Linguistic harmonic mean operators and their applications to group decision making

Abstract

Harmonic mean is the reciprocal of arithmetic mean of the reciprocal, which is a conservative average to be used to provide for aggregation lying between max and min operators. In this paper, we develop some new aggregation operators such as linguistic harmonic mean (LHM) operator, linguistic weighted harmonic mean (LWHM) operator, linguistic ordered weighted harmonic mean operator, and linguistic hybrid harmonic mean (LHHM) operator, which can be utilized to aggregate preference information taking the form of linguistic variables and then study some desirable properties of the operators. Based on the LHM and the LHHM operators, we propose a practical method for group decision making with linguistic preference relations and also give an illustrative example. Furthermore, based on the LWHM and LHHM operators, we develop a multiple attribute decision making applied in the group decision making to improving advanced manufacturing technology selection process.