On the reinforcement of uninorms and absorbing norms

DUKE_HCERES2020Aggregation operators Reinforcement ... We propose a n-ary extension of absorbing norms, defined with the help of generative functions, and its relationship with additive generating functions of uninorms. In this paper, we also present new aggregation operators, namely the k-uninorms and k-absorbing norms. These operators are a generalization of usual uninorms and absorbing norms for which a set combination of inputs is introduced. Their main ability is to provide reinforcement for contradictory inputs, as nullnorms and as opposed to uninorms. On the other hand it still provides full reinforcement for agreeing inputs, as uninorms and as opposed to nullnorms. Numerous examples are given in order to illustrate the behavior of the proposed operators

Understanding the Aggregation of Model Island and Archipelago Asphaltene Molecules near Kaolinite Surfaces using Molecular Dynamics

The solubility of asphaltenes in hydrocarbons changes with pressure, composition, and temperature, leading to precipitation and deposition, thereby causing one of the crucial problems that negatively affects oil production, transportation, and processing. Because, in some circumstances, it might be advantageous to promote asphaltene agglomeration into small colloidal particles, molecular dynamics simulations were conducted here to understand the impacts of a chemical additive inspired by cyclohexane on the mechanism of aggregation of model island and archipelago asphaltene molecules in toluene. We compared the results in the presence and absence of a kaolinite surface at 300 and 400 K. Cluster size analyses, radial distribution functions, angles between asphaltenes, radius of gyration, and entropic and energetic calculations were used to provide insights on the behavior of these systems. The results show that the hypothetical additive inspired by cyclohexane promoted the aggregation of both asphaltenes. Structural differences were observed among the aggregates obtained in our simulations. These differences are attributed to the number of aromatic cores and side chains on the asphaltene molecules as well as to that of heteroatoms. For the island structure, aggregation in the bulk phase was less pronounced than that in the proximity of the kaolinite surface, whereas the opposite was observed for the archipelago structure. In both cases, the additive promoted stacking of asphaltenes, yielding more compact aggregates. The results provided insights into the complex nature of asphaltene aggregation, although computational approaches that can access longer time and larger size scales should be chosen for quantifying emergent meso- and macroscale properties of systems containing asphaltenes in larger numbers than those that can currently be sampled via atomistic simulations

Super- and sub-additive envelopes of aggregation functions: interplay between local and global properties, and approximation

Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and Sipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, Fuzzy Sets and Systems 291 (2016), 40{53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with a preassigned super- and sub-additive transformation, and address approximation of these transformations. The underpinning feature of the presented results is dependence of global properties of super- and sub-additive transformations on local properties of aggregation functions

Aggregation functions with given super-additive and sub-additive transformations

Aggregation functions and their transformations have found numerous applications in various kinds of systems as well as in economics and social science. Every aggregation function is known to be bounded above and below by its super-additive and sub-additive transformations. We are interested in the “inverse” problem of whether or not every pair consisting of a super-additive function dominating a sub-additive function comes from some aggregation function in the above sense. Our main results provide a negative answer under mild extra conditions on the super- and sub-additive pair. We also show that our results are, in a sense, best possible

Segmentation of articular cartilage and early osteoarthritis based on the fuzzy soft thresholding approach driven by modified evolutionary ABC optimization and local statistical aggregation

Articular cartilage assessment, with the aim of the cartilage loss identification, is a crucial task for the clinical practice of orthopedics. Conventional software (SW) instruments allow for just a visualization of the knee structure, without post processing, offering objective cartilage modeling. In this paper, we propose the multiregional segmentation method, having ambitions to bring a mathematical model reflecting the physiological cartilage morphological structure and spots, corresponding with the early cartilage loss, which is poorly recognizable by the naked eye from magnetic resonance imaging (MRI). The proposed segmentation model is composed from two pixel's classification parts. Firstly, the image histogram is decomposed by using a sequence of the triangular fuzzy membership functions, when their localization is driven by the modified artificial bee colony (ABC) optimization algorithm, utilizing a random sequence of considered solutions based on the real cartilage features. In the second part of the segmentation model, the original pixel's membership in a respective segmentation class may be modified by using the local statistical aggregation, taking into account the spatial relationships regarding adjacent pixels. By this way, the image noise and artefacts, which are commonly presented in the MR images, may be identified and eliminated. This fact makes the model robust and sensitive with regards to distorting signals. We analyzed the proposed model on the 2D spatial MR image records. We show different MR clinical cases for the articular cartilage segmentation, with identification of the cartilage loss. In the final part of the analysis, we compared our model performance against the selected conventional methods in application on the MR image records being corrupted by additive image noise.Web of Science117art. no. 86

Axiomatizations of Lov\'asz extensions of pseudo-Boolean functions

Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity conditions, these functions coincide with the Lov\'asz extensions vanishing at the origin, which subsume the discrete Choquet integrals. We also propose a simultaneous generalization of horizontal min-additivity and horizontal max-additivity, called horizontal median-additivity, and we describe the corresponding function class. Additional conditions then reduce this class to that of symmetric Lov\'asz extensions, which includes the discrete symmetric Choquet integrals