OWA Operator Weights Research Articles

On stability of maximal entropy OWA operator weights

The maximal entropy OWA operator (MEOWA) weights can be obtained by solving a nonlinear programming problem with a linear constraint for the level of orness. Since the exact MEOWA weights are not known for the general case we can only find approximate solutions. We will prove that the nonlinear programming problem for obtaining MEOWA weights is well-posed: it has a unique solution and each MEOWA weight changes continuously with the initial level of orness. Using the implicit function theorem we will show that MEOWA weights are Lipschitz-continuous functions of the orness level. The stability property of the MEOWA weights under small changes of the orness level guarantees that small rounding errors of digital computation and small errors of measurement of the orness level can cause only a small deviation in MEOWA weights, i.e. every successive approximation method can be applied to the computation of the approximation of the exact MEOWA weights.

Approach for Multi-Attribute Decision Making Based on Gini Aggregation Operator and Its Application to Carbon Supplier Selection

This paper provides a new multi-attributes decision making approach on the basis of the Gini OWA ( $\text{G}^{\mathrm {p,q}}$ -OWA) operator, in which the Gini operator is the combination of the Gini mean and the OWA operator. Desired properties and several generalized forms of the $\text{G}^{\mathrm {p,q}}$ -OWA operator are investigated. In order to determine the $\text{G}^{\mathrm {p,q}}$ -OWA operator weights, an orness measure is proposed, and a generalized least squares deviation model (GLSD) is put forward. Finally, a case study of low carbon supplier selection is shown to illustrate the effectiveness and practicality of the proposed method.

An Alternative Approach to Obtaining an Analytical Solution to Dujmovic’s Iterative OWA

Troiano and Díaz presented the analytic solution to the iterative ordered weights averaging (ItOWA) operator weights. Their findings validate Dujmović and Larsen’s conjecture and profoundly contribute to the ItOWA operator due to the closed formula derived. This paper attempts to present another way of deriving the ItOWA operator weights based on other theories. Further, as iterative OWA performs repeated computations for a higher dimension, the orness of the resulting ItOWA operator weights is different from the one initially used in aggregating two input arguments. To resolve this unwanted situation, we suggest some weighting functions that generate the OWA operator weights having a property of constant orness irrespective of the number of input arguments.

Comprehensive evaluation of airport economic zone development quality based on OWA operator weights

Based on GEMS model and the quality development of airport economic zone is defined firstly, the quality development evaluation index system is set up which included four first-degree indexes. The indexes obtain basic conditions, industrial development, radiation effects and development environment, and combines the methods of OWA operators and Fuzzy comprehensive assessment method to establish the evaluation model. Finally, though empirical analysis, evaluation result of the model is close to current situation of quality development of Zhengzhou airport economic zone, which shows that the model is effective and feasible.

The least absolute deviation problem for OWA operator weights

The least absolute deviation problem for OWA operator weights

Supplier Selection in Supply Chain Management with OWA Operator Weights

Supplier Selection in Supply Chain Management with OWA Operator Weights

A combination approach for obtaining the minimize disparity OWA operator weights

One of the key issues in the theory of ordered weighted averaging operator is the determination of OWA operator weights. In this paper, a simple combination approach for obtaining minimal disparity OWA operator weights is proposed. The proposed approach generates the OWA operator weights by minimizing the combination disparity between any two adjacent weights and its expectation. This involves the formulation and solution of a linear programming model and a quadratic programming model for a given degree of orness. A numerical example demonstrated simpleness and effectiveness of the methods proposed in this paper.

A linear programming model for determining ordered weighted averaging operator weights with maximal Yager’s entropy

It has a wide attention about the methods for determining OWA operator weights. At the beginning of this dissertation, we provide a briefly overview of the main approaches for obtaining the OWA weights with a predefined degree of orness. Along this line, we next make an important generalization of these approaches as a special case of the well-known and more general problem of calculation of the probability distribution in the presence of uncertainty. All these existed methods for dealing these kinds of problems are quite complex. In order to simplify the process of computation, we introduce Yager’s entropy based on Minkowski metric. By analyzing its desirable properties and utilizing this measure of entropy, a linear programming (LP) model for the problem of OWA weight calculation with a predefined degree of orness has been built and can be calculated much easier. Then, this result is further extended to the more realistic case of only having partial information on the range of OWA weights except a predefined degree of orness. In the end, two numerical examples are provided to illustrate the application of the proposed approach.

Choosing OWA operator weights in the field of Social Choice

One of the most important issues in the theory of OWA operators is the determination of associated weights. This matter is essential in order to use the best-suited OWA operator in each aggregation process. Given that some aggregation processes can be seen as extensions of majority rules to the field of gradual preferences, it is possible to determine the OWA operator weights by taking into account the class of majority rule that we want to obtain when individuals do not grade their pairwise preferences. However, a difficulty with this approach is that the same majority rule can be obtained through a wide variety of OWA operators. For this reason, a model for selecting the best-suited OWA operators is proposed in this paper.

Notes on properties of the OWA weights determination model

This paper solves the recently open problem related to the OWA weights determination minimax model presented by Amin and Emrouznejad [Amin G. R., & Emrouznejad, A. (2006). An extended minimax disparity to determine the OWA operator weights. Computers &Industrial Engineering, 50, pp. 312-316]. So the contribution of this work is that it explains further the properties of the proposed OWA weights determination minimax model.

Note on “A preemptive goal programming method for aggregating OWA operator weights in group decision making”

Note on “A preemptive goal programming method for aggregating OWA operator weights in group decision making”

A preemptive goal programming method for aggregating OWA operator weights in group decision making

This paper reveals that OWA operator weights cannot be aggregated by the weighted arithmetic or geometric average method in group decision making. A preemptive goal programming method (PGPM) is proposed for aggregating OWA operator weights, which is an extension of the minimax disparity approach developed earlier by the same authors. The effectiveness of PGPM is illustrated with a numerical example.

Reply to “Comments on the paper: On the properties of equidifferent OWA operator”

In reply to Péter Majlender, the connection between the (maximum spread) equidifferent OWA operator weights and the analytical method for the minimum variance OWA operator problem [R. Fullér, P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets and Systems 136 (2003) 203–215] is pointed out and the differences between them are clarified.

Comments on the paper: “On the properties of equidifferent OWA operator” by Xinwang Liu

In this communication, we will point out an interesting correspondence between a recent paper “On the properties of equidifferent OWA operator” [International Journal of Approximate Reasoning, in press, doi:10.1016/j.ijar.2005.11.003] by Liu, and an earlier result “On obtaining minimal variability OWA operator weights” [Fuzzy Sets and Systems 136 (2003) 203–215] by Fullér and Majlender.

An argument-dependent approach to determining OWA operator weights based on the rule of maximum entropy

The methods for determining OWA operator weights have aroused wide attention. We first review the main existing methods for determining OWA operator weights. We next introduce the principle of maximum entropy for setting up probability distributions on the basis of partial knowledge and prove that Xu's normal distribution-based method obeys the principle of maximum entropy. Finally, we propose an argument-dependent approach based on normal distribution, which assigns very low weights to these “false” or “biased” opinions and can relieve the influence of the unfair arguments. A numerical example is provided to illustrate the application of the proposed approach. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 209–221, 2007.

On the issue of obtaining OWA operator weights

We first investigate the issue of obtaining the weights associated with the OWA aggregation in the situation when we have observed data on the arguments and the aggregated value. We next introduce a family of OWA operators called exponential OWA operators. Finally, we look at a simple procedure for generating the weights given a required degree of orness.