Family Of Aggregation Operators Research Articles

Maclaurin symmetric mean aggregation operators based on novel Frank T-norm and T-conorm for intuitionistic fuzzy multiple attribute group decision-making

Multi-attribute group decision-making (MAGDM) is an interesting technique to find the most optimal alternative among comparative alternatives. Several authors put forward to MAGDM by introducing different fuzzy frameworks and also different tools to deal with fuzzy information. Intuitionistic fuzzy set (IFS) is the fuzzy framework that deals with the uncertainty in MAGDM. Due to their flexibility and generality, Frank t-norm (FTNM) and t-conorm (FTCNM) play an essential role in information fusion. Moreover, as the generalization of some mean operators, the Maclaurin symmetric mean (MSM) operator considers the relationship between multi-criteria arguments, especially in MAGDM. This article aims to develop some MSM aggregation operators (AOs) for the intuitionistic fuzzy set (IFS) based on FTNM and FTCNM and to apply newly developed AOs in the MAGDM. To utilize the MAGDM algorithm, first, we defined the MSM by using the FTNM and FTCNM in the environment of IFS. Then we proposed intuitionistic fuzzy (IF) Frank MSM (IFFMSM) and IF Frank weighted MSM (IFFWMSM) operators. Then, the fundamental properties of these AOs are stated and proved. Then, the strategy is given that accounts for the application of the newly developed family of AOs. Further, freshly defined operators are applied to the MAGDM problem with the help of an example where the risk factors of the construction industry are assessed. To cope with the significance, the proposed AOs are compared with some existing AOs. This study also addresses the variation of these AOs' behavior based on the interpretation of sensitive parameters.

An Approach for the Assessment of Multi-National Companies Using a Multi-Attribute Decision Making Process Based on Interval Valued Spherical Fuzzy Maclaurin Symmetric Mean Operators

Many fuzzy concepts have been researched and described with uncertain information. Collecting data under uncertain information is a difficult task, especially when there is a difference between the opinions of experts. To deal with such situations, different types of operators have been introduced. This paper aims to develop the Maclaurin symmetric mean (MSM) operator for the information in the shape of the interval-valued spherical fuzzy set (IVSFS). In this article, a family of aggregation operators (AOs) is proposed which consists of interval valued spherical fuzzy Maclaurin symmetric mean operator (IVSFMSM), interval valued spherical fuzzy weighted Maclaurin symmetric mean (IVSFWMSM), interval valued spherical fuzzy dual Maclaurin symmetric mean (IVSFDMSM), and interval valued spherical fuzzy dual weighted Maclaurin symmetric mean (IVSFDWMSM) operators. In this paper, we studied an elucidative example to discuss the evaluation of multi-national companies for the application of the proposed operator. Then the obtained results from the proposed operators are compared. The results obtained are graphed and tabulated for a better understanding.

Banzhaf-Choquet-Copula-based aggregation operators for managing fractional orthotriple fuzzy information

The goal of the present research work is to develop a new family of aggregation operators (AOs) under the fractional orthotriple fuzzy (FOF) information and apply them to MCDM problems. At the start, the Archimedean coupla and co-coupla are extended to handle FOF information, and some operational law for fractional orthotriple fuzzy numbers (FOFNs) based on extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) is presented. The fractional orthotriple fuzzy Banzhaf Choquet-Copula aggregation operator and fractional orthotriple fuzzy Banzhaf Choquet-Copula geometric operators are defined based on the proposed operational laws of FOFNs. In addition, the modified maximum deviation approach and the Banzhaf function model are created to objectively determine the fuzzy measure (FM) of criteria sets. Finally, based on the defined AOs, the appropriate decision-making procedures are developed. The proposed approaches can effectively overcome the FMs of criteria sets that are subjectively assigned by decision makers, as well as some decision-making problems in which the weights of the criteria are incomplete (completely) unknown, and there is a correlation between all criteria set.

A hybrid decision-making model under q-rung orthopair fuzzy Yager aggregation operators

Aggregation operators perform a significant role in many decision-making problems. The purpose of this paper is to analyze the aggregation operators under the q-rung orthopair fuzzy environment with Yager norm operations. The q-rung orthopair fuzzy set is an extension of intuitionistic fuzzy set and Pythagorean fuzzy set in which sum of qth power of membership and non-membership degrees is bounded by 1. By applying the Yager norm operations to q-rung orthopair fuzzy set, we developed six families of aggregation operators, namely q-rung orthopair fuzzy Yager weighted arithmetic operator, q-rung orthopair fuzzy Yager ordered weighted arithmetic operator, q-rung orthopair fuzzy Yager hybrid weighted arithmetic operator, q-rung orthopair fuzzy Yager weighted geometric operator, q-rung orthopair fuzzy Yager ordered weighted geometric operator and q-rung orthopair fuzzy Yager hybrid weighted geometric operator. To prove the validity and feasibility of proposed work, we discuss two multi-attribute decision-making problems. Moreover, we investigate the influence of some values of parameter on decision-making results. Finally, we give a comparison with existing operators.

