Learning aggregation weights from 3-tuple comparison sets

An important task in multiple-criteria decision making is how to learn the weights and parameters of an aggregation function from empirical data. We consider this in the context of quantifying ecological diversity, where such data is to be obtained as a set of pairwise comparisons specifying that one community should be considered more diverse than another. A problem that arises is how to collect a sufficient amount of data for reliable model determination without overloading individuals with the number of comparisons they need to make. After providing an algorithm for determining criteria weights and an overall ranking from such information, we then investigate the improvement in accuracy if ranked 3-tuples are supplied instead of pairs. We found that aggregation models could be determined accurately from significantly fewer 3-tuple comparisons than pairs. © 2013 IEEE.

Consistency and stability in aggregation operators : an application to missing data problems

In this work we analyze the key issue of the relationship that should hold between the operators in a family {An} of aggregation operators in order to understand they properly define a consistent whole. Here we extend some of the ideas about stability of a family of aggregation operators into a more general framework, formally defining the notions of i – L and j – R strict stability for families of aggregation operators. The notion of strict stability of order k is introduced as well. Finally, we also present an application of the strict stability conditions to deal with missing data problems in an information aggregation process. For this analysis, we have focused in the weighted mean family and the quasi-arithmetic weighted means families.

A penalty-based aggregation operator for non-convex intervals

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.

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.

Aggregation of a dibenzo[b,def]chrysene based organic photovoltaic material in solution

Detailed electrochemical studies have been undertaken on molecular aggregation of the organic semiconductor 7,14-bis((triisopropylsilyl)-ethynyl) dibenzo[b,def]chrysene (TIPS-DBC), which is used as an electron donor material in organic solar cells. Intermolecular association of neutral TIPS-DBC molecules was established by using 1H NMR spectroscopy as well as by the pronounced dependence of the color of TIPS-DBC solutions on concentration. Diffusion limited current data provided by near steady-state voltammetry also reveal aggregation. Furthermore, variation of concentration produces large changes in shapes of transient DC and Fourier transformed AC (FTAC) voltammograms for oxidation of TIPS-DBC in dichloromethane. Subtle effects of molecular aggregation on the reduction of TIPS-DBC are also revealed by the highly sensitive FTAC voltammetric method. Simulations of FTAC voltammetric data provide estimates of the kinetic and thermodynamic parameters associated with oxidation and reduction of TIPS-DBC. Significantly, aggregation of TIPS-DBC facilitates both one-electron oxidation and reduction by shifting the reversible potentials to less and more positive values, respectively. EPR spectroscopy is used to establish the identity of one-electron oxidized and reduced forms of TIPS-DBC. Implications of molecular aggregation on the HOMO energy level in solution are considered with respect to efficiency of organic photovoltaic devices utilizing TIPS-DBC as an electron donor material. © 2014 American Chemical Society.

A hybrid weighted aggregation method based on consistency and consensus in group decision making

A recent study in Science indicated that the confidence of a decision maker played an essential role in group decision making problems. In order to make use of the information of each individual's confidence of the current decision problem, a new hybrid weighted aggregation method to solve a group decision making peoblem is proposed in this paper. Specifically, the hybrid weight of each expert is generated by a convex combination of his/her subjective experience-based weight and objective problem-domain-based weight. The experience-based weight is derived from the expert's historical experiences and the problem-domain-based weight is characterized by the confidence degree and consensus degree of each expert's opinions in the current decision making process. Based on the hybrid weighted aggregation method, all the experts' opinions which are expressed in the form of fuzzy preference relations are consequently aggregated to obtain a collective group opinion. Some valuable properities of the proposed method are discussed. A nurse manager hiring problem in a hospital is employed to illustrate that the proposed method provides a rational and valid solution for the group decision making problem when the experts are not willing to change their initial preferences, or the cost of change is high due to time limitation.

Aggregation of Pi-based forecast to enhance prediction accuracy

In contrast to point forecast, prediction interval-based neural network offers itself as an effective tool to quantify the uncertainty and disturbances that associated with process data. However, single best neural network (NN) does not always guarantee to predict better quality of forecast for different data sets or a whole range of data set. Literature reported that ensemble of NNs using forecast combination produces stable and consistence forecast than single best NN. In this work, a NNs ensemble procedure is introduced to construct better quality of Pis. Weighted averaging forecasts combination mechanism is employed to combine the Pi-based forecast. As the key contribution of this paper, a new Pi-based cost function is proposed to optimize the individual weights for NN in combination process. An optimization algorithm, named simulated annealing (SA) is used to minimize the PI-based cost function. Finally, the proposed method is examined in two different case studies and compared the results with the individual best NNs and available simple averaging Pis aggregating method. Simulation results demonstrated that the proposed method improved the quality of Pis than individual best NNs and simple averaging ensemble method.

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.