摘要：
Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we deal with the algebraic structure of soft sets. The lattice structures of soft sets are constructed. The concept of soft equality is introduced and some related properties are derived. It is proved that soft equality is a congruence relation with respect to some operations and the soft quotient algebra is established. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
摘要：
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a class of three-weight cyclic codes over F-p whose duals have two zeros is presented, where p is an odd prime. The weight distribution of this class of cyclic codes is settled. Some of the cyclic codes are optimal. The duals of a subclass of the cyclic codes are also studied and proved to be optimal. (C) 2013 Elsevier Inc. All rights reserved.
关键词：
Rough sets, interesting knowledge, accuracy, coverage, dynamic information systems, data mining
摘要：
Knowledge in an information system evolves with its dynamical environment. A new concept of interesting knowledge based on both accuracy and coverage is defined in this paper for dynamic information systems. An incremental model and approach as well as its algorithm for inducing interesting knowledge are proposed when the object set varies over time. A case study validates the feasibility of the proposed method.
摘要：
The aim of this paper is to develop the filter theory of general residuated lattices. First, we extend some particular types of filters and fuzzy filters in BL-algebras and MTL-algebras naturally to general residuated lattices, and further enumerate some relative results obtained in BL-algebras or MTL-algebras, which still hold in general residuated lattices. Next, we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices, which are two new types of filters and fuzzy filters, and derive some of their characterizations. Finally, we discuss the relations between (fuzzy) regular filters and several other special (fuzzy) filters, and also characterize some special classes of residuated lattices by filters or fuzzy filters. (C) 2010 Elsevier Inc. All rights reserved.
摘要：
Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed. (C) 2011 Elsevier Ltd. All rights reserved.
摘要：
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a family of p-ary cyclic codes whose duals have three pairwise nonconjugate zeros is proposed. The weight distribution of this family of cyclic codes is determined. It turns out that the proposed cyclic codes have five nonzero weights.
摘要：
In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263-74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier-Stokes equations Indiana Univ. Math. J. 57 2643-61; 2011 Gobal regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919-32) for 3D incompressible Navier-Stokes equations.
作者机构：
[Hu, Yanqing; Makse, Hernan A.] CUNY City Coll, Levich Inst, New York, NY 10031 USA.;[Hu, Yanqing; Makse, Hernan A.] CUNY City Coll, Dept Phys, New York, NY 10031 USA.;[Hu, Yanqing] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China.;[Havlin, Shlomo] Bar Ilan Univ, Minerva Ctr, IL-52900 Ramat Gan, Israel.;[Havlin, Shlomo] Bar Ilan Univ, Dept Phys, IL-52900 Ramat Gan, Israel.
通讯机构：
[Hu, Yanqing] CUNY City Coll, Levich Inst, New York, NY 10031 USA.
摘要：
A fundamental problem in network science is to predict how certain individuals are able to initiate new networks to spring up “new ideas.” Frequently, these changes in trends are triggered by a few innovators who rapidly impose their ideas through “viral” influence spreading, producing cascades of followers and fragmenting an old network to create a new one. Typical examples include the rise of scientific ideas or abrupt changes in social media, like the rise of Facebook to the detriment of Myspace. How this process arises in practice has not been conclusively demonstrated. Here, we show that a condition for sustaining a viral spreading process is the existence of a multiplex-correlated graph with hidden “influence links.” Analytical solutions predict percolation-phase transitions, either abrupt or continuous, where networks are disintegrated through viral cascades of followers, as in empirical data. Our modeling predicts the strict conditions to sustain a large viral spreading via a scaling form of the local correlation function between multilayers, which we also confirm empirically. Ultimately, the theory predicts the conditions for viral cascading in a large class of multiplex networks ranging from social to financial systems and markets.
摘要：
In this paper, the partial Hamming correlation properties of frequency-hopping sequences (FHSs) are discussed. The Peng-Fan bounds on sets of FHSs are generalized to the case of partial correlation. Both individual FHSs with optimal partial autocorrelation and sets of FHSs with optimal partial correlation are presented. The former has more new parameters compared with the known individual FHSs with optimal partial autocorrelation, while the later is obtained in the literature for the first time.
关键词：
Linear code;Optimal code;Bent function;Quadratic form;Weight distribution
摘要：
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of p-ary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field \({\mathbb {F}}_p\), where p is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined.
关键词：
Economic time series;fuzzy forecasting;sparse representation;clustering
摘要：
This paper addresses the problem of economic time series forecasting, and a new prediction method is proposed. The method fully capitalizes on the two key technologies, sparse representation, and fuzzy set theory, to handle the stock time series forecasting problems. First, sparse representation is applied to smooth the time series. Then, the fuzzy technology is used to convert time series into fuzzy series. Based on the number of the occurrence of fuzzy sets, the weights are calculated. Finally, the future value of the time series can be forecasted using the weights and inverse transformation of sparse representation. The experimental results show that the proposed method produces more accurate forecasted results.
作者机构：
[Tang, Chunming] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Peoples R China.;[Helleseth, Tor; Li, Nian; Helleseth, T] Univ Bergen, Dept Informat, N-5020 Bergen, Norway.;[Qi, Yanfeng] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China.;[Zhou, Zhengchun] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China.
通讯机构：
[Tang, Chunming] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Peoples R China.;[Li, N; Helleseth, T] Univ Bergen, Dept Informat, N-5020 Bergen, Norway.;[Qi, Yanfeng] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China.;[Zhou, Zhengchun] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China.
关键词：
Linear codes;weight distribution;weakly regular bent functions;cyclotomic fields;secret sharing schemes
摘要：
Linear codes with a few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. and Zhou et al. to general weakly regular bent functions and determines the weight distributions of these linear codes. It solves an open problem proposed by Ding et al. Furthermore, this paper constructs new linear codes with two or three weights and presents their weight distributions. They contain some optimal codes meeting certain bound on linear codes.
摘要：
In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employing d-form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets using m-sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriate d-form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets.
摘要：
Key issues for resolution-based automated reasoning in lattice-valued first-order logic LF(X) are investigated with truth-values in a lattice-valued logical algebraic structure lattice implication algebra (LIA). The determination of resolution at a certain truth-value level (called alpha-resolution) in LF(X) is proved to be equivalently transformed into the determination of alpha-resolution in lattice-valued propositional logic LP(X) based on LIA. The determination of alpha-resolution of any quasi-regular generalized literals and constants under various cases in LP(X) is further analyzed, specified, and subsequently verified. Hence the determination of alpha-resolution in LF(X) can be accordingly solved to a very broad extent. which not only lays a foundation for the practical implementation of automated reasoning algorithms in LF(X). but also provides a key support for alpha-resolution-based automated reasoning approaches and algorithms in LIA based linguistic truth-valued logics. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.
关键词：
Cyclic codes;Linear codes;Permutation monomials;Weight distribution
摘要：
Cyclic codes have been an important topic of both mathematics and engineering for decades. They have been widely used in consumer electronics, data transmission technologies, broadcast systems, and computer applications as they have efficient encoding and decoding algorithms. The objective of this paper is to provide a survey of three-weight cyclic codes and their weight distributions. Information about the duals of these codes is also given when it is available. (c) 2015 Elsevier B.V. All rights reserved.
关键词：
Group decision making;Consensus models;Attitude;OWA operators;Linguistic quantifiers
摘要：
Nowadays, important decisions that have a significant impact either in societies or in organizations are commonly made by a group rather than a single decision maker, which might require more than a majority rule to obtain a real acceptance. Consensus-reaching processes provide a way to drive group decisions which are more accepted and appreciated by people affected by such a decision. These processes care about different consensus measures to determine the agreement in the group. The correct choice of a consensus measure that reflects the attitude of decision makers is a key issue for improving and optimizing consensus-reaching processes, which still requires further research. This paper studies the concept of group's attitude towards consensus, and presents a consensus model that integrates it in the measurement of consensus, through an extension of OWA aggregation operators, the so-called Attitude-OWA. The approach is applied to the solution of a real-like group decision making problem with the definition of different attitudes, and the results are analysed.
摘要：
Visible light communication has gained tremendous attention recently and has become a favorable complementary technology to millimeter-wave communication in short-range communication scenarios for future 5G networks. VLC possesses a number of prominent features to address the highly demanding 5G system requirements for high capacity, high data rate, high spectral efficiency, high energy efficiency, low battery consumption, and low latency. These prominent features include but are not limited to abundant license-free spectrum, the ability to provide multiple gigabit-per-second data rates, low energy consumption, and low implementation costs. In this article a heterogeneous multi-layer 5G cellular architecture with a control plane and user plane separation scheme is presented. Three layers - the macrocell layer operating below 3 GHz, the picocell layer operating in the mmWave spectrum, and the optical attocell layer operating at the visible spectrum - are considered in this architecture, with each layer targeting a different coverage and communication need. We further address potential solutions for uplink communications, backhaul connections, and downlink communications in an optical attocell. Several key technologies employed in VLC downlink communications, including modulation, multiple access, and error control schemes, are also discussed.
摘要：
Advancement and application of rule-based systems have always been a key research area in computer-aided support for human decision making due to the fact that rule base is one of the most common frameworks for expressing various types of human knowledge in an intelligent system. In this paper, a novel rule-based representation scheme with a belief structure is proposed firstly along with its inference methodology. Such a rule base is designed with belief degrees embedded in the consequent terms as well as in the all antecedent terms of each rule, which is shown to be capable of capturing vagueness, incompleteness, uncertainty, and nonlinear causal relationships in an integrated way. The overall representation and inference framework offers a further improvement and great extension of the recently developed belief Rule base Inference Methodology (refer to as RIMER), although they still share a common scheme at the final step of inference, i.e., the evidential reasoning (ER) approach is applied to the rule combination. It is worth noting that this new extended belief rule base representation is a great extension of traditional rule base as well as fuzzy rule base by encompassing the uncertainty description in the rule antecedent and consequent. Subsequently, a simple but efficient and powerful method for automatically generating such extended belief rule base from numerical data is proposed involving neither time-consuming iterative learning procedure nor complicated rule generation mechanisms but keeping the relatively good performance, which thanks to the new features of the extended rule base with belief structures. Then some case studies in oil pipeline leak detection and software defect detection are provided to illustrate the proposed new rule base representation, generation, and inference procedure as well as demonstrate its high performance and efficiency by comparing with some existing approaches. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.