A monotonicity index for the monotone fuzzy modeling problem

In this paper, the problem of maintaining the (global) monotonicity and local monotonicity properties between the input(s) and the output of an FIS model is addressed. This is known as the monotone fuzzy modeling problem. In our previous work, this problem has been tackled by developing some mathematical conditions for an FIS model to observe the monotonicity property. These mathematical conditions are used as a set of governing equations for undertaking FIS modeling problems, and have been extended to some advanced FIS modeling techniques. Here, we examine an alternative to the monotone fuzzy modeling problem by introducing a monotonicity index. The monotonicity index is employed as an approximate indicator to measure the fulfillment of an FIS model to the monotonicity property. It allows the FIS model to be constructed using an optimization method, or be tuned to achieve a better performance, without knowing the exact mathematical conditions of the FIS model to satisfy the monotonicity property. Besides, the monotonicity index can be extended to FIS modeling that involves the local monotonicity problem. We also analyze the relationship between the FIS model and its monotonicity property fulfillment, as well as derived mathematical conditions, using the Monte Carlo method.

A new framework with similarity reasoning and monotone fuzzy rule relabeling for fuzzy inference systems

A complete and monotonically-ordered fuzzy rule base is necessary to maintain the monotonicity property of a Fuzzy Inference System (FIS). In this paper, a new monotone fuzzy rule relabeling technique to relabel a non-monotone fuzzy rule base provided by domain experts is proposed. Even though the Genetic Algorithm (GA)-based monotone fuzzy rule relabeling technique has been investigated in our previous work [7], the optimality of the approach could not be guaranteed. The new fuzzy rule relabeling technique adopts a simple brute force search, and it can produce an optimal result. We also formulate a new two-stage framework that encompasses a GA-based rule selection scheme, the optimization based-Similarity Reasoning (SR) scheme, and the proposed monotone fuzzy rule relabeling technique for preserving the monotonicity property of the FIS model. Applicability of the two-stage framework to a real world problem, i.e., failure mode and effect analysis, is further demonstrated. The results clearly demonstrate the usefulness of the proposed framework.

Parallel monotone spline interpolation and approximation on GPUs

Monotonicity preserving interpolation and approximation have received substantial attention in the last thirty years because of their numerous applications in computer aided-design, statistics, and machine learning [9, 10, 19]. Constrained splines are particularly popular because of their flexibility in modeling different geometrical shapes, sound theoretical properties, and availability of numerically stable algorithms [9,10,26]. In this work we examine parallelization and adaptation for GPUs of a few algorithms of monotone spline interpolation and data smoothing, which arose in the context of estimating probability distributions.

Weakly monotone averaging functions

Averaging behaviour of aggregation functions depends on the fundamental property of monotonicity with respect to all arguments. Unfortunately this is a limiting property that ensures that many important averaging functions are excluded from the theoretical framework. We propose a definition for weakly monotone averaging functions to encompass the averaging aggregation functions in a framework with many commonly used non-monotonic means. Weakly monotonic averages are robust to outliers and noise, making them extremely important in practical applications. We show that several robust estimators of location are actually weakly monotone and we provide sufficient conditions for weak monotonicity of the Lehmer and Gini means and some mixture functions. In particular we show that mixture functions with Gaussian kernels, which arise frequently in image and signal processing applications, are actually weakly monotonic averages. Our concept of weak monotonicity provides a sound theoretical and practical basis for understanding both monotone and non-monotone averaging functions within the same framework. This allows us to effectively relate these previously disparate areas of research and gain a deeper understanding of averaging aggregation methods. © Springer International Publishing Switzerland 2014.

Non-monotone insurance contracts and their empirical consequences

The goal of this paper is to show the possibility of a non-monotone relation between coverage ans risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). We present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuous parameter which is correlated with lenience and for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cosr of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and iplies a positive correlation between overage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the SCP be broken, but also the monotonocity of contracts, i.e., the prediction that high (low) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case there are some coverage levels associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation between coverage and riskiness may have every sign (even though the ex-post correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to desentangle single crossing ans non single croosing under an ex-post zero correlation result: the monotonicity of coverage as a function os riskiness. Since by controlling for risk aversion (no asymmetric information), coverage is monotone function of riskiness, this also fives a test for asymmetric information. Finally, we relate this theoretical results to empirical tests in the recent literature, specially the Dionne, Gouruéroux and Vanasse (2001) work. In particular, they found an empirical evidence that seems to be compatible with asymmetric information and non single crossing in our framework. More generally, we build a hidden information model showing how omitted variables (asymmetric information) can bias the sign of the correlation of equilibrium variables conditioning on all observable variables. We show that this may be the case when the omitted variables have a non-monotonic relation with the observable ones. Moreover, because this non-dimensional does not capture this deature. Hence, our main results is to point out the importance of the SPC in testing predictions of the hidden information models.

