A group decision-making methodology with incomplete individual beliefs applied to e-Democracy

We consider the situation where there are several alternatives for investing a quantity of money to achieve a set of objectives. The choice of which alternative to apply depends on how citizens and political representatives perceive that such objectives should be achieved. All citizens with the right to vote can express their preferences in the decision-making process. These preferences may be incomplete. Political representatives represent the citizens who have not taken part in the decision-making process. The weight corresponding to political representatives depends on the number of citizens that have intervened in the decision-making process. The methodology we propose needs the participants to specify for each alternative how they rate the different attributes and the relative importance of attributes. On the basis of this information an expected utility interval is output for each alternative. To do this, an evidential reasoning approach is applied. This approach improves the insightfulness and rationality of the decision-making process using a belief decision matrix for problem modeling and the Dempster?Shafer theory of evidence for attribute aggregation. Finally, we propose using the distances of each expected utility interval from the maximum and the minimum utilities to rank the alternative set. The basic idea is that an alternative is ranked first if its distance to the maximum utility is the smallest, and its distance to the minimum utility is the greatest. If only one of these conditions is satisfied, a distance ratio is then used

Verification of Uncertain POMDPs Using Barrier Certificates

We consider a class of partially observable Markov decision processes (POMDPs) with uncertain transition and/or observation probabilities. The uncertainty takes the form of probability intervals. Such uncertain POMDPs can be used, for example, to model autonomous agents with sensors with limited accuracy, or agents undergoing a sudden component failure, or structural damage [1]. Given an uncertain POMDP representation of the autonomous agent, our goal is to propose a method for checking whether the system will satisfy an optimal performance, while not violating a safety requirement (e.g. fuel level, velocity, and etc.). To this end, we cast the POMDP problem into a switched system scenario. We then take advantage of this switched system characterization and propose a method based on barrier certificates for optimality and/or safety verification. We then show that the verification task can be carried out computationally by sum-of-squares programming. We illustrate the efficacy of our method by applying it to a Mars rover exploration example.Comment: 8 pages, 4 figure

Paradox Elimination in Dempster–Shafer Combination Rule with Novel Entropy Function: Application in Decision-Level Multi-Sensor Fusion

Multi-sensor data fusion technology in an important tool in building decision-making applications. Modified Dempster–Shafer (DS) evidence theory can handle conflicting sensor inputs and can be applied without any prior information. As a result, DS-based information fusion is very popular in decision-making applications, but original DS theory produces counterintuitive results when combining highly conflicting evidences from multiple sensors. An effective algorithm offering fusion of highly conflicting information in spatial domain is not widely reported in the literature. In this paper, a successful fusion algorithm is proposed which addresses these limitations of the original Dempster–Shafer (DS) framework. A novel entropy function is proposed based on Shannon entropy, which is better at capturing uncertainties compared to Shannon and Deng entropy. An 8-step algorithm has been developed which can eliminate the inherent paradoxes of classical DS theory. Multiple examples are presented to show that the proposed method is effective in handling conflicting information in spatial domain. Simulation results showed that the proposed algorithm has competitive convergence rate and accuracy compared to other methods presented in the literature

