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Adaptive fuzzy interpolative reasoning (AFIR) can overcome the limitation of the conventional fuzzy interpolation techniques because it can find and solve the contradictions of the fuzzy interpolative reasoning (FIR) results in order to ensure that the derived FIR results are consistent. In this paper, we propose a new AFIR method to solve the inconsistencies occurring after the FIR process. The proposed AFIR method is based on the general representative values of polygonal fuzzy sets and the proposed shift and modification techniques. The proposed AFIR method includes a new contradictions solving method to get a higher similarity degree between the AFIR results. In order to demonstrate the higher consistency of the AFIR results obtained by the proposed AFIR method, we apply the proposed AFIR method to deal with the diarrheal disease prediction problem. The experimental results show that the proposed AFIR method outperforms Yang and Shen's AFIR method (2011) and Cheng et al.’s AFIR method (2016) in terms of the degree of similarity between the AFIR results. [ABSTRACT FROM AUTHOR]

Abstract: Some real-world optimization problems are plagued by a limited hardware availability. This situation can occur, for example, when the optimization must be performed on a device whose hardware is limited due to cost and space limitations. This paper addresses this class of optimization problems and proposes a novel algorithm, namely compact Particle Swarm Optimization (cPSO). The proposed algorithm employs the search logic typical of Particle Swarm Optimization (PSO) algorithms, but unlike classical PSO algorithms, does not use a swarm of particles and does not store neither the positions nor the velocities. On the contrary, cPSO employs a probabilistic representation of the swarm’s behaviour. This representation allows a modest memory usage for the entire algorithmic functioning, the amount of memory used is the same as what is needed for storing five solutions. A novel interpretation of compact optimization is also given in this paper. Numerical results show that cPSO appears to outperform other modern algorithms of the same category (i.e. which attempt to solve the optimization despite a modest memory usage). In addition, cPSO displays a very good performance with respect to its population-based version and a respectable performance also with respect to some more complex population-based algorithms. A real world application in the field of power engineering and energy generation is given. The presented case study shows how, on a model of an actual power plant, an advanced control system can be online and real-time optimized. In this application example the calculations are embedded directly on the real-time control system. [Copyright &y& Elsevier]

This paper presents a novel meta-heuristic optimization algorithm, named Adaptive Simplified Human Learning Optimization (ASHLO), which is inspired by the human learning mechanisms. Three learning operators, i.e. the random learning operator, the individual learning operator, and the social learning operator, are developed to generate new solutions and search for the optima by mimicking the learning behaviors of humans. The numerical functions, deceptive functions and 0–1 knapsack problems are adopted as benchmark problems to validate the performance of ASHLO, and the results are compared with those of binary particle swarm optimization (BPSO), modified binary differential evolution (MBDE), the binary fruit fly optimization algorithm (bFOA) and adaptive binary harmony search (ABHS). The experimental results demonstrate that the developed ASHLO significantly outperforms BPSO, MBDE, bFOA and ABHS and has a robust search ability for various problems. With the adaptive strategy, the search ability of ASHLO is improved further especially on the high-dimensional and complicated problems. Considering the ease of implementation, the excellence of global search ability and the robustness for various problems, ASHLO is a promising optimization tool for scientific research and engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, generalized versions of two ensemble methods for regression based on variants of the original AdaBoost algorithm are proposed. The generalization of these regression methods consists in restricting the unit simplex for the weights of the instances to a smaller set of weighting probabilities. Various imprecise statistical models can be used to obtain a restricted set of weighting probabilities, whose sizes each depend on a single parameter. For particular choices of this parameter, the proposed algorithms reduce to standard AdaBoost-based regression algorithms or to standard regression. The main advantage of the proposed algorithms compared to the basic AdaBoost-based regression methods is that they have less tendency to over-fitting, because the weights of the hard instances are restricted. Several simulations and applications furthermore indicate a better performance of the proposed regression methods in comparison with the corresponding standard regression methods. [ABSTRACT FROM AUTHOR]

