In Dempster-Shafer belief theory, general beliefs are expressed as belief mass distribution functions over frames of discernment. In Subjective Logic beliefs are expressed as belief mass distribution functions over binary frames of discernment. Belief representations in Subjective Logic, which are called opinions, also contain a base rate parameter which express the a priori belief in the absence of evidence. Philosophically, beliefs are quantitative representations of evidence as perceived by humans or by other intelligent agents. The basic operators of classical probability calculus, such as addition and multiplication, can be applied to opinions, thereby making belief calculus practical. Through the equivalence between opinions and Beta probability density functions, this also provides a calculus for Beta probability density functions. This article explains the basic elements of belief calculus.

Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars for computing with (some special) words in a probabilistic framework, where the words are interpreted as probabilistic distributions or possibility distributions over a set of crisp symbols. By probabilistic conditioning, we then establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling arbitrary inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with some special words. To compare the transition probabilities of two near inputs, we also examine some analytical properties of the transition probability functions of generalized extensions. Moreover, the retractions and the generalized extensions are shown to be equivalence-preserving. Finally, we clarify some relationships among the retractions, the generalized extensions, and the extensions studied recently by Qiu and Wang.

In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As the real unit interval is embedded in the Bloch sphere, every fuzzy set is automatically a quantum fuzzy set. However, a generic quantum fuzzy set can be seen as a (possibly entangled) superposition of many fuzzy sets at once, offering new opportunities for modeling uncertainty. After introducing the main framework of quantum fuzzy set theory, we analyze the standard operations of fuzzification and defuzzification from our viewpoint. We conclude this preliminary paper with a list of possible applications of quantum fuzzy sets to pattern recognition, as well as future directions of pure research in quantum fuzzy set theory.

Department of Mathematics, University of New Mexico, Gallu p, NM 87301, U.S.A. Abstract: This paper presents two new promising combination rules for the fusion of uncertain and potentially highl y conflicting sources of evidences in the theory of belief func - tions established first in Dempster-Shafer Theory (DST) and then recently extended in Dezert-Smarandache Theory (DSmT). Our work is to provide here new issues to palliate the well-known limitations of Dempster's rule and to work beyond its limits of applicability. Since the famous Zadeh' s criticism of Dempster's rule in 1979, many researchers have proposed new interesting alternative rules of combination to palliate the weakness of Dempster's rule in order to provide acceptable results specially in highly conflicting situati ons. Bot h rules allow to deal with highly conflicting sources for stati c and dynamic fusion applications. W e present some interesting properties for ACR and PCR rules and discuss some simulation results obtained with both rules for Zadeh's pro b-lem and for a target identification problem.

Given a finite set of words w1,...,wn independently drawn according to a fixed unknown distribution law P called a stochastic language, an usual goal in Grammatical Inference is to infer an estimate of P in some class of probabilistic models, such as Probabilistic Automata (PA). Here, we study the class of rational stochastic languages, which consists in stochastic languages that can be generated by Multiplicity Automata (MA) and which strictly includes the class of stochastic languages generated by PA. Rational stochastic languages have minimal normal representation which may be very concise, and whose parameters can be efficiently estimated from stochastic samples. We design an efficient inference algorithm DEES which aims at building a minimal normal representation of the target. Despite the fact that no recursively enumerable class of MA computes exactly the set of rational stochastic languages over Q, we show that DEES strongly identifies tis set in the limit. We study the intermediary MA output by DEES and show that they compute rational series which converge absolutely to one and which can be used to provide stochastic languages which closely estimate the target.

Abstract: This paper presents a robotics vision-based heuristic reasoning system for underwater target tracking and navigation. This system is introduced to improve the level of automation of underwater Remote Operated Vehicles (ROVs) operations. A prototype which combines computer vision with an underwater robo tics system is successfully designed and developed to perform target tracking and intelligent navigation. Th is study focuses on developing image processing algorithms and fuzzy inference system for the analys is of the terrain. The visi on system developed is capable of interpreting underwater scene by extracting subjective uncertainties of the object of interest.

A resolved acceleration control (RAC) and proportional-integral active force control (PIAFC) is proposed as an approach for the robust motion control of a mobile manipulator (MM) comprising a differentially driven wheeled mobile platform with a two-link planar arm mounted on top of the platform. The study emphasizes on the integrated kinematic and dynamic control strategy in which the RAC is used to manipulate the kinematic component while the PIAFC is implemented to compensate the dynamic effects including the bounded known/unknown disturbances and uncertainties. The effectivenss and robustness of the proposed scheme are investigated through a rigorous simulation study and later complemented with experimental results obtained through a number of experiments performed on a fully developed working prototype in a laboratory environment. A number of disturbances in the form of vibratory and impact forces are deliberately introduced into the system to evaluate the system performances. The investigation clearly demonstrates the extreme robustness feature of the proposed control scheme compared to other systems considered in the study.

Path planning and obstacle avoidance are the two major issues in any navigation system. Wavefront propagation algorithm, as a good path planner, can be used to determine an optimal path. Obstacle avoidance can be achieved using possibility theory. Combining these two functions enable a robot to autonomously navigate to its destination. This paper presents the approach and results in implementing an autonomous navigation system for an indoor mobile robot. The system developed is based on a laser sensor used to retrieve data to update a two dimensional world model of therobot environment. Waypoints in the path are incorporated into the obstacle avoidance. Features such as ageing of objects and smooth motion planning are implemented to enhance efficiency and also to cater for dynamic environments.

A fuzzy controller is usually designed by formulating the knowledge of a human expert into a set of linguistic variables and fuzzy rules. Among the most successful methods to automate the fuzzy controllers development process are evolutionary algorithms. In this work, we propose the Recurrent Fuzzy Voronoi (RFV) model, a representation for recurrent fuzzy systems. It is an extension of the FV model proposed by Kavka and Schoenauer that extends the application domain to include temporal problems. The FV model is a representation for fuzzy controllers based on Voronoi diagrams that can represent fuzzy systems with synergistic rules, fulfilling the $ε$-completeness property and providing a simple way to introduce a priory knowledge. In the proposed representation, the temporal relations are embedded by including internal units that provide feedback by connecting outputs to inputs. These internal units act as memory elements. In the RFV model, the semantic of the internal units can be specified together with the a priori rules. The geometric interpretation of the rules allows the use of geometric variational operators during the evolution. The representation and the algorithms are validated in two problems in the area of system identification and evolutionary robotics.

It is commonly-accepted wisdom that more information is better, and that information should never be ignored. Here we argue, using both a Bayesian and a non-Bayesian analysis, that in some situations you are better off ignoring information if your uncertainty is represented by a set of probability measures. These include situations in which the information is relevant for the prediction task at hand. In the non-Bayesian analysis, we show how ignoring information avoids dilation, the phenomenon that additional pieces of information sometimes lead to an increase in uncertainty. In the Bayesian analysis, we show that for small sample sizes and certain prediction tasks, the Bayesian posterior based on a non-informative prior yields worse predictions than simply ignoring the given information.