Uncertain Shapley value of coalitional game with application to supply chain alliance

Uncertain coalitional game deals with situations in which the transferable payoffs are uncertain variables. The uncertain core has been proposed as the solution of uncertain coalitional game. This paper goes further by presenting two definitions of uncertain Shapley value: expected Shapley value and α-optimistic Shapley value. Meanwhile, some characterizations of the uncertain Shapley value are investigated. Finally, as an application, uncertain Shapley value is used to solve a profit allocation problem of supply chain alliance.     

Chance-constrained programming on sugeno measure space

Uncertain programming is a theoretical tool to handle optimization problems under uncertain environment, it is mainly established in probability, possibility, or credibility measure spaces. Sugeno measure space is an interesting and important extension of probability measure space. This motivates us to discuss the uncertain programming based on Sugeno measure space. We have constructed the first type of uncertain programming on Sugeno measure space, i.e. the expected value models of uncertain programming on Sugeno measure space. In this paper, the second type of uncertain programming on Sugeno measure space, i.e. chance-constrained programming on Sugeno measure space, is investigated. Firstly, the definition and the characteristic of α-optimistic value and α-pessimistic value as a ranking measure are provided. Secondly, Sugeno chance-constrained programming (SCCP) is introduced. Lastly, in order to construct an approximate solution to the complex SCCP, the ideas of a Sugeno random number generation and a Sugeno simulation are presented along with a hybrid approach.     

Connectivity reliability in uncertain networks with stability analysis

This paper treats the fundamental problems of reliability and stability analysis in uncertain networks. Here, we consider a collapsed, post-disaster, traffic network that is composed of nodes (centers) and arcs (links), where the uncertain operationality or reliability of links is evaluated by domain experts. To ensure the arrival of relief materials and rescue vehicles to the disaster areas in time, uncertainty theory, which neither requires any probability distribution nor fuzzy membership function, is employed to originally propose the problem of choosing the most reliable path (MRP). We then introduce the new problems of α-most reliable path (α-MRP), which aims to minimize the pessimistic risk value of a path under a given confidence level α, and very most reliable path (VMRP), where the objective is to maximize the confidence level of a path under a given threshold of pessimistic risk. Then, exploiting these concepts, we give the uncertainty distribution of the MRP in an uncertain traffic network. The objective of both α-MRP and VMRP is to determine a path that comprises the least risky route for transportation from a designated source node to a designated sink node, but with different decision criteria. Furthermore, a methodology is proposed to tackle the stability analysis issue in the framework of uncertainty programming; specifically, we show how to compute the arcs’ tolerances. Finally, we provide illustrative examples that show how our approaches work in realistic situation.     

Fuzzy random programming models for location-allocation problem with applications

Three types of fuzzy random programming models based on the mean chance for the capacitated location-allocation problem with fuzzy random demands are proposed according to different criteria, including the expected cost minimization model, the α-cost minimization model, and the chance maximization model. In order to solve the proposed models, some hybrid intelligent algorithms are designed by integrating the network simplex algorithm, fuzzy random simulation, and genetic algorithm. Finally, some numerical examples about a container freight station problem are given to illustrate the effectiveness of the devised algorithms.     

Prediction of time-dependent structural behaviour with recurrent neural networks for fuzzy data

In the paper, an approach is described which permits the numerical, model-free prediction of uncertain time-dependent structural responses. Uncertain time-dependent structural actions and responses are modelled by means of fuzzy processes. The prediction approach is based on recurrent neural networks for fuzzy data trained by time-dependent results of measurements or numerical analyses. An efficient solution for network training and prediction is developed utilizing α-cuts and fuzzy arithmetic. The approach is verified using a fractional rheological model. The capability of the approach is demonstrated by predicting the long-term structural behaviour of reinforced concrete plates strengthened by textile reinforced concrete layers.     