Petri nets and Fuzzy Petri nets as modeling formalism are not adaptable according to the changes of the arc weight. Weights are the parameters that represent the new incoming data of the system modeled by a (Fuzzy) Petri net. The weight changes meet the system changes in a variety of application domains (e.g. Intelligent E-learning, Computer Numerical Control, Weather Forecasting, and Expert Systems). In this paper, we introduce a new class of Fuzzy Petri nets that takes into account the weight changes of the arc in the Fuzzy reasoning process. We give the formal description of the model, an algorithm for learning the weights without the need to transfer into a neural network, an algorithm for the fuzzy reasoning, the algebraic forms of the new state equation, and the stability analysis. Finally, we introduce a weather forecasting application as a real example. [ABSTRACT FROM AUTHOR]

Abstract: The possibility of missing or incomplete data is often ignored when describing statistical or machine learning methods, but as it is a common problem in practice, it is relevant to consider. A popular strategy is to fill in the missing values by imputation as a pre-processing step, but for many methods this is not necessary, and can yield sub-optimal results. Instead, appropriately estimating pairwise distances in a data set directly enables the use of any machine learning methods using nearest neighbours or otherwise based on distances between samples. In this paper, it is shown how directly estimating distances tends to result in more accurate results than calculating distances from an imputed data set, and an algorithm to calculate the estimated distances is presented. The theoretical framework operates under the assumption of a multivariate normal distribution, but the algorithm is shown to be robust to violations of this assumption. The focus is on numerical data with a considerable proportion of missing values, and simulated experiments are provided to show accurate performance on several data sets. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a multiobjective credibilistic model with fuzzy chance constraints of the portfolio selection problem. The key financial criteria used are short-term return, long-term return, risk and liquidity. The model generates portfolios which are optimal to the extent of achieving the highest credibility values for the objective functions. The problem is solved using a hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm. The approach adopted here has advantage of handling the multiobjective portfolio selection problem where fuzzy parameters are characterized by general functional forms. Numerical examples are provided to demonstrate effectiveness of the solution approach and efficiency of the model. [Copyright &y& Elsevier]

Abstract: This paper explores the simultaneous batch splitting and scheduling problem for identical parallel production lines, which is different from the parallel machine scheduling in that the processing time of a batch on parallel production lines is not fully proportional to that of a product. To solve the problem, a formula is derived to determine the processing time of a batch on a production line which is not taken as a single machine for each item in the batch. A lower bound is provided for the starting time of a batch production, which overlaps the previous one. A sufficient condition for guaranteeing the constant availability of the end buffer is given and proven mathematically with respect to a continuously delivered batch. Based on the above, an algorithm whose complexity is unrelated to the batch size is proposed to obtain the starting time of a batch production. Finally, a heuristic method based on genetic algorithm is constructed to solve the splitting and scheduling problems simultaneously. Numerical experiments show that this method functions well to balance the loads of the production lines. In fact, the proposed approach is significantly more effective than the existing methods for production planning and scheduling on production lines (each of which is considered as a single machine for both batch and item). [Copyright &y& Elsevier]

Abstract: The occurrence of imprecision in the real world is inevitable due to some unexpected situations. The imprecision is often involved in any engineering design process. The imprecision and uncertainty are often interpreted as fuzziness. Fuzzy systems have an essential role in the uncertainty modelling, which can formulate the uncertainty in the actual environment. In this paper, a new approach is proposed to solve a system of fuzzy polynomial equations based on the Gröbner basis. In this approach, first, the h-cut of a system of fuzzy polynomial equations is computed, and a parametric form for the fuzzy system with respect to the parameter of h is obtained. Then, a Gröbner basis is computed for the ideal generated by the h-cuts of the system with respect to the lexicographical order using Faugère’s algorithm, i.e., F 4 algorithm. The Gröbner basis of the system has an upper triangular structure. Therefore, the system can be solved using the forward substitution. Hence, all the solutions of the system of fuzzy polynomial equations can easily be obtained. Finally, the proposed approach is compared with the current numerical methods. Some theorems together with some numerical examples and applications are presented to show the efficiency of our method with respect to the other methods. [Copyright &y& Elsevier]

