Weighted Averaging Aggregation Operator Research Articles

A novel multi-criteria group decision making algorithm for enhancing supply chain efficiency under high uncertainty during crisis based on q-rung orthopair fuzzy information

In recent years, q-rung orthopair fuzzy sets (q-ROFSs) have been becoming gradually more advantageous in handling information with high uncertainty. Several multi-criteria group decision-making (MCGDM) algorithms under q-ROFS information have been proposed in literature and used to solve various real-life problems. However, several shortcomings of some existing MCGDM algorithms under certain circumstances also emerged which limit their applicability. To overcome these challenges and deal with information under high uncertainty more accurately and reasonably, we propose a novel MCGDM algorithm under q-ROF information, i.e., (q-ROF-MCGDM), that retains the advantages of currently available methods, but extend its applicability by introducing a new q-rung orthopair fuzzy weighted averaging aggregation operator (q-ROFWAAO) along with a new entropy measure. The proposed q-ROF-MCGDM algorithm involves the steps: firstly, the input requirement in terms of alternatives, criteria and expert evaluations are required. Secondly, aggregating expert opinions using weights and normalizing decision matrices, and finally, calculating entropy weights and aggregating overall evaluations for final prioritization. Further, new operational laws have been developed and several necessary properties of the proposed q-ROFWAAO are also proved. Moreover, a sensitivity and comparative analysis has been carried out for validity and effectiveness of the proposed q-ROF-MCGDM algorithm. The proposed q-ROF-MCGDM algorithm has been implemented to enhance the efficiency of the United Arab Emirates (UAE) food industry under high uncertainty during the recent crisis. Finally, an evaluation of identifying and prioritizing the most severe food SC disruptions and appropriate mitigation strategies under crisis is provided to demonstrate applicability of the proposed q-ROF-MCGDM algorithm, and the obtained real case results confirm its usefulness. Findings of the study offer valuable insights to both food industry researchers and managers in developing effective recovery strategies, mitigating risks, and improving overall efficiency to ensure the survival of food businesses during the crisis.

Lifetime Extension of Wireless Sensor Networks by Perceptive Selection of Cluster Head Using K-Means and Einstein Weighted Averaging Aggregation Operator under Uncertainty

Lifetime Extension of Wireless Sensor Networks by Perceptive Selection of Cluster Head Using K-Means and Einstein Weighted Averaging Aggregation Operator under Uncertainty

Cubic Pythagorean Hesitant Fuzzy Linear Spaces and Its Relevance in Multi Criteria Decision Making

Pythagorean fuzzy sets and interval valued Pythagorean fuzzy sets have an important role in decision making techniques. Pythagorean hesitant fuzzy sets are time and again used in dealing with uncertain and vague data. The motive of this paper is to introduce the notion cubic Pythagorean hesitant fuzzy linear spaces. We also present the notion of P(R)-intersection, P(R)-union of cubic Pythagorean hesitant fuzzy linear spaces with examples. Secondly, a series of operators like cubic Pythagorean hesitant fuzzy weighted averaging aggregation operators, cubic Pythagorean hesitant fuzzy order weighted averaging aggregation operators and cubic Pythagorean hesitant fuzzy hybrid order weighted averaging aggregation operators are developed. Then, these aggregation operators are further extended to cubic Pythagorean hesitant fuzzy prioritized weighted averaging aggregation operators by assigning priorities to the criteria. A real life MCDM problem has been illustrated and the effectiveness of the results are compared with those solved using cubic picture hesitant fuzzy prioritized weighted averaging aggregation operators.

Multi-Criteria Group Decision-Making Method Based on an Improved Single-Valued Neutrosophic Hamacher Weighted Average Operator and Grey Relational Analysis

This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.

Group decision making based on advanced interval-valued intuitionist fuzzy weighted averaging aggregation operator and score function of interval-valued intuitionist fuzzy values

This paper proposes a new group decision making (GDM) approach in the environments of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score function of IVIFVs, where the proposed score function of IVIFVs can overcome the drawbacks of the existing score function of IVIFVs. The properties of the proposed score function of IVIFVs are also presented. Then, we propose the advanced interval-valued intuitionist fuzzy averaging (AIVIFA) aggregation operator of IVIFVs. We also provide the proofs of the properties of the proposed AIVIFA aggregation operator. Then, we propose the advanced interval-valued intuitionist fuzzy weighted averaging (AIVIFWA) aggregation operator of IVIFVs. Then, we propose a new GDM approach based on the proposed AIVIFWA aggregation operator of IVIFVs and the proposed score function of IVIFVs. Finally, we apply the proposed GDM approach to deal with a real-world application of cloud service selection. The proposed GDM approach can overcome the drawbacks of the existing GDM approach, which is unable to distinguish the ranking orders of alternatives in some situations. The proposed GDM approach gives us a very useful way to deal with GDM problems in the environments of IVIFVs.