A generalization of stability for families of aggregation operators

In this paper we extend the notion of stability of each aggregation function as presented in a previous paper of the authors, where an aggregation function was denominated Family of Aggregation Operators (FAO) in order to stress that aggregation operators within an aggregation function should be consistent. We will show that the previous definition presents certain problems when dealing with a FAO that is not idempotent or continuous. Meanwhile the previous definition was based on the study of fixed points, without taking into account the environment of each point, as many applications demand, the new approach we propose now is more flexible, and at the end allows a more appropriate definition of the consistency of a FAO. It will be shown that under certain conditions our new proposal is equivalent to the previous definition of strict stability, but the new definition covers families of aggregation operators that are not strictly stable, but intuitively stable, and vice versa. In short, we will see that our new proposal fits much better the intuition of stability of a FAO. This reformulation of stability is based upon the concept of penalty function as a measure of proximity between a value and an array of values.

Development of child's home environment indexes based on consistent families of aggregation operators with prioritized hierarchical information

The interventions aimed at the early childhood are of a main interest in educational policy, since it is in this period when it is possible to produce a major impact in the subsequent human development. The quality of children's social environment is the main influence to consider in achieving sound child development, affecting throughout school life. For this reason, the development of child's environment indexes appears in a natural way in the evaluation of all kind of educational policy research and social programs. However, crisp measures and indexes, based on usual linear techniques, do not ensure an adequate representation of social reality, since this last has a fuzzy nature and a nonlinear behavior. The development of indexes can be seen as an aggregation problem. In this paper, we extend the notions of consistency and strict stability of a family of aggregation operators (FAO), proposed in a previous work of the authors for the case of an aggregation process in which the data have no particular structure, to the case in which the information has a prioritized hierarchical structure. This extended notion of strict stability is then used to address the construction of indexes. Particularly, we apply this approach to develop a construction method of child's home environment indexes in which a stable family of prioritized aggregation operators is used in order to ensure robustness of the aggregation process when the information has a lineal structure. These indexes are built using fuzzy data that fit into a hierarchical structure by means of a stable family of prioritized aggregation operators based on the prioritized operator formulated by Yager, where the order relationship over fuzzy information was defined by experts on child development.

Strictly stable families of aggregation operators

In this paper we analyze the notion of family of aggregation operators (FAO), also refereed to as extended aggregation functions (EAF), i.e., a set of aggregation operators defined in the unit interval which aggregate several input values into a single output value. In particular, we address the key issue of the relationship that should hold between the operators in a family in order to understand that they properly define a consistent FAO. We focus on the idea of strict stability of a family of aggregation operators in order to propose an operative notion of consistency between operators of such a family. In this way, robustness of the aggregation process can be guaranteed. Some strict stability definitions for FAOs are proposed, leading to a classification of the main aggregation operators in terms of the properties they satisfy. Furthermore, we apply this approach to analyze the stability of some families of aggregation operators based on weights.

Fraud measurement using ordered weighted aggregation

The expansion of modern technologies and global communication is giving rise to a dramatic increase of frauds, resulting in the loss of billions of dollars world-wide each year. Fraud is an ’unpleasant and expensive reality that all banks, retailers and credit granting companies face. It is important to provide expertise to help financial institutions to resolve and recover assets and develop a solid business experience and base its policy on successful fraud prevention and recovery. The aim of the present paper is to investigate the use of ordered weighted averaging (OWA) operators and their extensions for fraud measurement in financial transactions. We consider the fraudulent behaviour in some components (criteria) and argue that the aggregation of the corresponding information can be effectively carried on introducing a parameterized family of aggregation operators (OWA,GOWA) that provide a fusion of pieces of information when the selection of the weights supports the modelling of some aggregation imperative depending on the rationality of the experts.

Semiautoduality in a restricted family of aggregation operators

In this paper we consider aggregation operators satisfying non-decreasingness and some specific boundary conditions. We then analyze some properties of such a family of aggregation operators, introducing the semiautoduality condition, which is weaker than the standard autoduality condition (i.e., the standard self De Morgan identity). Particular families of aggregation operators will appear depending on the context.