35 research outputs found

    A method to solve two-player zero-sum matrix games in chaotic environment

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    This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment. In a fast growing world, the real life situations are characterized by their chaotic behaviors and chaotic processes. The chaos variables are defined to study such type of problems. Classical mathematics deals with the numbers as static and less value-added, while the chaos mathematics deals with it as dynamic evolutionary, and comparatively more value-added. In this research article, the payoff is characterized by chaos numbers. While the chaos payoff matrix converted into the corresponding static payoff matrix. An approach for determining the chaotic optimal strategy is developed. In the last, one solved example is provided to explain the utility, effectiveness and applicability of the approach for the problem.Abbreviations: DM= Decision Maker; MCDM = Multiple Criteria Decision Making; LPP = Linear Programming Problem; GAMS= General Algebraic Modeling System

    Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected Works), Vol. 4

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    The fourth volume on Advances and Applications of Dezert-Smarandache Theory (DSmT) for information fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics. The contributions (see List of Articles published in this book, at the end of the volume) have been published or presented after disseminating the third volume (2009, http://fs.unm.edu/DSmT-book3.pdf) in international conferences, seminars, workshops and journals. First Part of this book presents the theoretical advancement of DSmT, dealing with Belief functions, conditioning and deconditioning, Analytic Hierarchy Process, Decision Making, Multi-Criteria, evidence theory, combination rule, evidence distance, conflicting belief, sources of evidences with different importance and reliabilities, importance of sources, pignistic probability transformation, Qualitative reasoning under uncertainty, Imprecise belief structures, 2-Tuple linguistic label, Electre Tri Method, hierarchical proportional redistribution, basic belief assignment, subjective probability measure, Smarandache codification, neutrosophic logic, Evidence theory, outranking methods, Dempster-Shafer Theory, Bayes fusion rule, frequentist probability, mean square error, controlling factor, optimal assignment solution, data association, Transferable Belief Model, and others. More applications of DSmT have emerged in the past years since the apparition of the third book of DSmT 2009. Subsequently, the second part of this volume is about applications of DSmT in correlation with Electronic Support Measures, belief function, sensor networks, Ground Moving Target and Multiple target tracking, Vehicle-Born Improvised Explosive Device, Belief Interacting Multiple Model filter, seismic and acoustic sensor, Support Vector Machines, Alarm classification, ability of human visual system, Uncertainty Representation and Reasoning Evaluation Framework, Threat Assessment, Handwritten Signature Verification, Automatic Aircraft Recognition, Dynamic Data-Driven Application System, adjustment of secure communication trust analysis, and so on. Finally, the third part presents a List of References related with DSmT published or presented along the years since its inception in 2004, chronologically ordered

    An Uncertainty Measure for Interval-valued Evidences

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    Interval-valued belief structure (IBS), as an extension of single-valued belief structures in Dempster-Shafer evidence theory, is gradually applied in many fields. An IBS assigns belief degrees to interval numbers rather than precise numbers, thereby it can handle more complex uncertain information. However, how to measure the uncertainty of an IBS is still an open issue. In this paper, a new method based on Deng entropy denoted as UIV is proposed to measure the uncertainty of the IBS. Moreover, it is proved that UIV meets some desirable axiomatic requirements. Numerical examples are shown in the paper to demonstrate the efficiency of UIV by comparing the proposed UIV with existing approaches.

    Combination of Evidential Sensor Reports with Distance Function and Belief Entropy in Fault Diagnosis

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    Although evidence theory has been applied in sensor data fusion, it will have unreasonable results when handling highly conflicting sensor reports. To address the issue, an improved fusing method with evidence distance and belief entropy is proposed. Generally, the goal is to obtain the appropriate weights assigning to different reports. Specifically, the distribution difference between two sensor reports is measured by belief entropy. The diversity degree is presented by the combination of evidence distance and the distribution difference. Then, the weight of each sensor report is determined based on the proposed diversity degree. Finally, we can use Dempster combination rule to make the decision. A real application in fault diagnosis and an example show the efficiency of the proposed method. Compared with the existing methods, the method not only has a better performance of convergence, but also less uncertainty

    Game theory based multi criteria decision making problem under uncertainty: a case study on Indian Tea Industry

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    The long-term evolution of multi agent multi criteria decision making (MCDM) and to obtain sustainable decision a novel methodology is proposed based on evolutionary game theory. In this paper multi agent MCDM is represented as an evolutionary game and the evolutionary strategies are defined as sustainable decisions. Here we consider the problem of decision making in Indian Tea Industry. The agents in this game are essentially Indian Tea Estate owner and Indian Tea board. The replicator dynamics of the evolutionary game are studied to obtain evolutionary strategies which could be defined as sustainable strategies. The multi agent MCDM in Indian Tea Industry is considered under different socio-political and Corporate Social Responsibility scenario and groups of Indian Tea Industry. Again, the impacts of imprecision and market volatility on the outcome of some strategies (decisions) are studied. In this paper the imprecision on the impact of the strategies are modelled as fuzzy numbers whereas the market volatility is taken into account as white noise. Hence the MCDM problem for Indian Tea Industry is modelled as a hybrid evolutionary game. The probabilities of strategies are obtained by solving hybrid evolutionary game and could be represented as a Dempster-Shafer belief structure. The simulation results facilitate the Decision Makers to choose the strategies (decisions) under different type of uncertainty

    FORETELL: Aggregating Distributed, Heterogeneous Information from Diverse Sources Using Market-based Techniques

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    Predicting the outcome of uncertain events that will happen in the future is a frequently indulged task by humans while making critical decisions. The process underlying this prediction and decision making is called information aggregation, which deals with collating the opinions of different people, over time, about the future eventā€™s possible outcome. The information aggregation problem is non-trivial as the information related to future events is distributed spatially and temporally, the information gets changed dynamically as related events happen, and, finally, peopleā€™s opinions about eventsā€™ outcomes depends on the information they have access to and the mechanism they use to form opinions from that information. This thesis addresses the problem of distributed information aggregation by building computational models and algorithms for different aspects of information aggregation so that the most likely outcome of future events can be predicted with utmost accuracy. We have employed a commonly used market-based framework called a prediction market to formally analyze the process of information aggregation. The behavior of humans performing information aggregation within a prediction market is implemented using software agents which employ sophisticated algorithms to perform complex calculations on behalf of the humans, to aggregate information efficiently. We have considered five different yet crucial problems related to information aggregation, which include: (i) the effect of variations in the parameters of the information being aggregated, such as its reliability, availability, accessibility, etc., on the predicted outcome of the event, (ii) improving the prediction accuracy by having each human (software-agent) build a more accurate model of other humansā€™ behavior in the prediction market, (iii) identifying how various market parameters effect its dynamics and accuracy, (iv) applying information aggregation to the domain of distributed sensor information fusion, and, (v) aggregating information on an event while considering dissimilar, but closely-related events in different prediction markets. We have verified all of our proposed techniques through analytical results and experiments while using commercially available data from real prediction markets within a simulated, multi-agent based prediction market. Our results show that our proposed techniques for information aggregation perform more efficiently or comparably with existing techniques for information aggregation using prediction markets

    Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5

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    This ļ¬fth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different ļ¬elds of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modiļ¬ed Proportional Conļ¬‚ict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classiļ¬ers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identiļ¬cation of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classiļ¬cation. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classiļ¬cation, and hybrid techniques mixing deep learning with belief functions as well

    Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

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    Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment
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