Induced and heavy aggregation operators with distance measures

Decision-making in sport management based on the OWA operator

OWA (Ordered Weighted Averaging) Distance Based CxK Nearest Neighbor Algorithm (CxK-NN) via L-R fuzzy data is performed with two different fuzzy metric measures. We use fuzzy metric defined by Diamond and a weighted dissimilarity measure composed by spread distances and center distances in order to evaluate the effects of different metric measures. K neighbors are considered for each class and the algorithm perform OWA operator in order to calculate the distance between being classified fuzzy point and its K-nearest set. It is observed that the OWA distance behavior by changing its weights as inter-cluster distance approaches single, complete, and average linkages. The performance of this novel approach is evaluated by using nfold cross validation. After experiments with well-known three classification dataset, it is observed that single linkage approach by using two different metric measures has significant different results.

Interval numbers multiple attribute decision-making (MADM) is an important branch of uncertainty decision theory, and the decision result largely depends on the selection of the aggregation operator. In this paper, we analyze the ordered weighted average (OWA) operator, which is an averaging aggregation operator. The OWA operator provides an aggregation method between the minimum and maximum operators. Moreover, we further analyze some of extensions about OWA operator, and pay special attention to the Bonferroni means and OWA (BON-OWA) operator. Note that the BON-OWA operator only aggregate the input arguments which are exact numbers. Under normal circumstances, decision makers is difficult to provide a clear evaluation value for attribute and most of them are described by vague information. When the decision information is an interval numbers, the BON-OWA operator cannot describe decision result accurately. Under these environments, we proposed the interval numbers BON-OWA (IBr,q-OWA) operator to deal with the vague decision information in this paper. Then we consider their main properties, such as idempotence, monotonicity, and boundedness and prove them. Besides, a wide range of special aggregation operators are found in changing parameter values, such as the square mean and max operator, and so on. We also compare the ranking method of the interval numbers based on Boolean matrix. As a result, the combination of IBr,q-OWA operator makes the decision result more scientific. Finally, a new approach for decision-making problem is developed based on the IBr,q-OWA operator, which shows the effectiveness in practical examples.

Determination of the weights of an ordered weighted averaging (OWA) operator is a vital constituent of the operator's aggregation procedure. Consequently, several weight generation techniques have evolved in the literature. Here, using inverse hypergeometric distribution, we use a novel parametric function to generate the weight vector of an OWA operator. The proposed inverse hypergeometric OWA (InHyp-OWA) operator generates a unique weight vector for every choice of its parameter. Also, using the proposed weight function, OWA weight vectors can be generated without solving any complicated optimization problem. An important property of InHyp-OWA operator is that for a given parameter value, its orness value remains constant, regardless of the number of objectives aggregated. Hence, InHyp-OWA operator is a new member of the family of OWA operators with constant orness. This class of OWA operators can utilize a prejudiced preference to determine the corresponding weight vector. The proposed approach provides a number of advantages over existing weight generating methods for OWA operators. One of the remarkable advantages of the InHyp-OWA operator is the fact that it generates weight vectors with strictly monotonic components. It also generalizes the well-known Borda-Kendall OWA operator.

The objective of the paper is to present an extension of the ordered weighted average (OWA) operator, probability OWA (POWA) operator, distance measures and Pythagorean membership grades. These new operators are called the Pythagorean membership grade OWA distance (PMGOD) operator and the probabilistic Pythagorean membership grade OWA distance (PPMGOD) operator. This extension includes in one formulation the ability to measure the ideal vs. real situation of the distance operators, the weighting vector and reordering step of the OWA operator and the way in which it includes uncertainty based on the satisfaction of the criteria of the Pythagorean membership degree. These propositions are applied to new business ventures in the city of Colombia, where the decision maker can express his/her concerns about the uncertainty and probabilities of the current business environment and, thus, generate a better decision-making process.

Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion. If the data are real numbers, then OWA operators can be characterized either as a special kind of discrete Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of these characterizations when OWA operators are defined on a complete lattice. In addition, the set of all n-ary OWA operators is studied as a sublattice of the lattice of all the n-ary aggregation functions defined on a distributive lattice.

Some properties and representation methods for Ordered Weighted Averaging operators

The result of aggregation performed by the ordered weighted averaging (OWA) operator heavily depends upon the weighting vector used. A number of methods have been presented for obtaining the associated weights. In this paper, we present analytic forms of OWA operator weighting functions, each of which has properties of rank-based weights and a constant level of orness, irrespective of the number of objectives considered. These analytic forms provide significant advantages for generating the OWA weights over previously reported methods. First, the OWA weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program. Moreover, convex combinations of these specific OWA operators can be used to generate the OWA operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker. Those weights have a property of constant level of orness as well. Finally, the OWA weights generated at a predefined value of orness make almost no numerical difference with maximum entropy OWA weights in terms of dispersion.

