The Uncertain Generalized Probabilistic Weighted Average and its Application in the Theory of Expertons

Abstract

We introduce the uncertain generalized probabilistic weighted averaging (UGPWA) operator. It is an aggregation operator that unifies the probability and the weighted average in the same formulation considering the degree of importance that each concept has in the aggregation. Moreover, it is able to assess uncertain environments that can not be assessed with exact numbers but it is possible to use interval numbers. Thus, we can analyze imprecise information considering the minimum and the maximum result that may occur. We analyze the applicability of this new approach in a multiperson decision making problem by using the theory of expertons.

Expertons and uncertain averaging operators versus correlational approaches

“…In this sense, the use of Balanced Scorecard could not only assume the weaknesses related with its capacity to compare companies with each other (Richard et al, 2009), but also could be affected by the difficulty of what is evaluated at the individual level as a performance appraisal (Kang and Fredin, 2012). Another plausible explanation could be found in the methodology based on the correlational approach, which assumes that the data are unambiguous and clearly known (Merigó, 2011b).…”

“…The present study had as a purpose to go deeper in to the influence of CSR within the organization, particularly, on WLB and individual effectiveness using three methodological approaches: (a) the correlational approach, (b) expertons method (Kaufmann and Gil-Aluja, 1993), and (c) uncertain averaging operators (UA, UWA, UPA, and UPWA) (Merigó, 2011b).…”

“…This methodology has shown its suitability as an analysis tool in such different fields as quality assessment (Barreiro et al, 2007;Levrat et al, K y b e r n e t e s 3 weighted averaging distance (HAIOWAD) (Vizuete-Luciano et al, 2015), the uncertain linguistic hybrid geometric mean operator (Wei, 2009), or the uncertain induced Minkowski ordered weighted average distance (UIMOWAD) operator (Zeng, 2013). Merigó (2011b) proposed a new decision making approach based on an operator that is the result of the union between the uncertain weighted average (UWA) and the uncertain probabilistic aggregation (UPA) operators. This result considers not only the subjective part of the assessment of the individual but also the objective of the subject being treated, and it is called the uncertain probabilistic weighted averaging (UPWA) or the interval probabilistic weighted average (IPWA).…”

“…The purpose of this study is to explore the relationship between CSR, work-life balance (WLB) and effectiveness comparing (a) the correlational approach, (b) expertons method (Kaufmann and Gil-Aluja, 1993), and (c) uncertain averaging operators (UA, UWA, UPA, and UPWA) (Merigó, 2011b).…”

Uncertain Induced Heavy Aggregation Distance Operator and its Application to Decision Making

“…By using interval numbers, we can consider a wide range of possible results between the maximum and the minimum. Note that in the literature, there are many studies dealing with uncertain information represented in the form of interval numbers (Chen and Zhou 2011;Liu and Jin 2012;Merigó 2011;Merigó and Casanovas 2011d;Xu 2008;Yue 2011;Zeng et al 2013;Zhou and Chen 2013a;Zhou et al 2012).…”