Generalized Ordered Weighted Averaging Research Articles

Generalized Ordered Weighted Simplified Neutrosophic Cosine Similarity Measure for Multiple Attribute Group Decision Making

The paper proposes a generalized ordered weighted simplified neutrosophic cosine similarity (GOWSNCS) measure by combining the cosine similarity measure of simplified neutrosophic sets (SNSs) with the generalized ordered weighted averaging (GOWA) operator and investigates its properties and special cases. Then, the author develops a simplified neutrosophic group decision-making method based on the GOWSNCS measure to handle multiple attribute group decision-making problems with simplified neutrosophic information. The prominent characteristics of the GOWSNCS measure are that it not only is a generalization of the cosine similarity measure but also considers the associated weights for attributes and decision makers in the aggregation of the cosine similarity measures of SNSs to alleviate the influence of unduly large or small similarities in the process of information aggregation. Finally, an illustrative example of investment alternatives is provided to demonstrate the application and effectiveness of the developed approach.

GOWAWA Aggregation Operator-based Global Molecular Characterizations: Weighting Atom/bond Contributions (LOVIs/LOEIs) According to their Influence in the Molecular Encoding.

A different perspective to compute global weighted definitions of molecular descriptors from the contributions of each atom (LOVIs) or covalent bond (LOEIs) within a molecule is presented, using the generalized ordered weighted averaging - weighted averaging (GOWAWA) aggregation operator. This operator is rather different from the other norm-, mean- and statistic-based operators used up to date for the descriptors calculation from LOVIs/LOEIs. GOWAWA unifies the generalized ordered weighted averaging (GOWA) and the weighted generalized mean (WGM) functions and, in addition, it uses a smoothing parameter to assign different importance values to both functions depending on the problem under study. With the GOWAWA operator, diversity of novel global aggregations of molecular descriptors can be determined, where the influence that each atom (or covalent bond) has on the molecular characterization is taken into account. Therefore, this approach is completely different from the ones reported in the literature, where the values of LOVIs/LOEIs are considered equally important. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS descriptors (http://tomocomd.com/qubils-midas) were used and, as a result, a module was built into the corresponding software to compute them, being thus the only software reported in the literature that can be employed to determine weighted descriptors. Moreover, several modeling studies were performed on eight chemical datasets, which demonstrated that, with the GOWAWA aggregation operator, weighted QuBiLS-MIDAS descriptors that contribute to develop models with greater predictive power can be computed, if compared to the models based on the non-weighted descriptors calculated from the other operators used up to date. A non-parametric statistical assessment confirmed that the GOWAWA-based predictions are significantly superior to the others obtained. Therefore, all in all, it can be concluded that, from the results achieved, the GOWAWA operator constitutes a prominent alternative to codify relevant chemical information of the molecules, ultimately useful in improving the modeling ability of several old and recent descriptors whose definition is based on the LOVIs/LOEIs calculation.

Generalized exponential multiple averaging operator and its application to group decision making

The existing information aggregation operators are always the extensions of the ordered weighted averaging (OWA) oper- ator on weighting form or data type. In this paper, the generalized ordered weighted exponential multiple averaging (GOWEMA) operator is developed based on a minimization problem with penalty function. It unifies the geometric mean and the generalized ordered weighted averaging (GOWA) operator with the generalized ordered weighted harmonic averaging (GOWHA) operator in the same formulation. Then the main properties and families of the new operator are investigated. Moreover, an orness measure of the GOWEMA operator and the generalized lest squares method (GLSM) are presented to determine the GOWEMA operator weights. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWEMA operator to multiple attribute group decision making.

GENERALIZED MOVING AVERAGES, DISTANCE MEASURES AND OWA OPERATORS

The concept of moving average is studied. We analyze several extensions by using generalized aggregation operators, obtaining the generalized moving average. The main advantage is that it provides a general framework that includes a wide range of specific cases including the geometric and the quadratic moving average. This analysis is extended by using the generalized ordered weighted averaging (GOWA) and the induced GOWA (IGOWA) operator. Thus, we get the generalized ordered weighted moving average (GOWMA) and the induced GOWMA (IGOWMA) operator. Some of their main properties are studied. We further extend this approach by using distance measures suggesting the concept of distance moving average and generalized distance moving average. We also consider the case with the OWA and the IOWA operator, obtaining the generalized ordered weighted moving averaging distance (GOWMAD) and the induced GOWMAD (IGOWMAD) operator. The paper ends with an application in multi-period decision making.

Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure

The aim of this paper is to introduce the intuitionistic fuzzy ordered weighted cosine similarity (IFOWCS) measure by using the cosine similarity measure of intuitionistic fuzzy sets and the generalized ordered weighted averaging (GOWA) operator. Some desirable properties and different families of the IFOWCS measure are investigated. The prominent characteristics of the IFOWCS measure are that not only it is a generalization of some widely used similarity measure, but also it can deal with the correlation of different decision matrices or multi-dimensional arrays for intuitionistic fuzzy values. We further generalize the IFOWCS measure and obtain the intuitionistic fuzzy ordered weighted similarity (IFOWS) measure. In the end, the IFOWS measure with existing similarity measures are compared with the IFOWCS measure by an illustrative example.

The GOWA operator based approach to multiattribute decision making using intuitionistic fuzzy sets

The aim of this paper is to develop a methodology for solving multiattribute decision making (MADM) problems in which weights of attributes and ratings of alternatives on qualitative and quantitative attributes are expressed with intuitionistic fuzzy sets (IFSs). In this methodology, relative membership/satisfaction and non-membership/non-satisfaction degrees are formulated to construct IFSs for numerical values of alternatives on quantitative attributes. Alternatives on qualitative attributes are evaluated using linguistic variables and semantics which are parameterized by IFSs. Hereby, weights and ratings of alternatives on both qualitative attributes and quantitative attributes may be expressed with IFSs in a unified way. The generalized ordered weighted averaging (GOWA) operator is further extended to the situations in which the argument values are IFSs and thus a methodology is developed to solve MADM problems using IFSs. Validity and applicability of the proposed methodology in this paper are illustrated with a real numerical example.

GROUP DECISION MAKING METHODOLOGY BASED ON THE ATANASSOV'S INTUITIONISTIC FUZZY SET GENERALIZED OWA OPERATOR

The aim of this paper is to develop a new methodology for solving group decision making problems in which preference comparisons between alternatives are expressed with Atanassov's intuitionistic fuzzy (IF) preference relations. In this methodology, the generalized ordered weighted averaging (GOWA) operator is extended to develop the Atanassov's IF set (IFS) generalized ordered weighted averaging (IFSGOWA) operator, which can aggregate vague or imprecise information expressed with the Atanassov's IFSs. The Atanassov's IFSGOWA operator based methodology is further developed to solve group decision making problems with Atanassov's IF preference relations. A real example of the agroecological region assessment problem is used to illustrate the implementation and applicability of the proposed methodology. It is also shown that the obtained decision results could be affected by the choice of the parameter lambda and the nature of the weights.

Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets

The intuitionistic fuzzy (IF) set characterized by two functions was a generalization of the fuzzy set. In this paper, we investigate multiattribute decision making (MADM) problems with ratings of alternatives being expressed using IF sets and attribute weights given as real numbers. Firstly, the generalized ordered weighted averaging (GOWA) operators introduced by Yager [Yager, R. (2004). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 3, 93–107] are extended to aggregate IF sets. Secondly, MADM problems with IF sets are formulated through transforming the ratings of alternatives on both qualitative and quantitative attributes into IF sets in a unified way. The method and procedure based on the extended GOWA operators are developed to solve the MADM problems with IF sets. Finally, the effectiveness and practicability of the proposed method are illustrated with a numerical example.

Generalized aggregation operators for intuitionistic fuzzy sets

The generalized ordered weighted averaging (GOWA) operators are a new class of operators, which were introduced by Yager (Fuzzy Optim Decision Making 2004;3:93–107). However, it seems that there is no investigation on these aggregation operators to deal with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. In this paper, we first develop some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval-valued intuitionistic fuzzy weighted averaging operator, generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator, generalized interval-valued intuitionistic fuzzy hybrid average operator, which extend the GOWA operators to accommodate the environment in which the given arguments are both intuitionistic fuzzy sets that are characterized by a membership function and a nonmembership function, and interval-valued intuitionistic fuzzy sets, whose fundamental characteristic is that the values of its membership function and nonmembership function are intervals rather than exact numbers, and study their properties. Then, we apply them to multiple attribute decision making with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. © 2009 Wiley Periodicals, Inc.

Learning Weights in the Generalized OWA Operators

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods for functional defined GOWA and generalized Choquet integral based aggregation operators.

Generalized OWA Aggregation Operators

We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator.