Evidence Propagation and Consensus Formation in Noisy Environments

We study the effectiveness of consensus formation in multi-agent systems where there is both belief updating based on direct evidence and also belief combination between agents. In particular, we consider the scenario in which a population of agents collaborate on the best-of-n problem where the aim is to reach a consensus about which is the best (alternatively, true) state from amongst a set of states, each with a different quality value (or level of evidence). Agents' beliefs are represented within Dempster-Shafer theory by mass functions and we investigate the macro-level properties of four well-known belief combination operators for this multi-agent consensus formation problem: Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging operator. The convergence properties of the operators are considered and simulation experiments are conducted for different evidence rates and noise levels. Results show that a combination of updating on direct evidence and belief combination between agents results in better consensus to the best state than does evidence updating alone. We also find that in this framework the operators are robust to noise. Broadly, Yager's rule is shown to be the better operator under various parameter values, i.e. convergence to the best state, robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen

Fuzzy cardinality based evaluation of quanti®ed sentences

Quantified statements are used in the resolution of a great variety of problems. Several methods have been proposed to evaluate statements of types I and II. The objective of this paper is to study these methods, by comparing and generalizing them. In order to do so, we propose a set of properties that must be fulfilled by any method of evaluation of quantified statements, we discuss some existing methods from this point of view and we describe a general approach for the evaluation of quantified statements based on the fuzzy cardinality and fuzzy relative cardinality of fuzzy sets. In addition, we discuss some concrete methods derived from the mentioned approach. These new methods fulfill all the properties proposed and, in some cases, they provide an interpretation or generalization of existing methods

Application of decision trees and multivariate regression trees in design and optimization

Induction of decision trees and regression trees is a powerful technique not only for performing ordinary classification and regression analysis but also for discovering the often complex knowledge which describes the input-output behavior of a learning system in qualitative forms;In the area of classification (discrimination analysis), a new technique called IDea is presented for performing incremental learning with decision trees. It is demonstrated that IDea\u27s incremental learning can greatly reduce the spatial complexity of a given set of training examples. Furthermore, it is shown that this reduction in complexity can also be used as an effective tool for improving the learning efficiency of other types of inductive learners such as standard backpropagation neural networks;In the area of regression analysis, a new methodology for performing multiobjective optimization has been developed. Specifically, we demonstrate that muitiple-objective optimization through induction of multivariate regression trees is a powerful alternative to the conventional vector optimization techniques. Furthermore, in an attempt to investigate the effect of various types of splitting rules on the overall performance of the optimizing system, we present a tree partitioning algorithm which utilizes a number of techniques derived from diverse fields of statistics and fuzzy logic. These include: two multivariate statistical approaches based on dispersion matrices, an information-theoretic measure of covariance complexity which is typically used for obtaining multivariate linear models, two newly-formulated fuzzy splitting rules based on Pearson\u27s parametric and Kendall\u27s nonparametric measures of association, Bellman and Zadeh\u27s fuzzy decision-maximizing approach within an inductive framework, and finally, the multidimensional extension of a widely-used fuzzy entropy measure. The advantages of this new approach to optimization are highlighted by presenting three examples which respectively deal with design of a three-bar truss, a beam, and an electric discharge machining (EDM) process

Data fusion using expected output membership functions

Multi-sensor systems can improve accuracy, increase detection range, and enhance reliability compared to single sensor systems. The main problems in multi-sensor systems are how to select sensors, model the sensors, and combine the data;This dissertation proposes a new data fusion method based on fuzzy set methods. The expected output membership function (EOMF) method uses the fuzzy input set and the expected fuzzy output. This method uses the intersections of the fuzzy inputs with the expected fuzzy output in order to find relationships between the given inputs and the estimate of the output. The EOMF method creates a fuzzy confidence distance measurement by assessing the fusability of the data. The fusability measure is used for finding the best position of the EOMF and the best estimate of the system output. Adaptive methods can help deal with occasional bad measurements and set the EOMF to the proper width. The EOMF method can be used for both homogeneous and heterogeneous sensors, which give redundant, cooperative or complementary information. In addition, the EOMF method is robust in the sense that it can eliminate sensor measurements that are outliers. The EOMF method compares favorably with other methods of data fusion such as the weighted average method. An example from the control of automated vehicles shows the effectiveness of the adaptive EOMF method, compared to the fixed EOMF method and the weighted average method in the presence of Gaussian and impulsive noise. This method can also be applied to nondestructive evaluation (NDE) images from heterogeneous sensors

