Three types of monotonicity of averaging functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions, which are one of the basic tools in knowledge-based systems. The functions known as means (or averages) are idempotent and typically are monotone, however there are many important classes of means that are non-monotone. Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging functions. In this paper we discuss the concepts of directional and cone monotonicity, and monotonicity with respect to majority of inputs and coalitions of inputs. We establish the relations between various kinds of monotonicity, and illustrate it on various examples. We also provide a construction method for cone monotone functions.

Strong fuzzy subsethood measures and strong equalities via implication functions

In this work we present the definition of strong fuzzy subsethood measure as a unifiying concept for the different notions of fuzzy subsethood that can be found in the literature. We analyze the relations of our new concept with the definitions by Kitainik ( [20]), Young ( [26]) and Sinha and Dougherty ( [23]) and we prove that the most relevant properties of the latter are preserved. We show also several construction methods. © 2014 Old City Publishing, Inc.

Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs

Rather than denoting fuzzy membership with a single value, orthopairs such as Atanassov's intuitionistic membership and non-membership pairs allow the incorporation of uncertainty, as well as positive and negative aspects when providing evaluations in fuzzy decision making problems. Such representations, along with interval-valued fuzzy values and the recently introduced Pythagorean membership grades, present particular challenges when it comes to defining orders and constructing aggregation functions that behave consistently when summarizing evaluations over multiple criteria or experts. In this paper we consider the aggregation of pairwise preferences denoted by membership and non-membership pairs. We look at how mappings from the space of Atanassov orthopairs to more general classes of fuzzy orthopairs can be used to help define averaging aggregation functions in these new settings. In particular, we focus on how the notion of 'averaging' should be treated in the case of Yager's Pythagorean membership grades and how to ensure that such functions produce outputs consistent with the case of ordinary fuzzy membership degrees.

Weakly monotonic averaging functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important nonmonotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions, and proves that several families of important nonmonotonic means are actually weakly monotonic averaging functions. Specifically, we provide sufficient conditions for weak monotonicity of the Lehmer mean and generalized mixture operators. We establish weak monotonicity of several robust estimators of location and conditions for weak monotonicity of a large class of penalty-based aggregation functions. These results permit a proof of the weak monotonicity of the class of spatial-tonal filters that include important members such as the bilateral filter and anisotropic diffusion. Our concept of weak monotonicity provides a sound theoretical and practical basis by which (monotonic) aggregation functions and nonmonotonic averaging functions can be related within the same framework, allowing us to bridge the gap between these previously disparate areas of research.

Oxidative stress markers, cognitive functions, and psychosocial functioning in bipolar disorder: an empirical cross-sectional study

This study aimed to evaluate the relationship between oxidative stress markers and cognitive functions and domains of psychosocial functioning in bipolar disorder.

Influence functions of two families of robust estimators under proportional scatter matrices

In this paper, under a proportional model, two families of robust estimates for the proportionality constants, the common principal axes and their size are discussed. The first approach is obtained by plugging robust scatter matrices on the maximum likelihood equations for normal data. A projection- pursuit and a modified projection-pursuit approach, adapted to the proportional setting, are also considered. For all families of estimates, partial influence functions are obtained and asymptotic variances are derived from them. The performance of the estimates is compared through a Monte Carlo study. © 2006 Springer-Verlag.

Segmentation of gray scale image based on intuitionistic fuzzy sets constructed from several membership functions

Segmentation is the process of extraction of objects from an image. This paper proposes a new algorithm to construct intuitionistic fuzzy set (IFS) from multiple fuzzy sets as an application to image segmentation. Hesitation degree in IFS is formulated as the degree of ignorance (due to the lack of knowledge) to determine whether the chosen membership function is best for image segmentation. By minimizing entropy of IFS generated from various fuzzy sets, an image is thresholded. Experimental results are provided to show the effectiveness of the proposed method.

Leptin's metabolic and immune functions can be uncoupled at the ligand/receptor interaction level.

