Some geometric aggregation operators based on log-normally distributed random variables

Abstract

The weighted geometric averaging (WGA) operator and the ordered weighted geometric (OWG) operator are two of most basic operators for aggregating information. But these two operators can only be used in situations where the given arguments are exact numerical values. In this paper, we first propose some new geometric aggregation operators, such as the log-normal distribution weighted geometric (LNDWG) operator, log-normal distribution ordered weighted geometric (LNDOWG) operator and log-normal distribution hybrid geometric (LNDHG) operator, which extend the WGA operator and the OWG operator to accommodate the stochastic uncertain environment in which the given arguments are log-normally distributed random variables, and establish various properties of these operators. Then, we apply the LNDWG operator and the LNDHG operator to develop an approach for solving multi-criteria group decision making (MCGDM) problems, in which the criterion values take the form of log-normally distributed random variables and the criterion weight information is known completely. Finally, an example is given to illustrate the feasibility and effectiveness of the developed method.

Stochastic multicriteria decision‐making approach based on SMAA‐ELECTRE with extended gray numbers

“…According to the criteria evaluation information of each alternative, MCDM problems can be classified into three types: fuzzy, gray, and stochastic. Among these, stochastic MCDM problems are highly common in real life, and have been extensively applied to various areas (Liu et al., ; Tan et al., ; Wang et al., , ; Cao et al., ). In stochastic MCDM problems, criteria values are random variables with known or unknown probability density functions, and criteria weights are usually uncertain.…”