Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

A recursive rule base adjustment algorithm for a fuzzy logic controller

This paper introduces a recursive rule base adjustment to enhance the performance of fuzzy logic controllers. Here the fuzzy controller is constructed on the basis of a decision table (DT), relying on membership functions and fuzzy rules that incorporate heuristic knowledge and operator experience. If the controller performance is not satisfactory, it has previously been suggested that the rule base be altered by combined tuning of membership functions and controller scaling factors. The alternative approach proposed here entails alteration of the fuzzy rule base. The recursive rule base adjustment algorithm proposed in this paper has the benefit that it is computationally more efficient for the generation of a DT, and advantage for online realization. Simulation results are presented to support this thesis. (c) 2005 Elsevier B.V. All rights reserved.

A fast method for fuzzy neural modeling and refinement

In the identification of complex dynamic systems using fuzzy neural networks, one of the main issues is the curse of dimensionality, which makes it difficult to retain a large number of system inputs or to consider a large number of fuzzy sets. Moreover, due to the correlations, not all possible network inputs or regression vectors in the network are necessary and adding them simply increases the model complexity and deteriorates the network generalisation performance. In this paper, the problem is solved by first proposing a fast algorithm for selection of network terms, and then introducing a refinement procedure to tackle the correlation issue. Simulation results show the efficacy of the method.

Dynamic evolution of the genetic search region through fuzzy coding

A technique for automatic exploration of the genetic search region through fuzzy coding (Sharma and Irwin, 2003) has been proposed. Fuzzy coding (FC) provides the value of a variable on the basis of the optimum number of selected fuzzy sets and their effectiveness in terms of degree-of-membership. It is an indirect encoding method and has been shown to perform better than other conventional binary, Gray and floating-point encoding methods. However, the static range of the membership functions is a major problem in fuzzy coding, resulting in longer times to arrive at an optimum solution in large or complicated search spaces. This paper proposes a new algorithm, called fuzzy coding with a dynamic range (FCDR), which dynamically allocates the range of the variables to evolve an effective search region, thereby achieving faster convergence. Results are presented for two benchmark optimisation problems, and also for a case study involving neural identification of a highly non-linear pH neutralisation process from experimental data. It is shown that dynamic exploration of the genetic search region is effective for parameter optimisation in problems where the search space is complicated.

Logics for belief functions on MV-algebras

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism. © 2012 Elsevier Inc. All rights reserved.

Parental leave regulations and the persistence of the male breadwinner model: Using fuzzy-set ideal type analysis to assess gender equality in an enlarged Europe

his paper uses fuzzy-set ideal type analysis to assess the conformity of European leave regulations to four theoretical ideal typical divisions of labour: male breadwinner, caregiver parity, universal breadwinner and universal caregiver. In contrast to the majority of previous studies, the focus of this analysis is on the extent to which leave regulations promote gender equality in the family and the transformation of traditional gender roles. The results of this analysis demonstrate that European countries cluster into five models that only partly coincide with countries’ geographical proximity. Second, none of the countries considered constitutes a universal caregiver model, while the male breadwinner ideal continues to provide the normative reference point for parental leave regulations in a large number of European states. Finally, we witness a growing emphasis at the national and EU levels concerning the universal breadwinner ideal, which leaves gender inequality in unpaid work unproblematized.

Combining multiple prioritized knowledge bases by negotiation.

Recently, several belief negotiation models have been introduced to deal with the problem of belief merging. A negotiation model usually consists of two functions: a negotiation function and a weakening function. A negotiation function is defined to choose the weakest sources and these sources will weaken their point of view using a weakening function. However, the currently available belief negotiation models are based on classical logic, which makes them difficult to define weakening functions. In this paper, we define a prioritized belief negotiation model in the framework of possibilistic logic. The priority between formulae provides us with important information to decide which beliefs should be discarded. The problem of merging uncertain information from different sources is then solved by two steps. First, beliefs in the original knowledge bases will be weakened to resolve inconsistencies among them. This step is based on a prioritized belief negotiation model. Second, the knowledge bases obtained by the first step are combined using a conjunctive operator which may have a reinforcement effect in possibilistic logic.

