Using fuzzy numbers and OWA operators in the weighted average and its application in decision making

Se presenta un nuevo método para tratar situaciones de incertidumbre en los que se utiliza el operador OWAWA (media ponderada – media ponderada ordenada). A este operador se le denomina operador OWAWA borroso (FOWAWA). Su principal ventaja se encuentra en la posibilidad de representar la información incierta del problema mediante el uso de números borrosos los cuales permiten una mejor representación de la información ya que consideran el mínimo y el máximo resultado posible y la posibilidad de ocurrencia de los valores internos. Se estudian diferentes propiedades y casos particulares de este nuevo modelo. También se analiza la aplicabilidad de este operador y se desarrolla un ejemplo numérico sobre toma de decisiones en la selección de políticas fiscalesWe present a new approach for dealing with an uncertain environment when using the ordered weighted averaging – weighted averaging (OWAWA) operator. We call it the fuzzy OWAWA (FOWAWA) operator. The main advantage of this new aggregation operator is that it is able to represent the uncertain information with fuzzy numbers. Thus, we are able to give more complete information because we can consider the maximum and the minimum of the problem and the internal information between these two results. We study different properties and different particular cases of this approach. We also analyze the applicability of the new model and we develop a numerical example in a decision making problem about selection of fiscal policies

An approach to multiple attribute decision making based on the induced Choquet integral with fuzzy number intuitionistic fuzzy information

In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Firstly, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: induced fuzzy number intuitionistic fuzzy choquet ordered averaging (IFNIFCOA) operator and induced fuzzy number intuitionistic fuzzy choquet ordered geometric (IFNIFCOG) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the IFNIFCOA and IFNIFCOG operators, such as commutativity, idempotency and monotonicity, and applied the IFNIFCOA and IFNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method

Decision making with Dempster-Shafer belief structure and the OWAWA operator

[EN] A new decision making model that uses the weighted average and the ordered weighted averaging (OWA) operator in the Dempster-Shafer belief structure is presented. Thus, we are able to represent the decision making problem considering objective and subjective information and the attitudinal character of the decision maker. For doing so, we use the ordered weighted averaging ¿ weighted average (OWAWA) operator. It is an aggregation operator that unifies the weighted average and the OWA in the same formulation. This approach is generalized by using quasi-arithmetic means and group decision making techniques. An application of the new approach in a group decision making problem concerning political management of a country is also developed.We would like to thank the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Spanish Ministry of Education under project JC2009-00189 , the University of Barcelona (099311) and the European Commission (PIEFGA-2011-300062) is gratefully acknowledgedMerigó, JM.; Engemann, KJ.; Palacios Marqués, D. (2013). Decision making with Dempster-Shafer belief structure and the OWAWA operator. Technological and Economic Development of Economy. 19(sup 1):S100-S118. https://doi.org/10.3846/20294913.2013.869517SS100S11819sup 1Antuchevičienė, J., Zavadskas, E. K., & Zakarevičius, A. (2010). MULTIPLE CRITERIA CONSTRUCTION MANAGEMENT DECISIONS CONSIDERING RELATIONS BETWEEN CRITERIA / DAUGIATIKSLIAI STATYBOS VALDYMO SPRENDIMAI ATSIŽVELGIANT Į RODIKLIŲ TARPUSAVIO PRIKLAUSOMYBĘ. Technological and Economic Development of Economy, 16(1), 109-125. doi:10.3846/tede.2010.07Brauers, W. K. M., & Zavadskas, E. K. (2010). PROJECT MANAGEMENT BY MULTIMOORA AS AN INSTRUMENT FOR TRANSITION ECONOMIES / PROJEKTŲ VADYBA SU MULTIMOORA KAIP PRIEMONĖ PEREINAMOJO LAIKOTARPIO ŪKIAMS. 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Generalized Hamacher aggregation operators for intuitionistic uncertain linguistic sets: Multiple attribute group decision making methods

© 2019 by the authors. In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method

Aggregation operators in group decision making: Identifying citation classics via H-classics

To analyze the past, present and future of a particular research field, classic papers are usually studied because they identify the highly cited papers being a relevant reference point in that specific research area. As a result of the possible mapping between high quality research and high citation counts, highly cited papers are very interesting. The objective of this study is to use the H-classics method, which is based on the popular h-index, to identify and analyze the highly cited documents published about aggregation operators in the research area of group decision making. According to the H-classics method, this research area is represented by 87 citation classics, which have been published from 1988 to 2014. Authors, affiliations (universities/institutions and countries), journals, books and conferences, and the topics covered by these 87 highly cited papers are studied.The authors would like to thank FEDER financial support from the Projects TIN2013-40658-P and TIN2016- 75850-P

Q-rung orthopair normal fuzzy aggregation operators and their application in multi-attribute decision-making

© 2019 by the authors. Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems

Quasi-arithmetic means and OWA functions in interval-valued and Atanassov's intuitionistic fuzzy set theory

In this paper we propose an extension of the well-known OWA functions introduced by Yager to interval-valued (IVFS) and Atanassov’s intuitionistic (AIFS) fuzzy set theory. We first extend the arithmetic and the quasi-arithmetic mean using the arithmetic operators in IVFS and AIFS theory and investigate under which conditions these means are idempotent. Since on the unit interval the construction of the OWA function involves reordering the input values, we propose a way of transforming the input values in IVFS and AIFS theory to a new list of input values which are now ordered

Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

This work studies the aggregation operators on the set of all possible membership degrees of typical hesitant fuzzy sets, which we refer to as H, as well as the action of H-automorphisms which are defined over the set of all finite non-empty subsets of the unitary interval. In order to do so, the partial order ≤H, based on α-normalization, is introduced, leading to a comparison based on selecting the greatest membership degrees of the related fuzzy sets. Additionally, the idea of interval representation is extended to the context of typical hesitant aggregation functions named as the H-representation. As main contribution, we consider the class of finite hesitant triangular norms, studying their properties and analyzing the H-conjugate functions over such operators. © 2013 Elsevier Inc. All rights reserved.Peer Reviewe