Estimations of expectedness and potential surprise in possibility theory

This note investigates how various ideas of 'expectedness' can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying 'I would not be surprised that...' before an event takes place, or by saying 'I knew it' after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined

Differential Evolution Methods for the Fuzzy Extension of Functions

The paper illustrates a differential evolution (DE) algorithm to calculate the level-cuts of the fuzzy extension of a multidimensional real valued function to fuzzy numbers. The method decomposes the fuzzy extension engine into a set of "nested" min and max box-constrained op- timization problems and uses a form of the DE algorithm, based on multi populations which cooperate during the search phase and specialize, a part of the populations to find the the global min (corresponding to lower branch of the fuzzy extension) and a part of the populations to find the global max (corresponding to the upper branch), both gaining efficiency from the work done for a level-cut to the subsequent ones. A special ver- sion of the algorithm is designed to the case of differentiable functions, for which a representation of the fuzzy numbers is used to improve ef- ficiency and quality of calculations. The included computational results indicate that the DE method is a promising tool as its computational complexity grows on average superlinearly (of degree less than 1.5) in the number of variables of the function to be extended.Fuzzy Sets, Differential Evolution Method, Fuzzy Extension of Functions

A High Performance Fuzzy Logic Architecture for UAV Decision Making

The majority of Unmanned Aerial Vehicles (UAVs) in operation today are not truly autonomous, but are instead reliant on a remote human pilot. A high degree of autonomy can provide many advantages in terms of cost, operational resources and safety. However, one of the challenges involved in achieving autonomy is that of replicating the reasoning and decision making capabilities of a human pilot. One candidate method for providing this decision making capability is fuzzy logic. In this role, the fuzzy system must satisfy real-time constraints, process large quantities of data and relate to large knowledge bases. Consequently, there is a need for a generic, high performance fuzzy computation platform for UAV applications. Based on Lees’ [1] original work, a high performance fuzzy processing architecture, implemented in Field Programmable Gate Arrays (FPGAs), has been developed and is shown to outclass the performance of existing fuzzy processors

Temporal fuzzy association rule mining with 2-tuple linguistic representation

This paper reports on an approach that contributes towards the problem of discovering fuzzy association rules that exhibit a temporal pattern. The novel application of the 2-tuple linguistic representation identifies fuzzy association rules in a temporal context, whilst maintaining the interpretability of linguistic terms. Iterative Rule Learning (IRL) with a Genetic Algorithm (GA) simultaneously induces rules and tunes the membership functions. The discovered rules were compared with those from a traditional method of discovering fuzzy association rules and results demonstrate how the traditional method can loose information because rules occur at the intersection of membership function boundaries. New information can be mined from the proposed approach by improving upon rules discovered with the traditional method and by discovering new rules

Web Usage Mining with Evolutionary Extraction of Temporal Fuzzy Association Rules

In Web usage mining, fuzzy association rules that have a temporal property can provide useful knowledge about when associations occur. However, there is a problem with traditional temporal fuzzy association rule mining algorithms. Some rules occur at the intersection of fuzzy sets' boundaries where there is less support (lower membership), so the rules are lost. A genetic algorithm (GA)-based solution is described that uses the flexible nature of the 2-tuple linguistic representation to discover rules that occur at the intersection of fuzzy set boundaries. The GA-based approach is enhanced from previous work by including a graph representation and an improved fitness function. A comparison of the GA-based approach with a traditional approach on real-world Web log data discovered rules that were lost with the traditional approach. The GA-based approach is recommended as complementary to existing algorithms, because it discovers extra rules. (C) 2013 Elsevier B.V. All rights reserved

Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory

We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagatorsComment: 46 pages, the wrong file was first submitte

On a Consensus Measure in a Group Multi-Criteria Decision Making Problem.

A method for consensus measuring in a group decision problem is presented for the multiple criteria case. The decision process is supposed to be carried out according to Saaty's Analytic Hierarchy Process, and hence using pairwise comparison among the alternatives. Using a suitable distance between the experts' judgements, a scale transformation is proposed which allows a fuzzy interpretation of the problem and the definition of a consensus measure by means of fuzzy tools as linguistic quantifiers. Sufficient conditions on the expert's judgements are finally presented, which guarantee any a priori fixed consensus level to be reached.group decision making; multiple criteria; degree of consensus; fuzzy preferences

Constraint-wish and satisfied-dissatisfied: an overview of two approaches for dealing with bipolar querying

In recent years, there has been an increasing interest in dealing with user preferences in flexible database querying, expressing both positive and negative information in a heterogeneous way. This is what is usually referred to as bipolar database querying. Different frameworks have been introduced to deal with such bipolarity. In this chapter, an overview of two approaches is given. The first approach is based on mandatory and desired requirements. Hereby the complement of a mandatory requirement can be considered as a specification of what is not desired at all. So, mandatory requirements indirectly contribute to negative information (expressing what the user does not want to retrieve), whereas desired requirements can be seen as positive information (expressing what the user prefers to retrieve). The second approach is directly based on positive requirements (expressing what the user wants to retrieve), and negative requirements (expressing what the user does not want to retrieve). Both approaches use pairs of satisfaction degrees as the underlying framework but have different semantics, and thus also different operators for criteria evaluation, ranking, aggregation, etc