An Application of Fuzzy Decision Theory in Combat Decision Simulation

In this paper a model of military command process under the combat situation is presented. The model is based on the Lanchester Equations and Fuzzy Decision Theory. The decision of a military commander is usually a process from precise to fuzzy and then from fuzzy to precise,and the model fitted this process well. The model was used in a Warfare Simulation System whose object is to evaluate the effectiveness of the military C3I systems.

Slope Stability Analysis Based on Group Decision Theory and Fuzzy Comprehensive Evaluation

A slope stability evaluation method is proposed combining group decision theory,the analytic hierarchy process and fuzzy comprehensive evaluation.The index weight assignment of each evaluation element is determined by group decision theory and the analytic hierarchy process,and the membership degree of each indicator is determined based on fuzzy set theory.According to the weights and memberships,the membership degrees of the criterion layer are obtained by fuzzy operations to evaluate the slope stability.The results show that(1)the evaluation method comprehensively combines the effects of multiple factors on the slope stability,and the evaluation results are accurate;(2)the evaluation method can fully leverage the experience of the expert group and effectively avoid evaluation errors caused by the subjective bias of a single expert;(3)based on a group decision theory entropy model,this evaluation method can quantitatively evaluate the reliability of expert decisions and effectively improve the efficiency of expert group discussion;and(4)the evaluation method can transform the originally fuzzy and subjective slope stability evaluation into a quantitative evaluation.

Visual detection of rice rows based on Bayesian decision theory and robust regression least squares method

Paddy field management is complicated and labor intensive.Correct row detection is important to automatically track rice rows.In this study,a novel method was proposed for accurate rice row recognition in paddy field transplanted by machine before the disappearance of row information.Firstly,Bayesian decision theory based on the minimum error was used to classify the period of collected images into three periods(T1:0-7 d;T2:7-28 d;T3:28-45 d),and resulting in the correct recognition rate was 97.03%.Moreover,secondary clustering of feature points was proposed,which can solve some problems such as row breaking and tilting.Then,the robust regression least squares method(RRLSM)for linear fitting was proposed to fit rice rows to effectively eliminate interference by outliers.Finally,a credibility analysis of connected region markers was proposed to evaluate the accuracy of fitting lines.When the threshold of credibility was set at 40%,the correct recognition rate of fitting lines was 96.32%.The result showed that the method can effectively solve the problems caused by the presence of duckweed,high-density inter-row weeds,broken rows,tilting(±60°),wind and overlap.

A Bayesian Theory of Games： An Analysis of Strategic Interactions with Statistical Decision Theoretic Foundation

This paper introduces a new game theoretic equilibrium which is based upon the Bayesian subjective view of probability, BEIC （Bayesian equilibrium iterative conjectures）. It requires players to make predictions, starting from first order uninformative predictive distribution functions （or conjectures） and keep updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. Information known by the players such as the reaction functions are thereby incorporated into their higher order conjectures and help to determine the convergent conjectures and the equilibrium. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and conjectures. The BEIC approach is capable of analyzing a larger set of games than current Nash Equilibrium based games theory, including games with inaccurate observations, games with unstable equilibrium and games with double or multiple sided incomplete information games. On the other hand, for the set of games analyzed by the current games theory, it generates far lesser equilibriums and normally generates only a unique equilibrium. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games. Finally, it also resolves inconsistencies in equilibrium results by different solution concepts in current games theory such as that between Nash Equilibrium and iterative elimination of dominated strategies and that between Perfect Bayesian Equilibrium and backward induction （Subgame Perfect Equilibrium）.

A Receiver-Forwarding Decision Scheme Based on Bayesian for NDN-VANET

Named Data Network(NDN) has caused wide concerns in VANET community because NDN uses a content-centric mechanism that naming content rather than the host. However, integrating NDN into VANET(NDN-VANET) also faces several challenges including consumer/provider mobile, broadcast storm problem and so on. In this paper, we propose a Bayesian-based Receiver Forwarding Decision(BRFD) scheme to mitigate the broadcast storm problem incurred by interest packets in NDN-VANET. In the BRFD, vehicles received an interest packet are required to make forwarding decisions based on Bayesian decision theory according to current network conditions obtained by neighbor interaction. However, the receiver-forwarding decision in BRFD can also cause a conflict issue because multiple vehicles forward copies of the same packet at the same time. So a back-off mechanism is introduced in BRFD. Experimental results show that the BRFD algorithm has better performance in several aspects in contrast to probability-based forwarding scheme and "bread crumb" routing.

New method for hybrid multiple attribute decision-making problems with decision maker's aspiration level

How can we account for decision maker's aspiration level in multiple attribute decision-making problems? This is a question that has recently gained much scholarly attention. This study draws on the prospect theory and the Dempster-Shafer theory to propose a method that can resolve this issue. First, the precise and interval numbers and linguistic labels are compared, and then, the decision matrix is transformed into a prospect decision matrix on the basis of decision maker's aspiration level. Second, the Dempster-Shafer theory is applied to aggregate the prospect values of all alternatives on each attribute using their prospect belief intervals. Third, the orders of alternatives are obtained for all decision methods by comparing prospect belief intervals. Final, the effectiveness and feasibility of the proposed method are demonstrated by using an illustrative example. © 1990-2011 Beijing Institute of Aerospace Information.