Non-monotone insurence contracts and their empirical consequences

The goal of t.his paper is to show the possibility of a non-monot.one relation between coverage and risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). We present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuou.'l parameter which is correlated with lenience and, for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cost of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and implies a positive correlation between coverage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the sep be broken, but also the monotonicity of contracts, i.e., the prediction that high (Iow) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case t,here are some coverage leveIs associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation bet,ween coverage and riskiness may have every sign (even though the ex-post correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to disentangle single crossing and non single crossing under an ex-post zero correlation result: the monotonicity of coverage as a function of riskiness. Since by controlling for risk aversion (no asymmetric informat, ion), coverage is a monotone function of riskiness, this also gives a test for asymmetric information. Finally, we relate this theoretical results to empirica! tests in the recent literature, specially the Dionne, Gouriéroux and Vanasse (2001) work. In particular, they found an empirical evidence that seems to be compatible with asymmetric information and non single crossing in our framework. More generally, we build a hidden information model showing how omitted variabIes (asymmetric information) can bias the sign of the correlation of equilibrium variabIes conditioning on ali observabIe variabIes. We show that this may be t,he case when the omitted variabIes have a non-monotonic reIation with t,he observable ones. Moreover, because this non-monotonic reIat,ion is deepIy reIated with the failure of the SCP in one-dimensional screening problems, the existing lit.erature on asymmetric information does not capture t,his feature. Hence, our main result is to point Out the importance of t,he SCP in testing predictions of the hidden information models.

Evaluation des effets de l’extrait aqueux des fleurs de Nymphaea lotus Linn. (Nymphéacées) sur la fonction de reproduction des rats normoglycémique et diabétique de type 1

In traditional medicine of Cameroon, Nymphaea lotus Linn. (Nympheaceae) is used for treatment of male sexual disorders. The aim of this study was to evaluate the effects of the N. lotus flowers aqueous extracts on general mating behavior, fertility and some androgenic parameters of normoglycemic and diabetic adult male rats. Mating behavior assessment was carried out with primiparous and with oestrus female rats. Male rats were divided into 5 groups and subjected once in a day to the following treatment: distilled water (10 mL/kg), Sildenafil citrate (5mg/kg), Testosterone enanthate (5mg/kg) and plant extract (75 mg/kg and 150 mg/kg). Treatment lasted for 8 and 55 days before sacrifice. Organ weight, epididymal sperm counts, motility, viability, histomorphometric analysis, muscular strength, seminal fructose, cholesterol level, epididymal and serum proteins testicular were determined. Results showed a dose- dependant influence of the treatment in sperm count and motility which significantly increases compared to the distilled water-administered control. An increase in some sexual performance parameters (mount and intromission frequencies) was observed in both diabetic and normal rats compared to respective controls. The latencies of mount and intromission were significantly reduced. Computed frequencies of penile licking, index of libido and sexual motivation were higher in normal and diabetic extract-treated animals; which suggest an enhancement of motivational parameters. The treatment also caused significant increases in the weight of the testis, prostate, epididymis, in serum cholesterol and epididymal protein level in normal rats compared to the distilled water-administered control. These results indicate an androgenic pro-sexual potential of N. lotus in male rats and justify the empirical use of N. lotus in the management of erectile dysfunction and fertility disorders in males. Key-words: Nymphaea lotus, prosexual, androgenic, fertility, diabetic, male rat. //Selon les tradipraticiens de l’Ouest-Cameroun, Nymphaea lotus Linn. (N. lotus), de la famille des Nymphéacées, est utilisé pour le traitement des dysfonctionnements sexuels chez les hommes. Dans cette étude, l’effet de l’extrait aqueux des fleurs de N. lotus sur la fonction de reproduction des rats mâles adultes normaux et diabétiques a été évalué. Dans le but d’évaluer les effets de l’extrait aqueux des fleurs de N. lotus sur les paramètres généraux de copulation, d’androgénicité et de fertilité, les rats normoglycémiques et diabétiques ont été divisé en 3 groupes contrôle [Groupe I- recevant de l’eau distillée, Groupe II et III recevant respectivement du citrate de sildénafil (5 mg/kg) et l’énanthate de testostérone (5 mg/kg)] et deux groupes expérimentaux traités à l’extrait aux doses 75 mg/kg (Groupe IV) et 150 mg/kg (Groupe V). L’eau distillée, l’extrait et la substance de référence était administré per os une fois par jour. Pour analyser le comportement sexuel et la fertilité, des femelles primipares et en oestrus étaient utilisées. Le traitement a duré 8 et 55 jours avant le sacrifice. Le poids relatif des organes, le nombre de spermatozoïde, la motilité, les analyses morphométriques, la force musculaire, le taux de cholestérol, le taux de protéines sériques et épididymaires étaient déterminé. Le temps de latence de monte et d’intromission a diminué significativement alors que la fréquence d’éjaculation a augmenté. L’index de libido, la fréquence de monte, d’intromission, d’éjaculation, d’orientation des mâles vis-à-vis d’eux même et l’index de motivation sexuelle a augmenté chez les animaux traités l’extrait comparés à ceux ayant reçu de l’eau distillée aussi bien chez les normaux que chez le diabétiques qui n’enregistrent d’ailleurs aucune éjaculation. Le traitement a augmenté significativement (P < 0,01) le poids des testicules, de la prostate et de l’épididyme. Il est observé une augmentation dose-dépendante du nombre et de la motilité des spermatozoïdes (P < 0,05), ainsi qu’une augmentation significative (P < 0,001) temps-dépendant du taux de cholestérol sérique et de protéines épididymaires. Ces résultats indiquent un potentiel androgénique pro-érectile de N. lotus chez les rats mâles et justifient l’utilisation empirique des fleurs de N. lotus dans le traitement des dysfonctions érectiles et des problèmes de fertilité chez les hommes. Mots-clés: Nymphaea lotus, pro-érectile, androgénique, fertilité, diabétiques, rat male

