ETI： an efficient index for set similarity queries

Set queries are an important topic and have attracted a lot of attention. Earlier research mainly concentrated on set containment queries. In this paper we focus on the T-Overlap query which is the foundation of the set similarity query. To address this issue, unlike traditional algorithms that are based on an inverted index, we design a new paradigm based on the prefix tree （trie） called the expanded trie index （ETI） which expands the trie node structure by adding some new properties. Based on ETI, we convert the T- Overlap problem to finding query nodes with specific query depth equaling to T and propose a new algorithm called T- Similarity to solve T-Overlap efficiently. Then we carry out a three-step framework to extend T-Overlap to other simi- larity predicates. Extensive experiments are carried out to compare T-Similarity with other inverted index based algorithms from cardinality of query, overlap threshold, dataset size, the number of distinct elements and so on. Results show that T-Similarity outperforms the state-of-the-art algorithms in many aspects.

Efficient secure and verifiable KNN set similarity search over outsourced clouds

KNN set similarity search is a foundational operation in various realistic applications in cloud computing.However,for security consideration,sensitive data will always be encrypted before uploading to the cloud servers,which makes the search processing a challenging task.In this paper,we focus on the problem of KNN set similarity search over the encrypted datasets.We use Yao’s garbled circuits and secret sharing as underlying tools.To achieve better querying efficiency,we construct a secure R-Tree index structure based on a novel secure grouping protocol,which enables grouping appropriate private values in an oblivious way.Along with several elaborately designed secure arithmetic subroutines,we propose an efficient secure and verifiable KNN set similarity search framework over outsourced clouds.Theoretically,we analyze the complexity of our schemes in detail,and prove the security in the presence of semi-honest adversaries.Finally,we evaluate the performance and feasibility of our proposed methods by extensive experiments.

The Convergence of Statistically Self Similar Sets and the Upper Bound and Lower Bound of Hausdorff Measure

We constructed a class of self-similar sets and proved the convergence in this paper.Besides these,the upper bound and lower bound of Hausdorff measures of them were given too.

The Advances of the Research for Random Recursive Sets(Ⅰ)

We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;

Multi-criteria decision making method based on improved cosine similarity measure with interval neutrosophic sets

Purpose–The fuzziness and complexity of evaluation information are common phenomenon in practical decision-making problem,interval neutrosophic sets(INSs)is a power tool to deal with ambiguous information.Similarity measure plays an important role in judging the degree between ideal and each alternative in decision-making process,the purpose of this paper is to establish a multi-criteria decision-making method based on similarity measure under INSs.Design/methodology/approach–Based on an extension of existing cosine similarity,this paper first introduces an improved cosine similarity measure between interval neutosophic numbers,which considers the degrees of the truth membership,the indeterminacy membership and the falsity membership of the evaluation values.And then a multi-criteria decision-making method is established based on the improved cosine similarity measure,in which the ordered weighted averaging(OWA)is adopted to aggregate the neutrosophic information related to each alternative.Finally,an example on supplier selection is given to illustrate the feasibility and practicality of the presented decision-making method.Findings–In the whole process of research and practice,it was realized that the application field of the proposed similarity measure theory still should be expanded,and the development of interval number theory is one of further research direction.Originality/value–The main contributions of this paper are as follows:this study presents an improved cosine similarity measure under INSs,in which the weights of the three independent components of an interval number are taken into account;OWA are adopted to aggregate the neutrosophic information related to each alternative;and a multi-criteria decision-making method using the proposed similarity is developed under INSs.

Fuzzy TOPSIS method to primary crusher selection for Golegohar Iron Mine(Iran)

Selection of the crusher required a great deal of design regarding to the mine planning. Selection of suitable primary crusher from all of available primary crushers is a multi-criterion decision making(MCDM) problem. The present work explores the use of technique for order performance by similarity to ideal solution(TOPSIS) with fuzzy set theory to select best primary crusher for Golegohar Iron Mine in Iran. Gyratory, double toggle jaw, single toggle jaw, high speed roll crusher, low speed sizer, impact crusher, hammer mill and feeder breaker crushers have been considered as alternatives. Also, the capacity, feed size, product size, rock compressive strength, abrasion index and application of primary crusher for mobile plants were considered as criteria for solution of this MCDM problem. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution(FPIS) and fuzzy negative ideal solution(FNIS). Results of our work based on fuzzy TOPSIS method show that the gyratory is the best primary crusher for the studied mine.

The Construction of Statisticaly Self-similar Measures

We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statistically self similar sets as well.

An Equivalent Condition for the Self Similar Sets on the Real Line to Have Best Coverings

In this paper, an equivalent condition for the self similar sets on the real line to have best coverings is given. As a result, it partly gives answer to the conjecture which was posed by Zhou and Feng [Zhou, Z. L., Feng, L.： Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17（2）, 493-502 （2004）].