Due to the uncertainty of decision environment and differences of decision makers’ culture and knowledge background, multi-granular HFLTSs are usually elicited by decision makers in a multi-attribute ...group decision making (MAGDM) problem. In this paper, a novel consensus model is developed for MAGDM based on multi-granular HFLTSs. First, it is defined the group consensus measure based on the fuzzy envelope of multi-granular HFLTSs. Afterwards, an optimization model which aims to minimize the overall adjustment amount of decision makers’ preference is established. Based on the model, an iterative algorithm is devised to help decision makers reach consensus in MAGDM with multi-granular HFLTSs. Numerical results demonstrate the characteristics of the proposed consensus model.
•Propose some formulae to calculate the gain and loss for unbalanced HFLTSs.•Extend the TODIM method to deal with MCGDM problems with unbalanced HFLTSs.•Provide three applications to demonstrate the ...proposed TODIM method.
Uncertainty and impreciseness usually exist widely in decision making problems nowadays. When eliciting assessments over alternatives, decision makers tend to have some hesitancy and thus provide hesitant fuzzy linguistic term sets (HFLTSs). Moreover, the unbalanced linguistic term set sometimes has advantages over the balanced one for dealing with practical linguistic decision making problems. The purpose of this paper is to develop a new method to deal with multi-criteria group decision making (MCGDM) problems with unbalanced HFLTSs by considering the psychological behavior of decision makers. To achieve this goal, some formulae are first proposed to calculate the gain and loss for an unbalanced HFLTS over another. As a special case of the unbalanced HFLTS, the formulae of gain and loss for a balanced HFLTS are also provided. Afterwards, the classical TODIM method is extended to develop a new MCGDM method based on unbalanced HFLTSs. Eventually, the proposed method is demonstrated by using three practical applications, including a personnel selection process, an investment alternative selection process and a telecommunication service provider selection process.
In this paper, the existence result of at least two positive solutions is obtained for a nonlinear Riemann-Liouville fractional differential equation subject to nonlocal boundary conditions, where ...fractional derivatives and Riemann-Stieltjes integrals are involved. The nonlinearity possesses singularities on both its time and space variables. The discussion is based on the fixed point index theory on cones.
In this paper, different height functions of the nonlinear term on special bounded sets together with Leggett–Williams and Krasnosel’skii fixed point theorems are employed to establish the existence ...of triple positive solutions for a class of higher-order fractional differential equations with integral conditions. The singularities are with respect not only to the time but also to the space variables.
Associative Classification (AC) is envisioned as one of the most attractive classification approaches to facilitate managers for prediction and decision making in a highly accurate and easily ...interpretable way. The most of existing AC algorithms mainly focus on the two static metrics of association rules: support and confidence. However, in this paper, we identify a potential limitation of the confidence and further point out these AC algorithms merely consider the explicit expression of classification information and knowledge of Class Association Rules (CARs) and neglect the implicit expression of classification information and knowledge of CARs. And even the explicit expression of classification information and knowledge of CARs is equivalent, the implicit expression of classification information and knowledge of them may be different. Thus, these CARs will cause different influence on prediction or decision-making in terms of the interpretability and rationality of classification, and will result in predictive bias or decision-making bias in practice. In response to this drawback, we introduce the notion of information entropy and propose an innovative approach for associative classification based on information entropy of frequent attribute set, named EAC. Different from the existing schemes, the proposed EAC algorithm enjoys the following promising merits: (1) lower predictive bias or decision-making bias by levering the information entropy of frequent attribute set; (2) better interpretability and rationality by setting higher support threshold; (3)setting global optimum parameter dynamically through repeated trials with reducing the dimension of data sets. Experiments on 20 well-known benchmark data sets demonstrate that our EAC approach is highly competitive to other state-of-the-art AC algorithms in terms of predictive bias or decision-making bias, interpretability, and efficiency, which can be used to construct a new classifier efficiently and effectively in many realistic scenarios.
This article deals with integral boundary value problems of the second-order differential equations
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In this article, by means of fixed point theorem on mixed monotone operator, we establish the uniqueness of positive solution for some nonlocal singular higher-order fractional differential equations ...involving arbitrary derivatives. We also give iterative schemes for approximating this unique positive solution.
In recent years, Internet-based firms have been increasingly engaged in recycling used products, taking advantage of economies of scale by serving a number of manufacturers. However, most studies on ...the recycling channel of remanufacturing to date only consider the case of a single manufacturer in a closed-loop supply chain. To address this gap, we develop a Stackelberg game model and show that the joint third-party (J3P) collection mode serving multiple manufacturers may outperform individual retailer- and manufacturer-managed modes, as opposed to existing findings considering a single manufacturer. It is optimal for manufacturers to authorise a large-scale J3P to collect used products. In addition, we show that the J3P can design a two-part tariff contract for the manufacturers to overcome the double marginalisation and collective action problems in decentralised supply chains. Our results provide guidance for enterprises and the government on recycling decisions in the era of a network economy.
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