Decision Making as Theorem Proving

We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types, and solutions and programs has been established to support this view which is much similar to the Curry-Howard isomorphism between propositions and types, and proofs and programs. To support our method, a proof development system called PowerEpsilon has been developed, and the synthesis of a decision procedure for validity of first-order propositional logic is discussed to show the power of the system.

Dual worth trade-off method and its application for solving multiple criteria decision making problems

To overcome the limitations of the traditional surrogate worth trade-off （SWT） method and solve the multiple criteria decision making problem more efficiently and interactively, a new method labeled dual worth tradeoff （DWT） method is proposed. The DWT method dynamically uses the duality theory related to the multiple criteria decision making problem and analytic hierarchy process technique to obtain the decision maker＇s solution preference information and finally find the satisfactory compromise solution of the decision maker. Through the interactive process between the analyst and the decision maker, trade-off information is solicited and treated properly, the representative subset of efficient solutions and the satisfactory solution to the problem are found. The implementation procedure for the DWT method is presented. The effectiveness and applicability of the DWT method are shown by a practical case study in the field of production scheduling.

New Explorations for Decision Trees

Traditionally, the decision tree method is defined and used for finding the optimal solution of a Bayesian decision problem. And it is difficult to use the decision tree method to find the sub-optimal solution, not to mention to rank alternatives. This paper discusses how to use the decision tree method for the alternative selecting and ranking. A practical case study is given to illustrate the applicability.

An Approach for Integrating Quantitative Decision Model with Qualitative Judgment

In this paper, decision making in complex environment is considered and an approach integrating quantitative decision model with qualitative judgment is proposed. The concept of belief degree for quantitative decision model in a complex environment is presented. The integration in formulation and reasoning of quantitative model with qualitative judgment is studied. The combination of various belief degree generated by quantitative model and qualitative judgment is discussed. A decision rule of tradeoff between optimality and belief degree of optimality is proposed.

Assessing Probabilities for Events Pertaining to Buy/Sell and Similar Decisions

Assessing probabilities for relevant and sometimes unique events in real-world decision situations can be problematic. This paper elucidates a 2-step process for assigning probabilities to relevant events enabling a rational decision process to supersede decision choices based only on a gut feeling. After assessing probabilities the decision maker can confirm or reverse a gut feeling choice using expected values for each available act and traditional decision theory methodology. A simple example involving a buy now or buy later situation with market uncertainty illustrates the process for typical yes or no decisions.

Travel modal choice analysis for traffic corridors based on decision-theoretic approaches

The rapid development of multimodal transportation system prompts travellers to choose multiple transportation modes, such as private vehicles or taxi, transit(subways or buses), or park-and-ride combinations for urban trips. Traffic corridor is a major scenario that supports travellers to commute from suburban residential areas to central working areas. Studying their modal choice behaviour is receiving more and more interests. On one hand, it will guide the travellers to rationally choose their most economic and beneficial mode for urban trips. On the other hand, it will help traffic operators to make more appropriate policies to enhance the share of public transit in order to alleviate the traffic congestion and produce more economic and social benefits. To analyze the travel modal choice, a generalized cost model for three typical modes is first established to evaluate each different travel alternative. Then, random utility theory(RUT) and decision field theory(DFT) are introduced to describe the decision-making process how travellers make their mode choices. Further, some important factors that may influence the modal choice behaviour are discussed as well. To test the feasibility of the proposed model, a field test in Beijing was conducted to collect the real-time data and estimate the model parameters. The improvements in the test results and analysis show new advances in the development of travel mode choice on multimodal transportation networks.

Sequential Track Monitoring with Multiple 2-D Passive Sensors

Track monitoring is a fast method of determining incorrect return-to-track and track-to-track assignments. An analytical method to evaluate the effectiveness of track monitoring was presented by reference [1]. In order to reduce the probability of initiating or accepting the ghost track, two sequential track monitoring algorithms, which use the inclination angles to form test statistics, are proposed in this paper. Two decision rules are given and the corresponding thresholds are derived. The paper also gives the estimation methods of the noncentral parameter of noncentral chi-square distribution when the true value of it is unknown, the algorithms can adaptively estimate the decision thresholds and can make sequential track monitoring decision on line. Simulation is also made and the results show that the proposed algorithms are effective and feasible.

Structuring Probability Assessments

A probability assessment framework is outlined that enables decision-makers to determine a probability distribution over possible events or scenarios they could face in the future.The methodology of the analytic hierarchy process can be utilized in the procedures.Bayesian revision accounting for new developments can be used to calculate posterior probabilities using the same procedures.