The adipocyte-derived cytokine leptin acts as a metabolic switch, connecting the body's metabolism to high-energy consuming processes such as reproduction and immune responses. We here provide genetic and biochemical evidence that the metabolic and immune functions of leptin can be uncoupled at the receptor level. First, homozygous mutant fatt/fatt mice carry a spontaneous splice mutation causing deletion of the leptin receptor (LR) immunoglobulin-like domain (IGD) in all LR isoforms. These mice are hyperphagic and morbidly obese, but display only minimal changes in size and cellularity of the thymus, and cellular immune responses are unaffected. These animals also displayed liver damage in response to concavalin A comparable to wild-type and heterozygous littermates. Second, treatment of healthy mice with a neutralizing nanobody targeting IGD induced weight gain and hyperinsulinaemia, but completely failed to block development of experimentally induced autoimmune diseases. These data indicate that leptin receptor deficiency or antagonism profoundly affects metabolism, with little concomitant effects on immune functions.

On weak monotonicity of some mixture functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. Here we study means that are not necessarily monotone. Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging functions. We provide results for the weak monotonicity of some importantclasses of mixture functions. With these results we are able to extend and improve the understanding of this very important class of functions.

Building fuzzy inference systems with similarity reasoning : NSGAII-based fuzzy rule selection and evidential functions

In our previous investigations, two Similarity Reasoning (SR)-based frameworks for tackling real-world problems have been proposed. In both frameworks, SR is used to deduce unknown fuzzy rules based on similarity of the given and unknown fuzzy rules for building a Fuzzy Inference System (FIS). In this paper, we further extend our previous findings by developing (1) a multi-objective evolutionary model for fuzzy rule selection; and (2) an evidential function to facilitate the use of both frameworks. The Non-Dominated Sorting Genetic Algorithms-p (NSGA-p) is adopted for fuzzy rule selection, in accordance with the Pareto optimal criterion. Besides that, two new evidential functions are developed, whereby given fuzzy rules are considered as evidence. Simulated and benchmark examples are included to demonstrate the applicability of these suggestions. Positive results were obtained.

Image reduction operators as aggregation functions: Fuzzy transform and undersampling

After studying several reduction algorithms that can be found in the literature, we notice that there is not an axiomatic definition of this concept. In this work we propose the definition of weak reduction operators and we propose the properties of the original image that reduced images must keep. From this definition, we study whether two methods of image reduction, undersampling and fuzzy transform, satisfy the conditions of weak reduction operators.

Metabolism and functions of copper in brain

Copper is an important trace element that is required for essential enzymes. However, due to its redox activity, copper can also lead to the generation of toxic reactive oxygen species. Therefore, cellular uptake, storage as well as export of copper have to be tightly regulated in order to guarantee sufficient copper supply for the synthesis of copper-containing enzymes but also to prevent copper-induced oxidative stress. In brain, copper is of importance for normal development. In addition, both copper deficiency as well as excess of copper can seriously affect brain functions. Therefore, this organ possesses ample mechanisms to regulate its copper metabolism. In brain, astrocytes are considered as important regulators of copper homeostasis. Impairments of homeostatic mechanisms in brain copper metabolism have been associated with neurodegeneration in human disorders such as Menkes disease, Wilson's disease and Alzheimer's disease. This review article will summarize the biological functions of copper in the brain and will describe the current knowledge on the mechanisms involved in copper transport, storage and export of brain cells. The role of copper in diseases that have been connected with disturbances in brain copper homeostasis will also be discussed.

Bioactive functions of milk proteins: a comparative genomics approach

The composition of milk includes factors required to provide appropriate nutrition for the growth of the neonate. However, it is now clear that milk has many functions and comprises bioactive molecules that play a central role in regulating developmental processes in the young while providing a protective function for both the suckled young and the mammary gland during the lactation cycle. Identifying these bioactives and their physiological function in eutherians can be difficult and requires extensive screening of milk components that may function to improve well-being and options for prevention and treatment of disease. New animal models with unique reproductive strategies are now becoming increasingly relevant to search for these factors.