Classification of osteoarthritic and normal knee function using three-dimensional motion analysis and the Dempster-Shafer theory of evidence

In this paper, a novel object classification method is introduced and developed within a biomechanical study of human knee function in which subjects are classified to one of two groups: subjects with osteoarthritic (OA) and normal (NL) knee function. Knee-function characteristics are collected using a three-dimensional motion-analysis technique. The classification method transforms these characteristics into sets of three belief values: a level of belief that a subject has OA knee function, a level of belief that a subject has NL knee function, and an associated level of uncertainty. The evidence from each characteristic is then combined into a final set of belief values, which is used to classify subjects. The final belief values are subsequently represented on a simplex plot, which enables the classification of a subject to be represented visually. The control parameters, which are intrinsic to the classification method, can be chosen by an expert or by an optimization approach. Using a leave-one-out cross-validation approach, the classification accuracy of the proposed method is shown to compare favorably with that of a well-established classifier-linear discriminant analysis. Overall, this study introduces a visual tool that can be used to support orthopaedic surgeons when making clinical decisions.     

Prosum-Prolog system for uncertainty management

In this paper we present a system which uses knowledge represented in the form of production rules accompanied by uncertainty degrees. The uncertainty of a rule is given by using the method from SLOP and FRIL: a support pair, which comprises a necessary and possible support and can be interpreted as an interval in which the unknown probability lies. Giving the knowledge in this form, our system generates a Turbo Prolog program which has included the operations for uncertainty management. In this version, two kinds of rules for support logic programming are implemented but the user can propose the other ones, by using the dialogue with the system. Semantic unification differs from that used in FRIL; we use generalized belief functions. © 1997 John Wiley & Sons, Inc.     

An evolutionary Bayesian belief network methodology for optimum management of groundwater contamination

An integrated methodology, based on Bayesian belief network (BBN) and evolutionary multi-objective optimization (EMO), is proposed for combining available evidence to help water managers evaluate implications, including costs and benefits of alternative actions, and suggest best decision pathways under uncertainty. A Bayesian belief network is a probabilistic graphical model that represents a set of variables and their probabilistic relationships, which also captures historical information about these dependencies. In complex applications where the task of defining the network could be difficult, the proposed methodology can be used in validation of the network structure and the parameters of the probabilistic relationship. Furthermore, in decision problems where it is difficult to choose appropriate combinations of interventions, the states of key variables under the full range of management options cannot be analyzed using a Bayesian belief network alone as a decision support tool. The proposed optimization method is used to deal with complexity in learning about actions and probabilities and also to perform inference. The optimization algorithm generates the state variable values which are fed into the Bayesian belief network. It is possible then to calculate the probabilities for all nodes in the network (belief propagation). Once the probabilities of all the linked nodes have been updated, the objective function values are returned to the optimization tool and the process is repeated. The proposed integrated methodology can help in dealing with uncertainties in decision making pertaining to human behavior. It also eliminates the shortcoming of Bayesian belief networks in introducing boundary constraints on probability of state values of the variables. The effectiveness of the proposed methodology is examined in optimum management of groundwater contamination risks for a well field capture zone outside Copenhagen city.     

认识逻辑(1):关于知识和信念的逻辑框架

知识和信念是人工智能领域研究中经常涉及到的两个重要概念。本文讨论了知识和信念的涵义与关系，定义了认识逻辑系统ＥＩ，讨论了它的语法和语义，证明了认识逻辑ＥＬ不但是可靠的而且是完备的，认为逻辑ＥＬ不但可以用来描述人类的认识过程，还可以用于对常识推理以及分布式系统的形式化描述。     

Towards a Self-Learning Agent: Using Ranking Functions as a Belief Representation in Reinforcement Learning

We propose a combination of belief revision and reinforcement learning which leads to a self-learning agent. The agent shows six qualities we deem necessary for a successful and adaptive learner. This is achieved by representing the agent’s belief in two different levels, one numerical and one symbolical. While the former is implemented using basic reinforcement learning techniques, the latter is represented by Spohn’s ranking functions. To make these ranking functions fit into a reinforcement learning framework, we studied the revision process and identified key weaknesses of the to-date approach. Despite the fact that the revision was modeled to support frequent updates, we propose and justify an alternative revision which leads to more plausible results. We show in an example application the benefits of the new approach, including faster learning and the extraction of learned rules.     