IDSS: Designing to Extend the Cognitive Limits

The paper presents the conceptual and operational basis of the creation of IDSS based on our recent research experience. In this paper, an intelligent decision support system, IDSS is defined as: any interactive system that is specially designed to improve the decision making of its user by extending the user's cognitive decision making abilities. As a result, this view of man-machine joint cognitive system stresses the need to use computational technology to aid the user in the decision making process. And the human's role is to achieve total systems's objectives. The paper outlines the designing procedure in successive steps. First, the decision maker's cognitive needs for decision support are identified. Second, the computationally realizable support functions are defined that could be provided by IDSS. Then, the specific techniques that would best fill the decision needs are discussed. And finally, for system implementation the modern computational technology infrastructure is emphasized.

Optimal Dispatch for Flexible Uncertainty Sets in Multi-energy Systems: An IGDT Based Two-stage Decision Framework

The operational stability and economy of multi-energy systems(MES)are threatened by various uncertainties,such as variable renewable energy power,energy demands,and weather conditions.Most of the existing methods for the dispatch decisions of MES are based on the prescribed probability distribution or uncertainty sets of random variables,which have many disadvantages,such as potential infeasibility and over-conservatism.In this paper,we propose a novel dispatch model for MES that integrates dispatch decision making,uncertainty set selection,and operational cost control into a unified framework.First,the deterministic dispatch model of MES is introduced,in which the physical characteristics of district heating systems and buildings are fully considered.Then,a novel decision framework that combines the two-stage dispatch strategy and info-gap decision theory(IGDT)is proposed for MES,where the uncertainty set is flexible and can be optimized based on the operational cost budget.Finally,a revised algorithm,based on the column-and-constraint generation method,is proposed for the model.Case studies are performed on MES that includes a 33-bus distribution system and a heating network modified from a real 51-node network located in Jinlin Province,China.The results verify the effectiveness of the proposed method.

A Multi-objective Chance-constrained Information-gap Decision Model for Active Management to Accommodate Multiple Uncertainties in Distribution Networks

The load demand and distributed generation(DG)integration capacity in distribution networks(DNs)increase constantly,and it means that the violation of security constraints may occur in the future.This can be further worsened by short-term power fluctuations.In this paper,a scheduling method based on a multi-objective chance-constrained information-gap decision(IGD)model is proposed to obtain the active management schemes for distribution system operators(DSOs)to address these problems.The maximum robust adaptability of multiple uncertainties,including the deviations of growth prediction and their relevant power fluctuations,can be obtained based on the limited budget of active management.The systematic solution of the proposed model is developed.The max term constraint in the IGD model is converted into a group of normal constraints corresponding to extreme points of the max term.Considering the stochastic characteristics and correlations of power fluctuations,the original model is equivalently reformulated by using the properties of multivariate Gaussian distribution.The effectiveness of the proposed model is verified by a modified IEEE 33-bus distribution network.The simulation result delineates a robust accommodation space to represent the adaptability of multiple uncertainties,which corresponds to an optional active management strategy set for future selection.

Multiple Objectives under Uncertainty:IRGSD-FD Method

This paper is devoted to study the multiobjective system programming under the assumption that some of the problem parameters are random variables. A method called Interactive Reference Goal Satisfied Degree and Feasible Degree (IRGSD-FD) is developed to solve stochastic multiobjective problems. It is an interactive method providing a so-called `dialogue' between the user and the model, the decision maker having the option conducting the search process for the (α, β)-efficient solutions by modifying the initial conditions according to the partial results obtained. During the iterations, the decision maker can improve upon the reference goal or called aspiration level already attained by one objective function as well as upon the probability of reaching the corresponding objective or called satisfied degree (or both), or/and the probability of satisfying the constraint or called feasible degree already attained by the constraint. Finally, the application of IRGSD-FD method in the resource allocation problem is discussed with a case study for project investment management.

Simulation Modeling by Fuzzy Nets

Fuzzy technology is a newly developed discipline based on fuzzy mathematics. In the recent years, it has been successfully applied into many areas, such as process control, diagnosis, evaluation, decision making and scheduling, especially in simulation where accurate mathematical models can not or very hard be established. In this paper, to meet the demands of fuzzy simulation, two fuzzy nets will first be presented, which are quite suitable for modeling the parallel or concurrent systems with fuzzy behavior. Then, a concept of active simulation will be introduced, in which the simulation model not only can show its fuzzy behavior, but also has a certain ability which can actively perform many very useful actions, such as automatic warning, realtime monitoring, simulation result checking, simulation model self-adapting, error recovery, simulating path tracing, system states inspecting and exception handling, by a unified approach while some specified events occur. The simulation model described by this powerful simulation modeling tool is concurrently driven by a network interpreter and an event monitor that all can be implemented by software or hardware. Besides, some interesting applications are given in the paper.

GENERAL MINIMAX ESTIMATORS ON THE LOCATION MATRIX OF A MIXTURE OF NORMALS

This paper considers the estimate problem on the mean matrix of mixture of normals. In order to evaluate estimators of the mean matrix, a fundamental frame of Φ-(general) decision problem is established. Under the frame, a class of Φ-minimax estimators are constructed.