Fuzzy C-ordered medoids clustering of interval-valued data

Fuzzy clustering for interval-valued data helps us to find natural vague boundaries in such data. The Fuzzy c-Medoids Clustering (FcMdC) method is one of the most popular clustering methods based on a partitioning around medoids approach. However, one of the greatest disadvantages of this method is its sensitivity to the presence of outliers in data. This paper introduces a new robust fuzzy clustering method named Fuzzy c-Ordered-Medoids clustering for interval-valued data (FcOMdC-ID). The Huber's M-estimators and the Yager's Ordered Weighted Averaging (OWA) operators are used in the method proposed to make it robust to outliers. The described algorithm is compared with the fuzzy c-medoids method in the experiments performed on synthetic data with different types of outliers. A real application of the FcOMdC-ID is also provided

Risk Analysis for Offshore Wind Turbines Using Aggregation Operators and VIKOR

In various engineering actions, potential hazards are reduced, calculated, or controlled using a variety of risk analysis methodologies. The FMEA, or Failure Mode and Effects Analysis, is a very efficient strategy that may be used in this situation. When evaluating safety concerns, failure modes\u27 likely causes and consequences are considered. Serious failures in the FMEA are identified using the Risk Priority Number (RPN). The RPN considers the effect of the probability of occurrence, probability of detection and severity by multiplying these three parameters. However, because of the formula\u27s various flaws, it is frequently criticized. In the current work, a hybrid approach using ViseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) and geometric averaging of ordered weights (OWGA) as an aggregation operator is used to assess risk for offshore wind turbines. While the OWGA technique is used to provide weight to risk indices, the VIKOR method is used to assess the relevance of failure modes of offshore wind turbine components. The method\u27s final findings show it solves the issues with the traditional RPN technique and produces more logical outcomes

Design decisions: concordance of designers and effects of the Arrow’s theorem on the collective preference ranking

The problem of collective decision by design teams has received considerable attention in the scientific literature of engineering design. A much debated problem is that in which multiple designers formulate their individual preference rankings of different design alternatives and these rankings should be aggregated into a collective one. This paper focuses the attention on three basic research questions: (i) “How can the degree of concordance of designer rankings be measured?”, (ii) “For a given set of designer rankings, which aggregation model provides the most coherent solution?”, and (iii) “To what extent is the collective ranking influenced by the aggregation model in use?”. The aim of this paper is to present a novel approach that addresses the above questions in a relatively simple and agile way. A detailed description of the methodology is supported by a practical application to a real-life case study

A fuzzy hierarchical multiple criteria group decision support system - Decider - and its applications

Decider is a Fuzzy Hierarchical Multiple Criteria Group Decision Support System (FHMC-GDSS) designed for dealing with subjective, in particular linguistic, information and objective information simultaneously to support group decision making particularly on evaluation. In this chapter, the fuzzy aggregation decision model, functions and structure of Decider are introduced. The ideas to resolve decision and evaluation problems we have faced in the development and application of Decider are presented. Two real applications of the Decider system are briefly illustrated. Finally, we discuss our further research in this area. © 2011 Springer-Verlag Berlin Heidelberg

Intersections between some families of (U,N)- and RU-implications

(U,N)-implications and RU-implications are the generalizations of (S,N)- and R-implications to the framework of uninorms, where the t-norms and t-conorms are replaced by appropriate uninorms. In this work, we present the intersections that exist between (U,N)-implications and the different families of RU-implications obtainable from the well-established families of uninorms