Representation of qualitative user preference by quantitativebelief functions

Many intelligent systems employ numeric degrees of belief supplied by the users to make decisions. However, the users may have difficulties in expressing their belief in terms of numeric values. The authors present a method for generating belief functions from symbolic information such as the qualitative preference relationships. The method of generating belief functions provides a practical interface between the users and a decision support system. It can be argued that the ability to generate numeric judgments with nonnumeric inputs is essential in the development of approximate reasoning systems. The proposed method can provide an important component for these systems by transforming qualitative information into quantitative information     

Liar liar,pants on fire; or how to use subjective logic and argumentation to evaluate information from untrustworthy sources

This paper presents a non-prioritized belief change operator, designed specifically for incorporating new information from many heterogeneous sources in an uncertain environment. We take into account that sources may be untrustworthy and provide a principled method for dealing with the reception of contradictory information. We specify a novel Data-Oriented Belief Revision Operator, that uses a trust model, subjective logic, and a preference-based argumentation framework to evaluate novel information and change the agent’s belief set accordingly. We apply this belief change operator in a collaborative traffic scenario, where we show that (1) some form of trust-based non-prioritized belief change operator is necessary, and (2) in a direct comparison between our operator and a previous proposition, our operator performs at least as well in all scenarios, and significantly better in some.     

Belief‐function representation of statistical audit evidence

The belief‐function representation of statistical evidence has always been a problematic issue. This problem is of particular importance to auditing because it is an application domain that fits the belief‐function framework very well, but that is also confronted with the frequent use of statistical evidence as well as nonstatistical evidence. Hence, there is a need for methods to represent statistical evidence as belief functions to combine them with belief functions from other evidence types and to obtain belief in final conclusions. This paper proposes such a method designed for application in an auditing context, although it can be useful in other contexts as well. The explanation of this method, as well as the comparison of its properties with those of other existing methods is the subject of this paper. © 2000 John Wiley & Sons, Inc.     

FAULT-TOLERANT MULTI-AGENT EXACT BELIEF PROPAGATION

Multiply sectioned Bayesian networks (MSBNs) support multi-agent probabilistic inference in distributed large problem domains, where agents (subdomains) are organized by a tree structure (called hypertree). In earlier work, all belief updating methods on a hypertree are made of two rounds of propagation, each of which is implemented as a recursive process. Both processes need to be started from the same designated (root) hypernode. Agents perform local belief updating at most in a partial parallel manner. Such methods may not be suitable for practical multi-agent environments because they are easy to crush for the problems happened in communication or local belief updating. In this paper, we present a fault-tolerant belief updating method for multi-agent probabilistic inference. In this method, multiple agents concurrently perform exact belief updating in a complete parallel. Temporary problems happened from time to time at some agents or some communication channels would not prevent agents from eventually converging to the correct beliefs. Permanently disconnected communication channels would not keep the properly connected portions of the system from appropriately finishing their belief updating within portions. Compared to the previous traversal-based belief updating, the proposed approach is not only fault-tolerant but also robust and scalable.     

Changes of disjunctively closed bases

An operator of contraction for a belief set (a theory) can be obtained by assigning to it a belief base and an operator of partial meet contraction for that base. It is argued that closure of the base under disjunction is an intuitively reasonable condition. Axiomatic characterizations are given of the contractions of belief sets that can be generated by (various types of) partial meet contraction on disjunctively closed bases. The corresponding revision operators are also characterized. Finally, some results are reported on operations on bases that are closed under material implication.I would like to thank Hans Rott and two anonymous referees for valuable comments and the Swedish Council for Research in the Humanities and Social Sciences for financial support.     

Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory

Measuring the uncertainty of pieces of evidence is an open issue in belief function theory. A rational uncertainty measure for belief functions should meet some desirable properties, where monotonicity is a very important property. Recently, measuring the total uncertainty of a belief function based on its associated belief intervals becomes a new research idea and has attracted increasing interest. Several belief interval based uncertainty measures have been proposed for belief functions. In this paper, we summarize the properties of these uncertainty measures and especially investigate whether the monotonicity is satisfied by the measures. This study provide a comprehensive comparison to these belief interval based uncertainty measures and is very useful for choosing the appropriate uncertainty measure in the practical applications.     

A robust continuous model for evidential reasoning

A 2-D model for evidential reasoning is proposed, in which the belief function of evidence is represented as a belief density function which can be in a continuous or discrete form. A vector form of mutual dependency relationship of the evidence is considered and a dependency propagation theorem is proved. This robust method can resolve the conflicts resulting from either the mutual dependency among evidences or the structural dependency in an inference network due to the evidence combination order. Belief conjunction, belief combination, belief propagation procedures, and AND/OR operations of an inference network based on the proposed 2-D model are all presented, followed by some examples demonstrating the advantages of this method over the conventional methods.     

