An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.
In this paper, a simple strategy to change the emission behaviour of luminogenic materials was developed. Tetraphenylethene (TPE)‐functionalised benzothiazolium salts with different counteranions (TPEBeX; X=I − , ClO 4 − and PF 6 − ) were designed and synthesised. All the luminogens show weak red emission in the solution state that originates from intramolecular charge transfer from TPE to the benzothiazolium unit. Whereas aggregate formation enhances the light emission of TPEBeClO 4 and TPEBePF 6 , that of TPEBeI is quenched, thus demonstrating the phenomena of aggregation‐induced emission and aggregation‐caused quenching. TPEBeI works as a light‐up fluorescent sensor for Hg 2+ in aqueous solution with high sensitivity and specificity owing to the elimination of the emission quenching effect of the iodide ion by the formation of HgI 2 as well as the induction in aggregate formation by the complexation of Hg 2+ with the S atom of the benzothiazolium unit of TPEBeI. A solid film of TPEBeI was prepared that can monitor the level of Hg 2+ in aqueous solution with a detection limit of 1 μ M . From darkness to light! A series of tetraphenylethene‐functionalised benzothiazolium salts with different counteranions (TPEBeX) was developed. By varying the counteranion from I − to ClO 4 − or PF 6 − , TPEBeX changes its emission behaviour from aggregation‐caused quenching to aggregationinduced emission (see figure). TPEBEI shows a light‐up response to Hg 2+ .
We consider the following problem: given a set of clusterings, find a single clustering that agrees as much as possible with the input clusterings. This problem, clustering aggregation , appears naturally in various contexts. For example, clustering categorical data is an instance of the clustering aggregation problem; each categorical attribute can be viewed as a clustering of the input rows where rows are grouped together if they take the same value on that attribute. Clustering aggregation can also be used as a metaclustering method to improve the robustness of clustering by combining the output of multiple algorithms. Furthermore, the problem formulation does not require a priori information about the number of clusters; it is naturally determined by the optimization function. In this article, we give a formal statement of the clustering aggregation problem, and we propose a number of algorithms. Our algorithms make use of the connection between clustering aggregation and the problem of correlation clustering . Although the problems we consider are NP-hard, for several of our methods, we provide theoretical guarantees on the quality of the solutions. Our work provides the best deterministic approximation algorithm for the variation of the correlation clustering problem we consider. We also show how sampling can be used to scale the algorithms for large datasets. We give an extensive empirical evaluation demonstrating the usefulness of the problem and of the solutions.
We report an effective modulation of the quantum transport in molecular junctions consisting of aggregation‐induced‐emission(AIE)‐active molecules. Theoretical simulations based on combined density functional theory and rate‐equation method calculations show that the low‐bias conductance of the junction with a single tetraphenylethylene (TPE) molecule can be completely suppressed by strong electron–vibration couplings, that is, the Franck‐Condon blockade effect. It is mainly associated with the low‐energy vibration modes, which is also the origin of the fluorescence quenching of the AIE molecule in solution. We further found that the conductance of the junction can be lifted by restraining the internal motion of the TPE molecule by either methyl substitution on the phenyl group or by aggregation, a mechanism similar to the AIE process. The present work demonstrates the correlation between optical processes of molecules and quantum transport in their junction, and thus opens up a new avenue for the application of AIE‐type molecules in molecular electronics and functional devices. Better together : Molecular junctions with aggregation‐induced‐emission(AIE)‐active molecules reveal a low‐bias current suppression also known as Franck–Condon blockade. The current blockade can be completely removed by aggregation, which indicates an electronic‐transport version of the AIE effect.
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference orders), when consolidating conflicting views regarding the relationships between arguments in a debate (graphs as abstract argumentation frameworks), or when computing a consensus between several alternative clusterings of a given dataset (graphs as equivalence relations). In this paper, we introduce a formal framework for graph aggregation grounded in social choice theory. Our focus is on understanding which properties shared by the individual input graphs will transfer to the output graph returned by a given aggregation rule. We consider both common properties of graphs, such as transitivity and reflexivity, and arbitrary properties expressible in certain fragments of modal logic. Our results establish several connections between the types of properties preserved under aggregation and the choice-theoretic axioms satisfied by the rules used. The most important of these results is a powerful impossibility theorem that generalises Arrow's seminal result for the aggregation of preference orders to a large collection of different types of graphs. (C) 2017 Elsevier B.V. All rights reserved.
Increasing evidence indicates that many peptides and proteins can be converted in vitro into highly organised amyloid structures, provided that the appropriate experimental conditions can be found. In this work, we define intrinsic propensities for the aggregation of individual amino acids and develop a method for identifying the regions of the sequence of an unfolded peptide or protein that are most important for promoting amyloid formation. This method is applied to the study of three polypeptides associated with neurodegenerative diseases, A beta 42, a-synuclein and tau. In order to validate the approach, we compare the regions of proteins that are predicted to be most important in driving aggregation, either intrinsically or as the result of mutations, with those determined experimentally. The knowledge of the location and the type of the "sensitive regions" for aggregation is important both for rationalising the effects of sequence changes on the aggregation of polypeptide chains and for the development of targeted strategies to combat diseases associated with amyloid formation. (c) 2005 Elsevier Ltd. All rights reserved.