Search

Linguistic hesitant fuzzy sets (LHFSs), which can be used to represent decision-makers’ qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning (ER) method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made. [ABSTRACT FROM AUTHOR]

Recently, hesitant fuzzy sets (HFSs) have been studied by many researchers as a powerful tool to describe and deal with uncertain data, but relatively, very few studies focus on the clustering analysis of HFSs. In this paper, we propose a novel hesitant fuzzy agglomerative hierarchical clustering algorithm for HFSs. The algorithm considers each of the given HFSs as a unique cluster in the first stage, and then compares each pair of the HFSs by utilising the weighted Hamming distance or the weighted Euclidean distance. The two clusters with smaller distance are jointed. The procedure is then repeated time and again until the desirable number of clusters is achieved. Moreover, we extend the algorithm to cluster the interval-valued hesitant fuzzy sets, and finally illustrate the effectiveness of our clustering algorithms by experimental results. [ABSTRACT FROM PUBLISHER]

In this paper, we define some Einstein operations on cubic fuzzy set (CFS) and develop three arithmetic averaging operators, which are cubic fuzzy Einstein weighted averaging (CFEWA) operator, cubic fuzzy Einstein ordered weighted averaging (CFEOWA) operator and cubic fuzzy Einstein hybrid weighted averaging (CFEHWA) operator, for aggregating cubic fuzzy data. The CFEHWA operator generalises both the CFEWA and CFEOWA operators. Furthermore, we develop various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. We apply CFEHWA operator to multiple attribute decision-making with cubic fuzzy data. Finally, a numerical example is constructed to demonstrate the established approach. [ABSTRACT FROM AUTHOR]

Supplier selection is an important multiple attribute group decision-making (MAGDM) problem. How to choose a suitable supplier is an evaluation process with different alternatives of multiple attributes, and it also relates to the expression of the evaluation value. Considering Schweizer-Sklar t-conorm and t-norm (SSTT) can make the information aggregation process more flexible than others, and the power average (PA) operator can eliminate effects of unreasonable data from biased decision-makers. So, we extend SSTT to interval-valued intuitionistic fuzzy numbers (IVIFNs) and define Schweizer-Sklar operational rules of IVIFNs. Then, we combine the PA operator with Schweizer-Sklar operations, and propose the interval-valued intuitionistic fuzzy Schweizer-Sklar power average operator, the interval-valued intuitionistic fuzzy Schweizer-Sklar power weighted average (IVIFSSPWA) operator, the interval-valued intuitionistic fuzzy Schweizer-Sklar power geometric operator and the interval-valued intuitionistic fuzzy Schweizer-Sklar power weighted geometric (IVIFSSPWG) operator, respectively. Furthermore, we study some desirable characteristics of them and develop two methods on the basis of IVIFSSPWA and IVIFSSPWG operators. At the same time, we apply the two methods to deal with the MAGDM problems based on supplier selection. Finally, an illustrative example of supplier selection problem is given to testify the availability of the presented operators. [ABSTRACT FROM AUTHOR]

Treatment selection is a multi-criteria decision-making problem of significant concern in the medical field. In this study, a fuzzy decision-making framework is established for treatment selection. The framework mitigates information loss by introducing single-valued trapezoidal neutrosophic numbers to denote evaluation information. Treatment selection has multiple criteria that remarkably exceed the alternatives. In consideration of this characteristic, the framework utilises the idea of the qualitative flexible multiple criteria method. Furthermore, it considers the risk-averse behaviour of a decision maker by employing a concordance index based on TODIM (an acronymin Portuguese of interactive and multi-criteria decision-making) method. A sensitivity analysis is performed to illustrate the robustness of the framework. Finally, a comparative analysis is conducted to compare the framework with several extant methods. Results indicate the advantages of the framework and its better performance compared with the extant methods. [ABSTRACT FROM AUTHOR]

Hesitant fuzzy set (HFS) is a powerful decision tool to express uncertain information more flexibly and comprehensively. The aim of this paper is to propose more reasonable information measures for HFSs in comparison with the existing ones. First, a series of distance measures is suggested for hesitant fuzzy element and hesitant fuzzy sets. These measures are directly calculated from hesitant fuzzy elements without judging the decision-makers’ risk preference and adding any values into the hesitant fuzzy element with the smaller number of elements. Then, some similarity and entropy measures are proposed based on the transforming relationship among the information measures. Additionally, based on the proposed information measures, a TOPSIS method for hesitant fuzzy information is provided. Finally, some numerical examples are used in order to illustrate the proposed decision method and a comparative analysis is made to demonstrate that the suggested measures are more objective and feasible in certain cases. [ABSTRACT FROM AUTHOR]

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided. [ABSTRACT FROM AUTHOR]

As a generalisation of the Fuzzy Sets theory, vague set has been proven to be a new tool in dealing with vague information. In this article, we attempt to generalise the techniques of fuzzy inference in a vague environment. In the rule-based inference system, an ‘if … then …’ rule can be considered a transformer that implements information conversion between input–output ends. Thus, according to the logical operations of vague linguistic variables, we introduce an approach to approximation inference based on linear transformation, and then discuss the representations for several inference structures regarding single rule, multi-rules and compound rules. By defining the inclusion function of vague sets, we provide vague rough approximation based on measure of inclusion, and then present a method on rule creation from a decision system. A case study on the prediction for welding deformation is used to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

Many practical optimisation problems are with the existence of uncertainties, among which a significant number belong to the dynamic optimisation problem (DOP) category in which the fitness function changes through time. In this study, we propose the cultural-based particle swarm optimisation (PSO) to solve DOP problems. A cultural framework is adopted incorporating the required information from the PSO into five sections of the belief space, namely situational, temporal, domain, normative and spatial knowledge. The stored information will be adopted to detect the changes in the environment and assists response to the change through a diversity-based repulsion among particles and migration among swarms in the population space, and also helps in selecting the leading particles in three different levels, personal, swarm and global levels. Comparison of the proposed heuristics over several difficult dynamic benchmark problems demonstrates the better or equal performance with respect to most of other selected state-of-the-art dynamic PSO heuristics. [ABSTRACT FROM PUBLISHER]

Many real-world optimisation problems are both dynamic and multi-modal, which require an optimisation algorithm not only to find as many optima under a specific environment as possible, but also to track their moving trajectory over dynamic environments. To address this requirement, this article investigates a memetic computing approach based on particle swarm optimisation for dynamic multi-modal optimisation problems (DMMOPs). Within the framework of the proposed algorithm, a new speciation method is employed to locate and track multiple peaks and an adaptive local search method is also hybridised to accelerate the exploitation of species generated by the speciation method. In addition, a memory-based re-initialisation scheme is introduced into the proposed algorithm in order to further enhance its performance in dynamic multi-modal environments. Based on the moving peaks benchmark problems, experiments are carried out to investigate the performance of the proposed algorithm in comparison with several state-of-the-art algorithms taken from the literature. The experimental results show the efficiency of the proposed algorithm for DMMOPs. [ABSTRACT FROM PUBLISHER]

This article presents a useful method for relating anchor dependency and accuracy functions to multiple attribute decision-making (MADM) problems in the context of Atanassov intuitionistic fuzzy sets (A-IFSs). Considering anchored judgement with displaced ideals and solution precision with minimal hesitation, several auxiliary optimisation models have proposed to obtain the optimal weights of the attributes and to acquire the corresponding TOPSIS (the technique for order preference by similarity to the ideal solution) index for alternative rankings. Aside from the TOPSIS index, as a decision-maker's personal characteristics and own perception of self may also influence the direction in the axiom of choice, the evaluation of alternatives is conducted based on distances of each alternative from the positive and negative ideal alternatives, respectively. This article originates from Li's [Li, D.-F. (2005), ‘Multiattribute Decision Making Models and Methods Using Intuitionistic Fuzzy Sets’, Journal of Computer and System Sciences, 70, 73–85] work, which is a seminal study of intuitionistic fuzzy decision analysis using deduced auxiliary programming models, and deems it a benchmark method for comparative studies on anchor dependency and accuracy functions. The feasibility and effectiveness of the proposed methods are illustrated by a numerical example. Finally, a comparative analysis is illustrated with computational experiments on averaging accuracy functions, TOPSIS indices, separation measures from positive and negative ideal alternatives, consistency rates of ranking orders, contradiction rates of the top alternative and average Spearman correlation coefficients. [ABSTRACT FROM PUBLISHER]

