZP-ZORA set,static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values.Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied. 展开更多
关键词 QZP-ZORA and AQZP-ZORA basis sets elements from H to Xe CCSD(T)method atomic and molecular properties
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Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction
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作者 Ran Yin Minge Chen +2 位作者 Yu Liu Yafei Zhao Jianwei Li 《Journal of Applied Mathematics and Physics》 2024年第7期2347-2366,共20页
As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and furth... As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value. 展开更多
关键词 Pseudo-Semi-Overlap Functions Fuzzy Rough set Fuzzy Mathematical Morphology Image Edge Extraction
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