Decision making towards large-scale alternatives from multiple online platforms by a multivariate time-series-based method

With the increasing popularity of Internet-related techniques, decision-making problems with large-scale alternatives from multiple online platforms, such as consumer choice decisions and movie selections, have been emerging hot topics. How to make a selection from a set of alternatives in multiple online platforms is challenge for consumers. In this study, we introduce a multivariate time-series-based decision-making method to solve the problem with large-scale alternatives. Firstly, we set up a multivariate time series from multiple-platforms regarding each alternative. The weights of these platforms are determined based on the information entropy of time series and the number of received evaluations given by platform users. To calculate the information entropy regarding a large number of alternatives, we adopt a time series clustering method to classify alternatives into different clusters, and then calculate the information entropy of clusters and take it as the information entropy of all alternatives. Afterwards, the scores of alternatives are calculated based on the weighted averaging aggregation operator and the alternatives are ranked according to their scores. We demonstrate the effectiveness of the proposed method in guaranteeing the consistency between ranking results and users' consumption behaviors based on real ratings collected from three film-review websites. It is hoped that the proposed method would be helpful for users to intelligently make a selection from large-scale candidate products or services in multiple platforms.

Group decision making based on improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging aggregation operator of linguistic interval-valued Atanassov intuitionistic fuzzy numbers

In this paper, we develop an improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (ILIVAIFWA) aggregation operator (AO) of linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs). The ILIVAIFWA AO of LIVAIFNs presented in this paper can conquer the drawbacks of the linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (LIVAIFWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy ordered weighted averaging (LIVAIFOWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy weighted geometric (LIVAIFWG) AO and the linguistic interval-valued Atanassov intuitionistic fuzzy ordered weighted geometric (LIVAIFOWG) AO of LIVAIFNs. We also develop a novel group decision making (GDM) method on the basis of the proposed ILIVAIFWA AO of LIVAIFNs. The GDM method presented in this paper can oconquer the drawbacks of the existing GDM methods in the context of LIVAIFNs.

Group decision making based on q-rung orthopair fuzzy weighted averaging aggregation operator of q-rung orthopair fuzzy numbers

In this paper, we propose the q-rung orthopair fuzzy weighted averaging (q-ROFWA) aggregation operator (AO) of q-rung orthopair fuzzy numbers (q-ROFNs). The proposed q-ROFWA AO of q-ROFNs can overcome the drawbacks of the q-rung orthopair fuzzy interaction weighted Hamy mean (q-ROFIWHM) AO and the q-rung orthopair fuzzy power weighted Maclaurian symmetric mean (q-ROFPWMSM) AO of q-ROFNs. Moreover, we propose a new group decision making (GDM) method based on the proposed q-ROFWA AO of q-ROFNs. The proposed GDM method can overcome the drawbacks of the existing GDM methods. It provides us a very useful approach to deal with GDM problems in q-rung orthopair fuzzy environments.

Multiple attribute group decision making based on advanced linguistic intuitionistic fuzzy weighted averaging aggregation operator of linguistic intuitionistic fuzzy numbers

In this paper, we propose a new multiple attribute group decision making (MAGDM) method based on the proposed advanced linguistic intuitionistic fuzzy weighted averaging (ALIFWA) aggregation operator of linguistic intuitionistic fuzzy numbers (LIFNs). The proposed ALIFWA aggregation operator of LIFNs can overcome the shortcomings of the linguistic intuitionistic fuzzy weighted averaging (LIFWA) aggregation operator, the improved LIFWA (ILIFWA) aggregation operator, and the linguistic intuitionistic fuzzy Einstein weighted averaging (LIFEWA) aggregation operator of LIFNs, which have the shortcomings that the membership degrees and the non-membership degrees of their obtained aggregated LIFNs are indeterminated in some situations. Based on the proposed ALIFWA aggregation operator of LIFNs, we propose a new MAGDM method in linguistic intuitionistic fuzzy environments. The proposed MAGDM method can overcome the drawbacks of the existing MAGDM methods. It offers us a very useful way for handling MAGDM problems in linguistic intuitionistic fuzzy environments.

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

Intuitionistic linguistic group decision-making methods based on generalized compensative weighted averaging aggregation operators

As one of the key research topic in multi-criteria group decision making (MCGDM), aggregation operator has been drawn widespread concern from academics and practitioners. In order to reflect the characteristics of human decision, it is necessary to introduce an operator with compensation ability to close the gap between the theoretical results and experimental results. Based on generalized compensative weighted averaging operator, intuitionistic linguistic generalized compensative weighted averaging (ILGCWA) operator, intuitionistic linguistic generalized compensative ordered weighted averaging (ILGCOWA) operator, and power generalized compensative weighted averaging aggregation (ILPGCWA) operator are developed in this paper. These operators provide two additional parameters to represent decision makers’ attitude and decision makers’ preference for all kinds of alternatives in the aggregation process, respectively. Moreover, some special cases with regard to the generalized parameters p and $$\lambda $$ are investigated in detail in ILGCWA operator and ILGCOWA operator. Some examples are employed to illustrate the effectiveness of the proposed methods, which can be applied to solve MCGDM problem with intuitionistic linguistic information.

Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods

Pythagorean fuzzy set initially developed by Yager (2014) is a new tool to model imprecise and ambiguous information in multicriteria decision making problems. In this paper, we propose a novel closeness index for Pythagorean fuzzy number (PFN) and also introduce a closeness index-based ranking method for PFNs. Next, we extend the Pythagorean fuzzy set to present the concept of interval-valued Pythagorean fuzzy set (IVPFS) which is parallel to interval-valued intuitionistic fuzzy set. The elements in IVPFS are called interval-valued Pythagorean fuzzy numbers (IVPFNs). We further introduce the basic operations of IVPFNs and investigate their desirable properties. Meanwhile, we also explore the ranking method and the distance measure for IVPFNs. Afterwards, we develop a closeness index-based Pythagorean fuzzy QUALIFLEX method to address hierarchical multicriteria decision making problems within Pythagorean fuzzy environment based on PFNs and IVPFNs. This hierarchical decision problem includes the main-criteria layer and the sub-criteria layer in which the relationships among main-criteria are interdependent, the relationships among sub-criteria are independent and the weights of sub-criteria take the form of IVPFNs. Therefore, in the developed method we first define the concept of concordance/discordance index based on the closeness index-based ranking methods and compute the sub-weighted concordance/discordance indices by employing the weighted averaging aggregation operator based on the closeness indices of IVPFNs. In order to take main-criteria interactions into account, we further employ Choquet integral to calculate the main-weighted concordance/discordance indices. By investigating all possible permutations of alternatives with the level of concordance and discordance of the complete preference order, we finally obtain the optimal rankings of alternatives. The proposed method is implemented in a risk evaluation problem in order to demonstrate its applicability and superiority. The salient features of the proposed method, compared to the state-of-the-art QUALIFLEX-based methods, are: (1) it can take the interactive phenomena among criteria into account; (2) it can manage simultaneously the PFN and IVPFN decision data; (3) it can deal effectively with the hierarchal structure of criteria. The proposed method provides us with a useful way for hierarchical multicriteria decision making problems within Pythagorean fuzzy contexts. In addition, we also extend the proposed method to manage heterogeneous information which includes five different types of information such as real numbers, interval numbers, fuzzy numbers, PFNs and hesitant fuzzy elements.

Generalized compensative weighted averaging aggregation operators

The compensative weighted averaging (CWA) operator is generalized to develop a class of powerful generalized compensative weighted averaging (GCWA) operators with a very fine range of compensatory effects. The conventional means are shown to be the special cases of the proposed GCWA operator. A few extensions are investigated by combining GCWA operator with ordered weighted averaging (OWA) and induced OWA (IOWA) operators. An exponential class of aggregation operators such as exponential CWA, exponential OWA and exponential IOWA operators are developed. The usefulness of GCWA operators is shown through several examples and a case-study.

Compensative weighted averaging aggregation operators

A class of compensative weighted averaging (CWA) aggregation operators, having a dedicated parameter to model compensation, is presented. The variants of CWA operator with ordered weighted averaging (OWA) operator are developed. The proposed operators are compared, both theoretically and empirically, with other operators in terms of their compensation abilities. Two approaches are proposed to learn the compensation parameter and the weight vector from the given data. The proposed learning approaches are applied in four case-studies, involving real experimental data. The usefulness of CWA operators in strategic multi-criteria decision making and supplier selection is also highlighted.

LINEAR DECAYING WEIGHTS FOR TIME SERIES SMOOTHING: AN ANALYSIS

In this paper, we investigate the use of weighted averaging aggregation operators as techniques for time series smoothing. We analyze the moving average, exponential smoothing methods, and a new class of smoothing operators based on linearly decaying weights from the perspective of ordered weights averaging to estimate a constant model. We examine two important features associated with the smoothing processes: the average age of the data and the expected variance, both defined in terms of the associated weights. We show that there exists a fundamental conflict between keeping the variance small while using the freshest data. We illustrate the flexibility of the smoothing methods with real datasets; that is, we evaluate the aggregation operators with respect to their minimal attainable variance versus average age. We also examine the efficiency of the smoothed models in time series smoothing, considering real datasets. Good smoothing generally depends upon the underlying method's ability to select appropriate weights to satisfy the criteria of both small variance and recent data.