Modelling linear fractional transportation problem in belief degree—based uncertain environment

A linear fractional transportation problem in uncertain environment is studied in this paper where the uncertain parameters of the problem are of belief degree—based uncertainty. For the first time, this type of uncertainty is considered for the linear fractional transportation problem. Belief degree—based uncertainty is useful for the cases that no historical information of an uncertain event is available. Zigzag type uncertainty distribution is used to show the belief degree—based uncertainty of the parameters of the problem. As solution methodology, the uncertain linear fractional transportation problem is converted to a crisp form using three approaches of expected value model, expected value and chance-constrained model, and chance-constrained model, separately. An extensive computational study on a real illustrative example shows the efficiency of the proposed formulation and the conversion approaches. The sensitivity analysis over the example illustrates the high dependency of the objective function value to the changes of the confidence level values of the chance constraints in the expected value and chance-constrained programming approach and the chance-constrained programming approach.     

Classical and superposed learning for quantum weightless neural networks

A supervised learning algorithm for quantum neural networks (QNN) based on a novel quantum neuron node implemented as a very simple quantum circuit is proposed and investigated. In contrast to the QNN published in the literature, the proposed model can perform both quantum learning and simulate the classical models. This is partly due to the neural model used elsewhere which has weights and non-linear activations functions. Here a quantum weightless neural network model is proposed as a quantisation of the classical weightless neural networks (WNN). The theoretical and practical results on WNN can be inherited by these quantum weightless neural networks (qWNN). In the quantum learning algorithm proposed here patterns of the training set are presented concurrently in superposition. This superposition-based learning algorithm (SLA) has computational cost polynomial on the number of patterns in the training set.     

Opportunistic information dissemination in mobile ad-hoc networks: the profit of global synchrony

The topic of this paper is the study of information dissemination in mobile ad-hoc networks by means of deterministic protocols. We assume a weak set of restrictions on the mobility of nodes, parameterized by α, the disconnection time, and β, the link stability time, such that the mobile ad-hoc networks considered are connected enough for dissemination. Such a connectivity model generalizes previous models in that we assume much less connectivity, or make explicit the assumptions in previous papers. The protocols studied are classified into three classes: oblivious (the transmission schedule of a node is only a function of its ID), quasi-oblivious (the transmission schedule may also depend on a global time), and adaptive. The main contribution of this work concerns negative results. Contrasting the lower and upper bounds derived, interesting complexity gaps among protocol-classes are observed. These results show that the gap in time complexity between oblivious and quasi-oblivious (hence, adaptive) protocols is almost linear. This gap is what we call the profit of global synchrony since it represents the gain the network obtains from global synchrony with respect to not having it. We note that the global synchrony required by the efficient quasi-oblivious protocol proposed is simply achieved by piggybacking in the messages sent the time at the source node, as a global reference.     

Shortest path problem with uncertain arc lengths

Uncertainty theory provides a new tool to deal with the shortest path problem with nondeterministic arc lengths. With help from the operational law of uncertainty theory, this paper gives the uncertainty distribution of the shortest path length. Also, it investigates solutions to the α-shortest path and the most shortest path in an uncertain network. It points out that there exists an equivalence relation between the α-shortest path in an uncertain network and the shortest path in a corresponding deterministic network, which leads to an effective algorithm to find the α-shortest path and the most shortest path. Roughly speaking, this algorithm can be broken down into two parts: constructing a deterministic network and then invoking the Dijkstra algorithm.     

Fast leader election in anonymous rings with bounded expected delay

We propose a probabilistic network model, called asynchronous bounded expected delay (ABE), which requires a known bound on the expected message delay. In ABE networks all asynchronous executions are possible, but executions with extremely long delays are less probable. Thus, the ABE model captures asynchrony that occurs in sensor networks and ad-hoc networks.At the example of an election algorithm, we show that the minimal assumptions of ABE networks are sufficient for the development of efficient algorithms. For anonymous, unidirectional ABE rings of known size n we devise a probabilistic election algorithm having average message and time complexity O(n).     

A fuzzy group data envelopment analysis model for high-technology project selection: A case study at NASA