Monotone Constrained Tensor-product B-spline with application to screening studies

When different markers are responsive to different aspects of a disease, combination of multiple markers could provide a better screening test for early detection. It is also resonable to assume that the risk of disease changes smoothly as the biomarker values change and the change in risk is monotone with respect to each biomarker. In this paper, we propose a boundary constrained tensor-product B-spline method to estimate the risk of disease by maximizing a penalized likelihood. To choose the optimal amount of smoothing, two scores are proposed which are extensions of the GCV score (O'Sullivan et al. (1986)) and the GACV score (Ziang and Wahba (1996)) to incorporate linear constraints. Simulation studies are carried out to investigate the performance of the proposed estimator and the selection scores. In addidtion, sensitivities and specificities based ona pproximate leave-one-out estimates are proposed to generate more realisitc ROC curves. Data from a pancreatic cancer study is used for illustration.

Smooth Estimation of a Monotone Density

We investigate the interplay of smoothness and monotonicity assumptions when estimating a density from a sample of observations. The nonparametric maximum likelihood estimator of a decreasing density on the positive half line attains a rate of convergence at a fixed point if the density has a negative derivative. The same rate is obtained by a kernel estimator, but the limit distributions are different. If the density is both differentiable and known to be monotone, then a third estimator is obtained by isotonization of a kernel estimator. We show that this again attains the rate of convergence and compare the limit distributors of the three types of estimators. It is shown that both isotonization and smoothing lead to a more concentrated limit distribution and we study the dependence on the proportionality constant in the bandwidth. We also show that isotonization does not change the limit behavior of a kernel estimator with a larger bandwidth, in the case that the density is known to have more than one derivative.

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Valeur, fonctionnement et fonction. La filiation Saussure-Jakobson: un malentendu?

Si Jakobson, par ailleurs si critique relativement à l’apport saussurien, s’inscrit, quant à la notion de valeur, dans la filiation de Saussure, il nous semble que cette filiation revendiquée par Jakobson repose sur un malentendu. La redéfinition jakobsonienne de la notion de valeur est en effet inséparable d’une disjonction des différentes dimensions constitutives du concept saussurien de valeur. Par ailleurs et corrélativement, la valeur jakobsonienne se caractérise d’emblée par sa positivité, qui se déploie sur deux plans : celui de la consistance objectale, qui répond à une problématique des rapports forme/substance et celui de la sémioticité, qui répond à une problématique des rapports son/sens, deux problématiques aussi étrangères l’une que l’autre à la linguistique saussurienne. A la définition saussurienne de la langue comme un fonctionnement dont son et sens apparaissent comme des effets, fonctionnement qu’est la division-combinaison des deux masses amorphes de la pensée et du son, se substitue la construction jakobsonienne d’une langue structure d’appariement du son et du sens, construction fondée sur l’évidence d’une définition de la langue comme instrument de communication. On peut cependant penser que cette substitution, ce malentendu, sont tout à fait révélateurs de la spécificité de l’objet de la linguistique, particulièrement résistant à la théorisation.

Monotone Methods for Distorted Economies

No abstract available.