Decision making with Dempster-Shafer belief structure and the OWAWA operator

[EN] A new decision making model that uses the weighted average and the ordered weighted averaging (OWA) operator in the Dempster-Shafer belief structure is presented. Thus, we are able to represent the decision making problem considering objective and subjective information and the attitudinal character of the decision maker. For doing so, we use the ordered weighted averaging ¿ weighted average (OWAWA) operator. It is an aggregation operator that unifies the weighted average and the OWA in the same formulation. This approach is generalized by using quasi-arithmetic means and group decision making techniques. An application of the new approach in a group decision making problem concerning political management of a country is also developed.We would like to thank the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Spanish Ministry of Education under project JC2009-00189 , the University of Barcelona (099311) and the European Commission (PIEFGA-2011-300062) is gratefully acknowledgedMerigó, JM.; Engemann, KJ.; Palacios Marqués, D. (2013). Decision making with Dempster-Shafer belief structure and the OWAWA operator. Technological and Economic Development of Economy. 19(sup 1):S100-S118. https://doi.org/10.3846/20294913.2013.869517SS100S11819sup 1Antuchevičienė, J., Zavadskas, E. K., & Zakarevičius, A. (2010). MULTIPLE CRITERIA CONSTRUCTION MANAGEMENT DECISIONS CONSIDERING RELATIONS BETWEEN CRITERIA / DAUGIATIKSLIAI STATYBOS VALDYMO SPRENDIMAI ATSIŽVELGIANT Į RODIKLIŲ TARPUSAVIO PRIKLAUSOMYBĘ. Technological and Economic Development of Economy, 16(1), 109-125. doi:10.3846/tede.2010.07Brauers, W. K. M., & Zavadskas, E. K. (2010). PROJECT MANAGEMENT BY MULTIMOORA AS AN INSTRUMENT FOR TRANSITION ECONOMIES / PROJEKTŲ VADYBA SU MULTIMOORA KAIP PRIEMONĖ PEREINAMOJO LAIKOTARPIO ŪKIAMS. 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The SECURE collaboration model

The SECURE project has shown how trust can be made computationally tractable while retaining a reasonable connection with human and social notions of trust. SECURE has produced a well-founded theory of trust that has been tested and refined through use in real software such as collaborative spam filtering and electronic purse. The software comprises the SECURE kernel with extensions for policy specification by application developers. It has yet to be applied to large-scale, multi-domain distributed systems taking different application contexts into account. The project has not considered privacy in evidence distribution, a crucial issue for many application domains, including public services such as healthcare and police. The SECURE collaboration model has similarities with the trust domain concept, embodying the interaction set of a principal, but SECURE is primarily concerned with pseudonymous entities rather than domain-structured systems

Adaptive imputation of missing values for incomplete pattern classification

In classification of incomplete pattern, the missing values can either play a crucial role in the class determination, or have only little influence (or eventually none) on the classification results according to the context. We propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory. At first, we try to classify the object (incomplete pattern) based only on the available attribute values. As underlying principle, we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information. In this case, the object is committed to this particular class. However, if the object cannot be classified without ambiguity, it means that the missing values play a main role for achieving an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and self-organizing map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is respectively classified according to each training class, and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (which are particular disjunctions of several single classes). The credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets

Midbrain Dopamine Neurons Signal Belief in Choice Accuracy during a Perceptual Decision

Central to the organization of behavior is the ability to predict the values of outcomes to guide choices. The accuracy of such predictions is honed by a teaching signal that indicates how incorrect a prediction was (“reward prediction error,” RPE). In several reinforcement learning contexts, such as Pavlovian conditioning and decisions guided by reward history, this RPE signal is provided by midbrain dopamine neurons. In many situations, however, the stimuli predictive of outcomes are perceptually ambiguous. Perceptual uncertainty is known to influence choices, but it has been unclear whether or how dopamine neurons factor it into their teaching signal. To cope with uncertainty, we extended a reinforcement learning model with a belief state about the perceptually ambiguous stimulus; this model generates an estimate of the probability of choice correctness, termed decision confidence. We show that dopamine responses in monkeys performing a perceptually ambiguous decision task comply with the model’s predictions. Consequently, dopamine responses did not simply reflect a stimulus’ average expected reward value but were predictive of the trial-to-trial fluctuations in perceptual accuracy. These confidence-dependent dopamine responses emerged prior to monkeys’ choice initiation, raising the possibility that dopamine impacts impending decisions, in addition to encoding a post-decision teaching signal. Finally, by manipulating reward size, we found that dopamine neurons reflect both the upcoming reward size and the confidence in achieving it. Together, our results show that dopamine responses convey teaching signals that are also appropriate for perceptual decisions