The assessment and selection of high-technology projects is a difficult decision making process at the National Aeronautic and Space Administration (NASA). This difficulty is due to the multiple and often conflicting objectives in addition to the inherent technical complexities and valuation uncertainties involved in the assessment process. As such, a systematic and transparent decision making process is needed to guide the assessment process, shape the decision outcomes and enable confident choices to be made. Various methods have been proposed to assess and select high-technology projects. However, applying these methods has become increasingly difficult in the space industry because there are many emerging risks implying that decisions are subject to significant uncertainty. The source of uncertainty can be vagueness or ambiguity. While vague data are uncertain because they lack detail or precision, ambiguous data are uncertain because they are subject to multiple interpretations. We propose a data envelopment analysis (DEA) model with ambiguity and vagueness. The vagueness of the objective functions is modeled by means of multi-objective fuzzy linear programming. The ambiguity of the input and output data is modeled with fuzzy sets and a new α-cut based method. The proposed models are linear, independent of α-cut variables, and capable of maximizing the satisfaction level of the fuzzy objectives and efficiency scores, simultaneously. Moreover, these models are capable of generating a common set of multipliers for all projects in a single run. A case study involving high-technology project selection at NASA is used to demonstrate the applicability of the proposed models and the efficacy of the procedures and algorithms.     

Standby redundancy optimization problems with fuzzy lifetimes

Three types of system performances—the expected system lifetime, α-system lifetime, and system reliability—characterized in the context of credibility are investigated in this paper. Some fuzzy simulations are designed to estimate these system performances. In order to formulate general standby redundancy optimization problems with fuzzy lifetimes, a spectrum of standby redundancy fuzzy programming models are proposed. Fuzzy simulation, neural network, and genetic algorithm are also integrated to produce a hybrid intelligent algorithm for solving those models. Finally, some numerical experiments on multi-stage system and network system are provided.     

The role of stochastic programming in communication network design

Conventional design and optimization methods are being challenged by the rapid evolution of electronic and optical communication networks. It becomes necessary to incorporate the stochastic effect of traffic flows into network models. This paper introduces the stochastic programming (SP) methodology to characterize the stochastic traffic. A multi-commodity network model is proposed. Two SP approaches, here-and-now and scenario tracking, are described through case studies for a prototype network.     

A Strategic Approach for Re-organizing the Internet Topology by Applying Social Behavior Dynamics

Recent studies have described the topologies of various networks including the Internet are categorized as scale-free networks. Scale-free network is extremely vulnerable to node attacks. However, the suitability of the topology of the Internet for communications has not been studied. We investigate whether the current Internet is optimized in both aspects of communication efficiency and attack tolerance. For this, we define three metrics to represent the capabilities of the network, which are Clustering coefficient, Efficiency, and Reachability. As a result, we found that the value of γ, a scaling exponent in power law function representing the degree distribution of a scale-free network, may be reduced in the present Internet. To reduce the value of γ, we propose four strategies for re-organizing a network. However, in real network, we cannot control the user’s preference directly. We use a diffusion model based on social behavior dynamics. Furthermore, we show the characteristics of the re-organized networks, and discuss which strategy is more appropriate for achieving a desired network.     

The N-intertwined SIS epidemic network model

Serious epidemics, both in cyber space as well as in our real world, are expected to occur with high probability, which justifies investigations in virus spread models in (contact) networks. The N-intertwined virus spread model of the SIS-type is introduced as a promising and analytically tractable model of which the steady-state behavior is fairly completely determined. Compared to the exact SIS Markov model, the N-intertwined model makes only one approximation of a mean-field kind that results in upper bounding the exact model for finite network size N and improves in accuracy with N. We review many properties theoretically, thereby showing, besides the flexibility to extend the model into an entire heterogeneous setting, that much insight can be gained that is hidden in the exact Markov model.     

Combining fuzzy weight average with fuzzy inference system for material substitution selection in electric industry

Material selection is a very important issue for an electronics company as it includes many qualitative or quantification factors. The material selection problem is associated with design and manufacturing problems which have been widely investigated. This study develops a hybrid fuzzy decision-making model which combines the fuzzy weight average (FWA) with the fuzzy inference system (FIS) for material substitution selection in the electronics industry. FWA is employed to select a substitute material in an uncertain environment, while FIS is used for reasoning purposes. FWA with α-cuts arithmetic (FWA_α-cut) is a popularly technology in decision-making problems. However, FWA_α-cut may result in the following unanticipated situations: (1) unclear decision situations; (2) undecided results expressed by fuzzy membership functions; and (3) high computational complexity. Therefore, a fuzzy weight average with the weakest t-norm (FWA_Tω) is designed as an alternative method for group decision making. In contrast to traditional FWA methods, FWA_Tω obtains more visible fuzzy results for decision makers with lower computational complexity, and can provide exacter estimation by the weakest t-norm operations in uncertain environment. Thus, the proposed hybrid fuzzy decision-making model imitates an expert’s experiences and can estimate substitution purchasing in various statuses. A real material substitution selection case is employed to examine the feasibility of the proposed model; experimental results reveal that the proposed model performs better than the traditional FWA model in coping with material substitution selection problems.     

