Variance measures with ordered weighted aggregation operators

Publication Type:
Journal Article
International Journal of Intelligent Systems, 2019, 34 (6), pp. 1184 - 1205
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© 2019 Wiley Periodicals, Inc. The variance is a statistical measure widely used in many real-life application areas. This article makes an extensive investigation on variance measure in the case when the uncertainty is not of a probabilistic nature. It generalizes the notion of variance as well as the theory of ordered weighted aggregation operators. First, we extend the idea of representative value/expected value of a decision maker and develop some new deviation measures based on ordered weighted geometric (OWG) average and ordered weighted harmonic average (OWHA) operators. These measures are developed with the consideration that decision maker can represent his/her attitudinal expected value by using any one of the ordered weighted aggregation (OWA) operators. Further, this study proposes some deviation measures by using the generalized-OWA (GOWA) and Quasi-OWA as an expected value of decision maker and discusses their particular cases. Second, a number of generalized deviation measures are introduced by taking the generalized arithmetic mean and quasi-arithmetic means for aggregation of the individual dispersion. This approach provides an ability to the user for considering the deviation under different realistic-scenario. These measures lead to many interesting particular and limiting cases and enrich the use of ordered weighted aggregation operators in the variance.
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