Ranking fuzzy numbers plays an important role in a fuzzy decision-making process. However, fuzzy numbers may not be easily ordered into one sequence due to the overlap between them. A new approach is introduced to detect the overlapped fuzzy numbers based on the concept of similarity measure, incorporating the preference of the decision-maker into the fuzzy ranking process. Numerical examples and comparisons with other methods are presented to evaluate the new method. The computational process of the proposed method is straightforward and is practically capable of comparing similar fuzzy numbers. The proposed method is an absolute ranking and no pairwise comparison of fuzzy numbers is necessary. Furthermore, through some examples discussed in this work, it is proved that the proposed method possesses several good characteristics compared to other methods examined in this work. [ABSTRACT FROM AUTHOR]

In this article, the remote fault detection (FD) problem over unreliable communication channels encountering bit errors and quantisation errors is studied, where data transmissions can be centralised or decentralised. The online channel reliability information represented by the so-called bit error rate (BER) is first analysed in the view of control engineering and then transformed into time-varying parameters and stochastic signals in the control systems. By using the information of BERs provided by communication systems, we propose a new remote FD system which consists of an observer-based residual generator and a residual evaluator. The design of the residual generator is formulated as a model matching problem such that an optimal FD performance can be achieved. Then the residual signals are evaluated and compared with a threshold to detect the occurrences of faults. The false alarm rate is guaranteed to be below a given level. All the solutions are presented in terms of linear matrix inequalities. A numerical example is used to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

A major reason for constructing gene regulatory networks is to use them as models for determining therapeutic intervention strategies by deriving ways of altering their long-run dynamics in such a way as to reduce the likelihood of entering undesirable states. In general, two paradigms have been taken for gene network intervention: (1) stationary external control is based on optimally altering the status of a control gene (or genes) over time to drive network dynamics; and (2) structural intervention involves an optimal one-time change of the network structure (wiring) to beneficially alter the long-run behaviour of the network. These intervention approaches have mainly been developed within the context of the probabilistic Boolean network model for gene regulation. This article reviews both types of intervention and applies them to reducing the metastatic competence of cells via intervention in a melanoma-related network. [ABSTRACT FROM AUTHOR]

In this work, we propose a neural networks-based machine vision system, which is intended to act as a reconfigurable inspection tool, for use in manufacturing environments. The processing engine of the system is a second-order neural network, which extracts geometric features invariant to translation and rotation. A major issue with the use of higher-order neural networks is the combinatorial explosion of the higher-order terms, which is addressed here with the use of the alternative image representation strategy of coarse coding. We developed a genetic algorithms tool, which allows the automated determination of the optimal number of hidden units in the neural networks architecture. The inspection system is tested in two application areas, namely inspection of axisymmetric components and classification of rivets. Numerous tests are carried out to evaluate the robustness of the proposed system to complex noise sources. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of realizing associative memories via cellular neural networks (CNNs). After introducing qualitative properties of the CNN model, we formulate the synthesis of CNNs that can store given binary vectors with improved performance as a constrained optimization problem. Next, we observe that this problem's constraints can be transformed into simple inequalities involving linear matrix inequalities. Finally, we reformulate the synthesis problem as a generalized eigenvalue problem, which can be efficiently solved by recently developed interior point methods. The validity of the proposed approach is illustrated by a design example. [ABSTRACT FROM AUTHOR]