Uncertain induced aggregation operators and its application in tourism management José M. Merigó a,⇑ , Anna M. Gil-Lafuente a , Onofre Martorell b a Department of Business Administration, University of Barcelona, Av. Diagonal 690, 08034 Barcelona, Spain b Department of Business Administration, University of Balearic Islands, Palma de Mallorca, Spain article info Keywords: Interval numbers Weighted average OWA operator Aggregation operators Tourism management Multi-person decision-making abstract We develop a new decision making approach for dealing with uncertain information and apply it in tour- ism management. We use a new aggregation operator that uses the uncertain weighted average (UWA) and the uncertain induced ordered weighted averaging (UIOWA) operator in the same formulation. We call it the uncertain induced ordered weighted averaging – weighted averaging (UIOWAWA) operator. We study some of the main advantages and properties of the new aggregation such as the uncertain arithmetic UIOWA (UA-UIOWA) and the uncertain arithmetic UWA (UAUWA). We study its applicability in a multi-person decision making problem concerning the selection of holiday trips. We see that depend- ing on the particular type of UIOWAWA operator used, the results may lead to different decisions. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The weighted average (WA) is one of the most common aggrega- tion operators found in the literature. It can be used in a wide range of problems including statistics, economics and engineering. An- other interesting aggregation operator is the ordered weighted averaging (OWA) operator (Yager, 1988). The OWA operator pro- vides a parameterized family of aggregation operators that range from the maximum to the minimum. For further reading on the OWA operator and some of its applications, refer to Ahn (2009), Beliakov, Pradera, and Calvo (2007), Chang and Wen (2010), Cheng, Wang, and Wu (2009), Kacprzyk and Zadrozny (2009), Liu, Cheng, Chen, and Chen (2010), Merigó (2010a, 2010b), Merigó, Casanovas, and Martínez (2010), Merigó and Gil-Lafuente (2008, 2010, 2011a), Wei (2010a), Xu (2009, 2010), Xu and Da (2003), Xu and Yager (2010), Yager (1993, 1998, 2009), and Yager and Kacprzyk (1997), Zhao, Xu, Ni, and Liu (2010), Zeng & Su (2011), Zhou and Chen (2010). An interesting generalization of the OWA operator is the induced OWA (IOWA) operator (Yager & Filev, 1999). Its main advantage is that it deals with complex reordering processes in the aggregation by using order inducing variables. Since its intro- duction it has been studied by a lot of authors. For example, Merigó and Gil-Lafuente (2009) developed a generalization by using gener- alized and quasi-arithmetic means. Chiclana, Herrera-Viedma, Herrera, and Alonso (2004) and Xu and Da (2003) introduced a geometric version and applied it in group decision making. Wu, Li, Li, and Duan (2009) presented a continuous geometric version. Merigó and Casanovas (2009) applied it in a decision making prob- lem with Dempster–Shafer belief structure. Chen and Chen (2003) and Merigó and Casanovas (2010) studied the use of fuzzy numbers in the IOWA operator. For further reading, see Merigó (2011), Merigó, Gil-Lafuente, and Gil-Aluja (2011a, 2011b), Tan and Chen (2010), Wei (2010b), Wei, Zhao, and Lin (2010) and Yager (2003). Usually, when using these approaches it is considered that the available information are exact numbers. However, this may not be the real situation found in the specific problem con- sidered. Sometimes, the available information is vague or impre- cise and it is not possible to analyze it with exact numbers. Therefore, it is necessary to use another approach that is able to assess the uncertainty such as the use of interval numbers. By using interval numbers we can consider a wide range of pos- sible results between the maximum and the minimum. Note that in the literature, there are a lot of studies dealing with uncertain information represented in the form of interval numbers (Merigó, López-Jurado, Gracia, & Casanovas, 2009; Merigó & Wei, 2011; Wei, 2009; Xu & Da, 2002; Xu & Da, 2003; Xu & Yager, 2010). Recently, some authors have tried to unify the WA and the OWA in the same formulation. It is worth noting the work developed by Torra (1997) with the introduction of the weighted OWA (WOWA) operator and the work of Xu and Da (2003) concerning the hybrid averaging (HA) operator. Both models arrived to a partial unifica- tion between the OWA and the WA because both concepts were in- cluded in the formulation as particular cases. However, as it has been studied by Merigó (2008), these models seem to be a partial unification but not a real one because they can unify them but they 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.07.085 ⇑ Corresponding author. Tel.: +34 93 402 19 62; fax: +34 93 403 98 82. E-mail addresses: jmerigo@ub.edu (J.M. Merigó), amgil@ub.edu (A.M. Gil- Lafuente), onofre.martorell@uib.es (O. Martorell). Expert Systems with Applications 39 (2012) 869–880 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa