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In this paper the comparison of a proposed neural network with generalized type-2 fuzzy weights (NNGT2FW) with respect to the monolithic neural network (NN) and the neural network with interval type-2 fuzzy weights (NNIT2FW) is presented. Generalized type-2 fuzzy inference systems are used to obtain the generalized type-2 fuzzy weights and are designed by a strategy of increasing and decreasing an epsilon variable for obtaining the different sizes of the footprint of uncertainty (FOU) for the generalized membership functions. The proposed method is based on recent approaches that handle weight adaptation using type-1 and type-2 fuzzy logic. The approach is applied to the prediction of the Mackey–Glass time series, and results are shown to outperform the results produced by other neural models. Gaussian noise was applied to the test data of the Mackey–Glass time series for finding out which of the presented methods in this paper shows better performance and tolerance to noise. [ABSTRACT FROM AUTHOR]

The problems to find attribute reduction in rough sets and to obtain the minimal vertex cover for graphs are both NP-hard problems. This paper studies the relationship between the two problems. The vertex cover problem for graphs from the perspective of rough sets is first investigated. The attribute reduction of an information system is then studied in the framework of graph theory. The results in this paper show that finding the minimal vertex cover of a graph is equivalent to finding the attribute reduction of an information system induced from the graph. Conversely, the attribute reduction computation can be translated into the calculation of the minimal vertex cover of a derivative graph. Finally, a new algorithm for the vertex cover problem based on rough sets is presented. Furthermore, experiments are conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The advantages and applications of rule-based systems have caused them to be widely recognized as one of the most popular systems in human decision-making, due to their accuracy and efficiency. To improve the performance of rule-based systems, there are several issues proposed to be focused. First, it is unnecessary to take the entire rule base into consideration during each decision-making process. Second, there is no need to visit the entire rule base to search for the key rules. Last, the key rules for each decision-making process should be different. This paper focuses on an advanced extended belief rule base (EBRB) system and proposes a multi-attribute search framework (MaSF) to reconstruct the relationship between rules in the EBRB to form the MaSF-based EBRB. MaSFs can be divided into k -dimensional tree (KDT)-based MaSFs and Burkhard–Keller (BKT)-based MaSFs. The former is targeted at decision-making problems with small-scale attribute datasets, while the latter is for those with large-scale attribute datasets. Based on the MaSF-based EBRB, the k -neighbor search and the best activated rule set algorithms are further proposed to find both the unique and the desired rules for each decision-making process without visiting the entire EBRB, especially when handling classification problems with large attribute datasets. Two sets of experiments based on benchmark datasets with different numbers of attributes are performed to analyze the difference between KDT-based MaSFs and BKT-based MaSFs, and to demonstrate how to use MaSFs to improve the accuracy and efficiency of EBRB systems. MaSFs and their corresponding algorithms are also regarded as a general optimization framework that can be used with other rule-based systems. [ABSTRACT FROM AUTHOR]

In this paper, the notions of α -migrative uninorms over semi t-operators and α -migrative semi t-operators over uninorms are introduced and investigated. All solutions of the migrativity equations for all possible combinations of semi t-operators and uninorms are characterized. [ABSTRACT FROM AUTHOR]

Nullnorms are generalization of triangular norms and triangular conorms with a zero element in the interior of the unit interval. In this paper, we generalize nullnorms to an arbitrary bounded lattices. We show the existence of nullnorms with zero element a for arbitrary element a ∈ L \{0, 1} using the fact that some t-norms and t-conorms on an arbitrary fixed bounded lattice L always exist. As a by-product we give a method of constructing nullnorms. Using this method, we obtain also the smallest nullnorm and the greatest nullnorm with given zero element a . Some other construction methods for nullnorms are also added. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules. First, the proposed method gets the characteristic points of the observation polygonal fuzzy sets and the characteristic points of the antecedent polygonal fuzzy sets of the fuzzy rules, respectively, by using the α-cut operations, respectively, where α ∈ [0, 1]. Then, it calculates the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set, respectively. Then, it calculates the difference between the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set. Then, it calculates the weight of each fuzzy rule based on the obtained differences between the ranking values of the observation polygonal fuzzy sets and the ranking values of the antecedent polygonal fuzzy sets. Then, based on the obtained characteristic points of the observation polygonal fuzzy sets, the obtained characteristic points of the antecedent polygonal fuzzy sets, and the obtained weights of the fuzzy rules, it gets the characteristic points of the fuzzy interpolative reasoning result represented by a polygonal fuzzy set. The experimental results show that the proposed method can overcome the drawbacks of the existing methods for fuzzy interpolative reasoning in sparse fuzzy rule-based systems. [ABSTRACT FROM AUTHOR]

Many real incidents demonstrate that users of Online Social Networks need mechanisms that help them manage their interactions by increasing the awareness of the different contexts that coexist in Online Social Networks and preventing them from exchanging inappropriate information in those contexts or disseminating sensitive information from some contexts to others. Contextual integrity is a privacy theory that conceptualises the appropriateness of information sharing based on the contexts in which this information is to be shared. Computational models of Contextual Integrity assume the existence of well-defined contexts, in which individuals enact pre-defined roles and information sharing is governed by an explicit set of norms. However, contexts in Online Social Networks are known to be implicit, unknown a priori and ever changing; users relationships are constantly evolving; and the information sharing norms are implicit. This makes current Contextual Integrity models not suitable for Online Social Networks. In this paper, we propose the first computational model of Implicit Contextual Integrity, presenting an information model for Implicit Contextual Integrity as well as a so-called Information Assistant Agent that uses the information model to learn implicit contexts, relationships and the information sharing norms in order to help users avoid inappropriate information exchanges and undesired information disseminations. Through an experimental evaluation, we validate the properties of the model proposed. In particular, Information Assistant Agents are shown to: (i) infer the information sharing norms even if a small proportion of the users follow the norms and in presence of malicious users; (ii) help reduce the exchange of inappropriate information and the dissemination of sensitive information with only a partial view of the system and the information received and sent by their users; and (iii) minimise the burden to the users in terms of raising unnecessary alerts. [ABSTRACT FROM AUTHOR]

Two primary properties of complex networks, controllability and modularity not only are closely related to each other, but also play an important role in understanding the networks’ characteristics. In this paper, we discuss an elastic model to enhance the control of undirected networks and study the controllability of random networks with built-in gradually varied modularity as well as real-world networks to elaborate the correlation between the networks’ controllability and modularity. The results show that it is easier to control the networks with stronger modularity than that of weaker modularity, and the networks with larger size communities probably need more driver nodes to control than that of smaller size communities when we fix both the number of nodes and the number of links of the networks. In addition, the robustness analysis indicates that the model enhances the resistance of networks against link failure. This work shows that the controllability of complex networks is highly associated with the networks’ degree distribution as well as the networks’ modularity, which gives a new insight into the understanding of controllability and modularity of complex networks. [ABSTRACT FROM AUTHOR]

In this paper, we first discuss some properties of residuum and deresiduum of a binary operation on a complete lattice. Then, we investigate the relations between residuum and deresiduum. Finally, we demonstrate how each individual logical character of a right infinitely ∧-distributive implication, such as the law of importation, the weak exchangeability principle, the exchange principle, the contrapositive symmetry and the contraction law, can be translated into a property of its deresiduum. Moreover, we give some conditions under which deresiduum of a right infinitely ∧-distributive implication is, respectively, a left (right) uninorm, pseudo-uninorm and uninorm, and show that right infinitely ∧-distributive implications, which satisfy the weak exchangeability principle and the contrapositive symmetry, can be presented by commutative conjunctors and strong negations. [ABSTRACT FROM AUTHOR]

The Intelligent Water Drop (IWD) algorithm is a recent stochastic swarm-based method that is useful for solving combinatorial and function optimization problems. In this paper, we propose an IWD ensemble known as the Master-River, Multiple-Creek IWD (MRMC-IWD) model, which serves as an extension of the modified IWD algorithm. The MRMC-IWD model aims to improve the exploration capability of the modified IWD algorithm. It comprises a master river which cooperates with multiple independent creeks to undertake optimization problems based on the divide-and-conquer strategy. A technique to decompose the original problem into a number of sub-problems is first devised. Each sub-problem is then assigned to a creek, while the overall solution is handled by the master river. To empower the exploitation capability, a hybrid MRMC-IWD model is introduced. It integrates the iterative improvement local search method with the MRMC-IWD model to allow a local search to be conducted, therefore enhancing the quality of solutions provided by the master river. To evaluate the effectiveness of the proposed models, a series of experiments pertaining to two combinatorial problems, i.e., the travelling salesman problem (TSP) and rough set feature subset selection (RSFS), are conducted. The results indicate that the MRMC-IWD model can satisfactorily solve optimization problems using the divide-and-conquer strategy. By incorporating a local search method, the resulting hybrid MRMC-IWD model not only is able to balance exploration and exploitation, but also to enable convergence towards the optimal solutions, by employing a local search method. In all seven selected TSPLIB problems, the hybrid MRMC-IWD model achieves good results, with an average deviation of 0.021% from the best known optimal tour lengths. Compared with other state-of-the-art methods, the hybrid MRMC-IWD model produces the best results (i.e. the shortest and uniform reducts of 20 runs) for all13 selected RSFS problems. [ABSTRACT FROM AUTHOR]

Measuring the similarity between two instances reliably, shape or image, is a challenging problem in shape and image retrieval. In this paper, a simple yet effective method called Neighbor Set Similarity (NSS) is proposed, which is superior to both traditional pairwise similarity and diffusion process. NSS makes full use of contextual information to capture the geometry of the underlying manifold, and obtains a more precise measure than the original pairwise similarity. Moreover, based on NSS, we propose a powerful fusion process to utilize the complementarity of different descriptors to further enhance the retrieval performance. The experimental results on MPEG-7 shape dataset, N-S image dataset and ORL face dataset demonstrate the effectiveness of the proposed method. In addition, the time complexity of NSS is much lower than diffusion process, which suggests that NSS is more suitable for large scale image retrieval than diffusion process. [ABSTRACT FROM AUTHOR]

In this paper, we propose two novel methods viz., counterpropagation auto-associative neural network (CPAANN) and grey system theory (GST) hybridised with CPAANN for data imputation. The effectiveness of these methods is demonstrated on 12 datasets and the results are compared with that of various extant methods. Wilcoxon signed rank test conducted at 1% level of significance, indicated that the proposed methods are statistically significant against all methods. The spectacular success of CPAANN can be attributed to the local learning, global approximation and auto-association that take place in tandem in a single architecture. Furthermore, significantly CPAANN turned out to be the best in the class of AANN architectures used for imputation. The reason could be the competitive learning that is intrinsic to the CPAANN architecture, but conspicuously absent in other auto-associative neural network architectures. [ABSTRACT FROM AUTHOR]

This paper presents two mathematical models representing imprecise capacitated fixed-charge transportation problems for a two-stage supply chain network in Gaussian fuzzy type-2 environment. It is a two-stage transportation process from a manufacturing center to m potential distribution centers (DCs) and then from DCs to business centers of n retailers with particular demands. Retailers are situated at some distances apart. Here unit transportation costs, fixed charges, availabilities, and demands are imprecise and represented by Gaussian type-2 fuzzy numbers. The proposed models are formulated as profit maximization problems in such a way that some DCs are selected in order to satisfy the demands at all retailers. The type-2 fuzziness has been removed by using generalized credibility measure developed with the help of CV-based reduction method and hence the models are reduced to chance constrained programming problems with different credibility labels. The deterministic models are then solved using both genetic algorithm (GA) based on Roulette wheel selection, arithmetic crossover with uniform mutation and modified particle swarm optimization (PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. Finally models are illustrated with some numerical data. Some sensitivity analyses on the proposed models are presented. [ABSTRACT FROM AUTHOR]

Although various efficient indexing techniques have been proposed to improve the performance in distributing road data to mobile clients to perform shortest path searches on road networks, how to minimize the tune-in and path searching costs are still important performance goals since the clients usually have limited processing capability and energy supply. In this paper, based on the Next Region ( NR ) approach, we propose a new method called Approximate Path Searching (APS) for constructing the broadcast index at mobile clients with soft arrival times to destinations. APS adopts an approximation technique in calculating the sets of required regions for each region pair in a road network to reduce the index generation cost at the road server and the tune-in and path searching costs at the clients. Different from NR , which only provides one set of required regions containing the shortest path from a client’s start region to its destination region, APS generates n -sets of required regions for a client to choose. Each set of required regions contains different numbers of regions. Although choosing a smaller region set may give a slightly longer delay in arrival, the tune-in and path searching costs could be significantly reduced. Theoretical analysis and extensive simulation experiments have been performed to demonstrate the effectiveness of APS in improving the system performance with just a few percentages delay in arrival time on average comparing with NR using data sets from real road networks. [ABSTRACT FROM AUTHOR]

Sparse representation based reconstruction methods are efficient for single image super resolution. They generally consist of the code stage and the linear combination stage. However, the simple linear combination has not considered the image edge constraint information of image, and hence the classical sparse representation based methods reconstruct the image with the unwanted edge artifacts and the unsharp edges. In this paper, considering that the local rank is able to extract better edge information than other edge operator, we propose a new single image super resolution method by combining the sparse representation and the local rank constraint information. In our method, we first learn the local rank of the HR image via the traditional sparse representation model, and then use it as the edge constraint to restrict the image edges during the linear combination stage to reconstruct the HR image. Furthermore, we propose a nonlocal and global optimization model to further improve the HR image quality. Compared with many state-of-art methods, extensive experimental results validate that the proposed method can obtain the less edge artifacts and sharper edges. [ABSTRACT FROM AUTHOR]

In some real-world decision processes, decision makers may prefer to provide their opinions using linguistic expressions instead of a single linguistic term. Particularly, they may hesitate between several linguistic terms. In this paper, we deal with the consensus issue in the hesitant linguistic group decision making (GDM) problem. Firstly, a novel distance-based consensus measure is proposed. Then, using this consensus measure we develop an optimization-based consensus model in the hesitant linguistic GDM, which minimizes the number of adjusted simple terms in the consensus building. Furthermore, a two-stage model is displayed to further optimize the solutions to the proposed consensus model, through which we obtain the unique optimal adjustment suggestion to support the consensus reaching process in the hesitant linguistic GDM. Finally, several desirable properties are proposed to justify the proposal, and two examples are used to demonstrate the validity of the models. [ABSTRACT FROM AUTHOR]