Abstract: This paper presents a novel Constrained Optimization based on Modified Differential Evolution algorithm (COMDE). In the new algorithm, a new directed mutation rule, based on the weighted difference vector between the best and the worst individuals at a particular generation, is introduced. The new directed mutation rule is combined with the modified basic mutation strategy DE/rand/1/bin, where only one of the two mutation rules is applied with the probability of 0.5. The proposed mutation rule is shown to enhance the local search ability of the basic Differential Evolution (DE) and to get a better trade-off between convergence rate and robustness. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability is utilized to balance the global exploration and local exploitation. COMDE also includes a modified constraint handling technique based on feasibility and the sum of constraints violations. A new dynamic tolerance technique to handle equality constraints is also adopted. The effectiveness and benefits of the new directed mutation strategy and modified basic strategy used in COMDE has been experimentally investigated. The effect of the parameters of the crossover probability function and the parameters of the dynamic tolerance equation on the performance of COMDE have been analyzed and evaluated by different experiments. Numerical experiments on 13 well-known benchmark test functions and five engineering design problems have shown that the new approach is efficient, effective and robust. The comparison results between the COMDE and the other 28 state-of-the-art evolutionary algorithms indicate that the proposed COMDE algorithm is competitive with, and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final solution. [Copyright &y& Elsevier]

Abstract: Fuzzy clustering is an effective clustering approach which associates a data point with multiple clusters. Standard fuzzy clustering models like fuzzy c-means are based on minimizing the total cluster variation, which is defined as the sum of the distances between the data points and their corresponding cluster centers weighted by the membership degrees. In this paper, we propose a fuzzy minimax clustering model by minimizing the maximum value of the set of weighted cluster variations in such a way that they satisfy a prior distribution. We derive a necessary condition for the extremum point of the fuzzy minimax clustering model, and then design an iterative algorithm for solving the extremum point. Several numerical examples on comparing fuzzy c-means and fuzzy minimax clustering models are given, which demonstrate that the prior distribution improves the quality of the clustering results significantly. [Copyright &y& Elsevier]

Abstract: A method of analysis for a class of Petri nets (PNs) called parallel process net with resources (PPNRs) is presented in this paper. The proposed analysis method is based on reduced reachability graph (RRG) of PPNRs to verify the correspondence between required specification of manufacturing system and its PN representation. In order to reduce the reachability graph (RG), a new technique is proposed which incorporates the transition vectors (TVs) to determine all the enabled transitions at a given state of system and to recognize them as dependent or independent. An algorithm, based on the idea of simultaneous execution of concurrently enabled independent transitions, is developed to reduce the RG and its analysis is also performed. Moreover, relationship between the reduction of RG and parallel structure in the PN model is discovered. The proposed technique replaces the RG by a structure which directly depicts concurrent execution and does not show the irrelevant states by presenting the concurrent behavior of system in the reduced state space. The analysis of PPNRs based on RRG generated by proposed method is also presented and demonstrated by a practical example. [Copyright &y& Elsevier]

Abstract: In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent. [Copyright &y& Elsevier]

Abstract: To predict the behavior of a complex engineering system, a model can be built and trained using historical data. However, it may be difficult to obtain a complete and accurate set of data to train the model. Consequently, the model may be incapable of predicting the future behavior of the system with reasonable accuracy. On the other hand, expert knowledge of a qualitative nature and partial historical information about system behavior may be available which can be converted into a belief rule base (BRB). Based on the unique features of BRB, this paper is devoted to overcoming the above mentioned difficulty by developing a forecasting model composed of two BRBs and two recursive learning algorithms, which operate together in an integrated manner. An initially constructed forecasting model has some unknown parameters which may be manually tuned and then trained or updated using the learning algorithms once data become available. Based on expert intervention which can reflect system operation patterns, two algorithms are developed on the basis of the evidential reasoning (ER) algorithm and the recursive expectation maximization (EM) algorithm with the former used for handling judgmental outputs and the latter for processing numerical outputs, respectively. Using the proposed algorithms, the training of the forecasting model can be started as soon as there are some data available, without having to wait until a complete set of data are all collected, which is critical when the forecasting model needs to be updated in real-time within a given time limit. A numerical simulation study shows that under expert intervention, the forecasting model is flexible, can be automatically tuned to predict the behavior of a complicated system, and may be applied widely in engineering. It is demonstrated that if certain conditions are met, the proposed recursive algorithms can converge to a local optimum. A case study is also conducted to show the wide potential applications of the forecasting model. [Copyright &y& Elsevier]