O(n) routing in rearrangeable networks

In (2n−1)-stage rearrangeable networks, the routing time for any arbitrary permutation is Ω(n²) compared to its propagation delay O(n) only. Here, we attempt to identify the sets of permutations, which are routable in O(n) time in these networks. We define four classes of self-routable permutations for Benes network. An O(n) algorithm is presented here, that identifies if any permutation P belongs to one of the proposed self-routable classes, and if yes, it also generates the necessary control vectors for routing P. Therefore, the identification, as well as the switch setting, both problems are resolved in O(n) time by this algorithm. It covers all the permutations that are self-routable by anyone of the proposed techniques. Some interesting relationships are also explored among these four classes of permutations, by applying the concept of ‘group-transformations’ [N. Das, B.B. Bhattacharya, J. Dattagupta, Hierarchical classification of permutation classes in multistage interconnection networks, IEEE Trans. Comput. (1993) 665–677] on these permutations. The concepts developed here for Benes network, can easily be extended to a class of (2n−1)-stage networks, which are topologically equivalent to Benes network. As a result, the set of permutations routable in a (2n−1)-stage rearrangeable network, in a time comparable to its propagation delay has been extended to a large extent.     

An expert system for setting parameters in machining processes

In this paper, an hybrid system is proposed for setting machining parameters from experimental data. A symbolic regression alpha–beta is used to build mathematical models. Every model is validated using statistical analysis then evolutionary computation is used to minimize or maximize the generated model. Symbolic regression α–β is used to build mathematical models by estimation of distribution algorithms. A practical case considering measured data of two machining process on three materials are used to illustrate the utility of the expert system because generates a set of parameters that improve the machining process.     

Network Performance Under Bimodal Traffic Loads

In actual multicomputer networks, communications consist of hybrid traffic in which messages exhibit a variety of sizes. However, to date, most studies on network performance are based on traffic loads of uniformly-sized messages. We investigate the performance of wormhole-routed networks under bimodal traffic distributions, a mix of short and long messages. Our studies show that the presence of long messages degrades network performance for short messages dramatically, qualitatively changing network behavior. We present an analytical model for wormhole-routed networks which not only models network performance under uniformly sized message loads more accurately than existing models, but also can be extended to support bimodal traffic distributions. The model is validated against detailed simulation of routing networks, over a variety of message size distributions and message lengths. In virtually all cases, the model accurately predicts both network throughput and average message latency to within 8%. Because the impact of long messages can be severe, we consider three techniques-packetization, virtual lanes, and adaptive routing-to alleviate their impact. Packetization reduces the blocking time of long messages, improving network performance in most cases. Virtual lanes and adaptive routing together provide sufficient routing freedom to eliminate much of the blocking, producing performance comparable or even superior to that produced by packetization. Together, all three techniques are complementary, providing robust performance over a variety of traffic mixes and message sizes.     

Shipment partitioning and routing to minimize makespan in a transportation network

This paper addresses the problem of partitioning and transporting a shipment of known size through an n-node public transportation network with known scheduled departure and arrival times and expected available capacities for each departure. The objective is to minimize the makespan of shipping. The problem while practical in its scope, has received very little attention in the literature perhaps because of the concentration of research in vehicle routing without regard to partitioning and partitioning without regard to routing. A general non-linear programming model is developed. The model is then converted into a linear model through the Routing First and Assignment Second approach. This approach is different from the general decomposition approaches since they normally do not guarantee optimality. However, the linear model still involves a large number of constraints, and solution is not attempted here. Instead, three heuristics are proposed for solving the problem. Two of the heuristics use iterative techniques to evaluate all possible paths. The third heuristic uses a max-flows approach based upon aggregated capacities to reduce the size of the network presented to the other heuristics. This allows for a good starting point for other heuristics, and may impact the total computational effort. We find that the heuristics developed perform well because in the case of networks that are not congested, they find the optimal solution.