Iterated belief change in the situation calculus

John McCarthy's situation calculus has left an enduring mark on artificial intelligence research. This simple yet elegant formalism for modelling and reasoning about dynamic systems is still in common use more than forty years since it was first proposed. The ability to reason about action and change has long been considered a necessary component for any intelligent system. The situation calculus and its numerous extensions as well as the many competing proposals that it has inspired deal with this problem to some extent. In this paper, we offer a new approach to belief change associated with performing actions that addresses some of the shortcomings of these approaches. In particular, our approach is based on a well-developed theory of action in the situation calculus extended to deal with belief. Moreover, by augmenting this approach with a notion of plausibility over situations, our account handles nested belief, belief introspection, mistaken belief, and handles belief revision and belief update together with iterated belief change.     

Belief-Driven Manipulator Visual Servoing for Less Controlled Environments

This paper presents the architecture of a feedforward manipulator control strategy based on a belief function that may be appropriate for less controlled environments. In this architecture, the belief about the environmental state, as described by a probability density function, is maintained by a recursive Bayesian estimation process. A likelihood is derived from each observation regardless of whether the targeted features of the environmental state have been detected or not. This provides continuously evolving information to the controller and allows an inaccurate belief to evolve into an accurate belief. Control actions are determined by maximizing objective functions using non-linear optimization. Forward models are used to transform control actions to a predicted state so that objective functions may be expressed in task space. The first set of examples numerically investigates the validity of the proposed strategy by demonstrating control in a two dimensional scenario. Then a more realistic application is presented where a robotic manipulator executes a searching and tracking task using an eye-in-hand vision sensor.     

An expectation operator for belief functions in the Dempster–Shafer theory*

ABSTRACT

The main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.     

Deriving evidence theoretical functions in multivariate data spaces: a systematic approach.

The mathematical theory of evidence is a generalization of the Bayesian theory of probability. It is one of the primary tools for knowledge representation and uncertainty and probabilistic reasoning and has found many applications. Using this theory to solve a specific problem is critically dependent on the availability of a mass function (or basic belief assignment). In this paper, we consider the important problem of how to systematically derive mass functions from the common multivariate data spaces and also the ensuing problem of how to compute the various forms of belief function efficiently. We also consider how such a systematic approach can be used in practical pattern recognition problems. More specifically, we propose a novel method in which a mass function can be systematically derived from multivariate data and present new methods that exploit the algebraic structure of a multivariate data space to compute various belief functions including the belief, plausibility, and commonality functions in polynomial-time. We further consider the use of commonality as an equality check. We also develop a plausibility-based classifier. Experiments show that the equality checker and the classifier are comparable to state-of-the-art algorithms.     

A Formal Model of Multi-Agent Belief-Interaction

A semantics is presented for belief revision in the face of common announcements to a group of agents that have beliefs about each other’s beliefs. The semantics is based on the idea that possible worlds can be viewed as having an internal-structure, representing the belief independent features of the world, and the respective belief states of the agents in a modular fashion. Modularity guarantees that changing one aspect of the world (a belief independent feature or a belief state) has no effect on any other aspect of the world. This allows us to employ an AGM-style selection function to represent revision. The semantics is given a complete axiomatisation (identical to the axiomatisation found by Gerbrandy and Groeneveld for a semantics based on non-wellfounded set theory) for the special case of expansion.     

基于信度函数的决策及应用

不确定环境下的风险决策通常用概率函数来描述事件的随机性,作为概率函数的推广,信度函数比概率函数能够更好地描述不确定信息,所适用的范围更为广泛。在随机集的框架下研究了基于信度函数的决策方法,并将其应用到一个导弹防御系统中风险评估中。     

基于交互历史的多Agent自动协商研究

在多Agent协商过程中,初始信念起到了至关重要的作用.而初始信念的形成是由设计者给予的部分专家知识和策略集,成功的交互历史是Agent在复杂环境中最后达成一致的提议集.通过学习机制从交互历史中获得知识,形成协商的初始信念,将更加有效地预测对方的策略,缩短协商过程的时间,再通过在线学习来协调己方Agent的行为.在此基础上优化协商模型,提高协商的效率和成功率.     

Extending stochastic ordering to belief functions on the real line

In this paper, the concept of stochastic ordering is extended to belief functions on the real line defined by random closed intervals. In this context, the usual stochastic ordering is shown to break down into four distinct ordering relations, called credal orderings, which correspond to the four basic ordering structures between intervals. These orderings are characterized in terms of lower and upper expectations. We then derive the expressions of the least committed (least informative) belief function credally less (respectively, greater) than or equal to a given belief function. In each case, the solution is a consonant belief function that can be described by a possibility distribution. A simple application to reliability analysis is used as an example throughout the paper.