The most important thing in using the ordered weighted averaging (OWA) operator which can easily describe the mental model of an Decision Maker (DM), is to characterize OWA weights. Determination of OWA weights cannot provide a characterization by itself. If we want to generalization and reusability of the OWA weights to aggregate various sized objects, we have to be determine more general form. In this paper, we propose a new approach for learning a stress function, which can be characterized as a DM strategy of OWA operator. For this aim the Kolmogorov-Smirnov test for similarity probability density functions is used.

Environmental indices (EI) constitute a common communication tool that is often used to describe the overall status of environmental systems (air, water and soil). EI development entails the use of mathematical operators to aggregate various non-commensurate input parameters in a logical manner. The ordered weighted averaging (OWA) operator is a general mean type operator that provides flexibility in the aggregation process such that the aggregated value is bounded between minimum and maximum values of the input parameters. This flexibility of the OWA operator is realized through the concept of orness, which is a surrogate for decision maker’s attitude. The type of input parameters also affects the choice of aggregation operators. If the input parameters are linguistic or fuzzy, the aggregation through OWA operators is not possible, and the use of fuzzy arithmetic is warranted. The concept of fuzzy number OWA (FN-OWA) operators is explored to handle situations in which one or more input parameter has fuzzy (or linguistic) values. The proposed approach is demonstrated using data provided in an earlier study by Swamee and Tyagi (ASCE J Environ Eng 126(5):451–455, 2000) for establishing water quality indices. Multiple hypothetical scenarios are also generated to highlight the utility and sensitivity of the proposed approach.

The classification accuracy of a classifier depends largely on the aggregation operator it uses in fusion of information. This paper presents a similarity classifier that utilizes a weighted ordered weighted averaging (WOWA) operator. The applicability of the WOWA operator for aggregation of similarities is studied and tested with several Regular Increasing Monotonic (RIM) type weight generators. The RIM quantifiers used here are of the basic, polynomial, trigonometric, exponential, and of the logarithmic type. The proposed approach is tested on three real world data sets. Results obtained with the new method are compared with those obtained using two previously presented similarity classifiers. The proposed new classifier shows better performance on the data sets studied, which indicates that benefits can be gained from using a WOWA operator in the aggregation.

This paper forwards an ordered weighted average (OWA) operator of linguistic label vague (LLV) set. The OWA operator evaluates the degrees to which the object described by linguistic label vague set satisfies, docs not satisfy and does not know whether it satisfies or not most individuals of universe. Secondly, it converts the vague value expressed by triangular fuzzy numbers (TFNs) into the ordinary vague value. Thirdly, it uses the score function of LLV set to measure the suitable degree of the object described by LLV set, and takes the score as an index for sorting. Lastly, it applies the OWA operator of LLV to our simulation example of decision making. The result shows the efficiency of OWA operator of LLV set.

How well does the OWA operator represent real preferences?

An automated methodology for combining Ground Penetrating Radar features from different depths is presented and analyzed. GPR data from the NIITEK system are processed by a depth-dependent, adaptive whitening algorithm. Shape and contrast features, including compactness, solidity, eccentricity, and relative area are computed at the different depths. These features must be combined to make a decision as to the presence of a landmine at a specific location. Since many of the depths contain no useful information and the depths of the mines are unknown, a strategy based on sorting is used. In a previous work, sorted features were combined via a rule-based system. In the current paper, an automated algorithm that builds a decision rule from sets of Ordered Weighted Average (OWA) operators is described. The OWA operator sorts the feature values, weights them, and performs a weighted sum of the sorted values, resulting in a nonlinear combination of the feature values. The weights of the OWA operators are trained off-line in combination with those of a decision-making network and held fixed during testing. The combination of OWA operators and decision-making network is called a FOWA network. The FOWA network is compared to the rule-based method on real data taken from multiple collections at two outdoor test sites.

The successful design and application of the ordered weighted averaging (OWA) method as a decision making tool depends on the efficient computation of its order weights. The most popular methods for determining the order weights are the fuzzy linguistic quantifiers approach and the minimal variability methods which give different behavior patterns for OWA. These methods will be compared by using sensitivity analysis on the outputs of OWA with respect to the optimism degree of the decision maker. The theoretical results are illustrated in a water resources management problem. The fuzzy linguistic quantifiers approach gives more information about the behavior of the OWA outputs in comparison to the minimal variability method. However, in using the minimal variability method, the OWA has a linear behavior with respect to the optimism degree and therefore it has better computation efficiency. A simulation study is also reported in this paper, where the dependence of the optimal decision on the uncertainty level is examined. Also based on obtained sensitivity measure, a new combined measure of goodness has been defined to have more reliability in obtaining optimal solutions