Abstract: Preference analysis is an important task in multi-criteria decision making. The rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations. The existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria. In this paper, we introduce a method to extract fuzzy preference relations from samples characterized by numerical criteria. Fuzzy preference relations are incorporated into a fuzzy rough set model, which leads to a fuzzy preference based rough set model. The measure of attribute dependency of the Pawlak’s rough set model is generalized to compute the relevance between criteria and decisions. The definitions of upward dependency, downward dependency and global dependency are introduced. Algorithms for computing attribute dependency and reducts are proposed and experimentally evaluated by using two publicly available data sets. [Copyright &y& Elsevier]

Abstract: Neuro-fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems. In this paper, a modified gradient-based neuro-fuzzy learning algorithm is proposed for zero-order Takagi–Sugeno inference systems. This modified algorithm, compared with conventional gradient-based neuro-fuzzy learning algorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. Some weak and strong convergence results for this algorithm are proved, indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value, respectively. A constant learning rate is used. Some conditions for the constant learning rate to guarantee the convergence are specified. Numerical examples are provided to support the theoretical findings. [Copyright &y& Elsevier]

Abstract: Efficient attribute reduction in large, incomplete decision systems is a challenging problem; existing approaches have time complexities no less than O(∣C∣2∣U∣2). This paper derives some important properties of incomplete information systems, then constructs a positive region-based algorithm to solve the attribute reduction problem with a time complexity no more than O(∣C∣2∣U∣log∣U∣). Furthermore, our approach does not change the size of the original incomplete system. Numerical experiments show that the proposed approach is indeed efficient, and therefore of practical value to many real-world problems. The proposed algorithm can be applied to both consistent and inconsistent incomplete decision systems. [Copyright &y& Elsevier]

Abstract: This paper proposes a bi-level programming for a logistics network design problem with system-optimized flows. We applied the Wardrop’s second principle to the logistics network design problem. A system-optimized logistics network design problem can be formulated as a bi-level program. For the system-optimized flows, a user equilibrium traffic assignment problem with marginal costs can be solved at the lower level problem. Due to the non-differentiability of the perturbed solutions in system-optimized flows, we present a novel solution algorithm to efficiently solve the logistics network design problem. By using the subgradients of the objective function, a new projection method is proposed with global convergence. Numerical calculations are implemented using a grid-size hypothetical network and comparisons are made with other alternatives in solving the logistics network design problem. Numerical results disclose that the proposed method has successful solved the logistics network design problem and achieved significant performance both in computational efficacy and cost reduction when compared to other alternatives. [Copyright &y& Elsevier]

Abstract: This paper deals with a general α-decomposition problem of fuzzy relations, which can be stated as follows: given a fuzzy relation , determine two fuzzy relations and such that , where X (resp. Y) is a finite set. Firstly we point out that every fuzzy relation R is always generally α-decomposable, and give an algorithm to construct Q and T with for a given R. Secondly, we show that the general content with is equal to the chromatic number of the simple graph F R generated by R. Therefore, finding an exact algorithm for calculating is an NP-complete problem. [Copyright &y& Elsevier]

Abstract: This paper examines the problem of static output feedback control of a Takagi–Sugeno (TS) fuzzy system. The existence of a static output feedback control law is given in terms of the solvability of bilinear matrix inequalities. An iterative algorithm based on the linear matrix inequality is proposed to compute the static output feedback gain. To reduce the conservatism of the design, the structural information of the membership function of the fuzzy rules is incorporated. Numerical examples are used to illustrate the validity of the methods. [Copyright &y& Elsevier]