Prediction of Fresh and Hardened Properties of Self-Consolidating Concrete Using Neurofuzzy Approach

Self-consolidating concrete (SCC) developed in Japan in the late 80s has enabled the construction industry to reduce demand on the resources, improve the work conditions and also reduce the impact on the environment by elimination of the need for compaction. This investigation aimed at exploring the potential use of the neurofuzzy (NF) approach to model the fresh and hardened properties of SCC containing pulverised fuel ash (PFA) as based on experimental data investigated in this paper. Twenty six mixes were made with water-to-binder ratio ranging from 0.38 to 0.72, cement content ranging from 183 to 317 kg/m3 , dosage of PFA ranging from 29 to 261 kg/m3 , and percentage of superplasticizer, by mass of powder, ranging from 0 to 1%. Nine properties of SCC mixes modeled by NF were the slump flow, JRing combined to the Orimet, JRing combined to cone, V-funnel, L-box blocking ratio, segregation ratio, and the compressive strength at 7, 28, and 90 days. These properties characterized the filling ability, the passing ability, the segregation resistance of fresh SCC, and the compressive strength. NF model is constructed by training and testing data using the experimental results obtained in this study. The results of NF models were compared with experimental results and were found to be quite accurate. The proposed NF models offers useful modeling approach of the fresh and hardened properties of SCC containing PFA.

Measuring conflict and agreement between two prioritized knowledge bases in possibilistic logic.

In this paper we investigate the relationship between two prioritized knowledge bases by measuring both the conflict and the agreement between them.First of all, a quantity of conflict and two quantities of agreement are defined. The former is shown to be a generalization of the well-known Dalal distance which is the hamming distance between two interpretations. The latter are, respectively, a quantity of strong agreement which measures the amount ofinformation on which two belief bases “totally” agree, and a quantity of weak agreement which measures the amount of information that is believed by onesource but is unknown to the other. All three quantity measures are based on the weighted prime implicant, which represents beliefs in a prioritized belief base. We then define a degree of conflict and two degrees of agreement based on our quantity of conflict and quantities of agreement. We also consider the impact of these measures on belief merging and information source ordering.

After the Male Breadwinner Model? Childcare Services and the Division of Labor in European Countries

Fundamental reforms in childcare services appear to have eroded traditional
support to the male breadwinner model across European states. There has been a strong debate about the direction of these changes, and the ways in which childcare services can alter the division of labor and promote gender equality. This paper deals with these issues by using fuzzy set ideal-type analysis to assess the conformity of childcare service provisions in European economies to Fraser’s four ideal typical models: male breadwinner, caregiver parity, universal breadwinner, and universal caregiver. We find that there is resilience of traditional gender roles in the majority of European countries, while there are different variants of the universal breadwinner shaping different forms of childcare policies. The more equalitarian universal caregiver model maintains its utopian character.

Qualitative Comparative Analysis as a Tool for Concept Clarification, Typology Building, and Contextualized Comparisons in Gender and Feminist Research

Qualitative Comparative Analysis (QCA) is a method for the systematic analysis of cases. A holistic view of cases and an approach to causality emphasizing complexity are some of its core features. Over the last decades, QCA has found application in many fields of the social sciences. In spite of this, its use in feminist research has been slower, and only recently QCA has been applied to topics related to social care, the political representation of women, and reproductive politics. In spite of the comparative turn in feminist studies, researchers still privilege qualitative methods, in particular case studies, and are often skeptical of quantitative techniques (Spierings 2012). These studies show that the meaning and measurement of many gender concepts differ across countries and that the factors leading to feminist success and failure are context specific. However, case study analyses struggle to systematically account for the ways in which these forces operate in different locations.

A two-step approach for the analysis of hybrids in comparative social policy analysis: a nuanced typology of childcare policies

Typologies have represented an important tool for the development of comparative social policy research and continue to be widely used in spite of growing criticism of their ability to capture the complexity of welfare states and their internal heterogeneity. In particular, debates have focused on the presence of hybrid cases and the existence of distinct cross-national pattern of variation across areas of social policy. There is growing awareness around these issues, but empirical research often still relies on methodologies aimed at classifying countries in a limited number of unambiguous types. This article proposes a two-step approach based on fuzzy-set-ideal-type analysis for the systematic analysis of hybrids at the level of both policies (step 1) and policy configurations or combinations of policies (step 2). This approach is demonstrated by using the case of childcare policies in European economies. In the first step, parental leave policies are analysed using three methods – direct, indirect, and combinatory – to identify and describe specific hybrid forms at the level of policy analysis. In the second step, the analysis focus on the relationship between parental leave and childcare services in order to develop an overall typology of childcare policies, which clearly shows that many countries display characteristics normally associated with different types (hybrids and. Therefore, this two-step approach enhances our ability to account and make sense of hybrid welfare forms produced from tensions and contradictions within and between policies.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.