Models to determine parameterized ordered weighted averaging operators using optimization criteria

  • Authors:

  • Xinwang Liu

  • Affiliations:

  • School of Economics and Management, Southeast University, Nanjing 210096, China and State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

This paper proposes a general optimization model for determining ordered weighted averaging (OWA) operators and three specific models for generating monotonic and symmetric OWA operators, as well as those with any function shape. In these models, entropy and variance concepts are generalized as general dispersion indices for use in the objective functions, while the ordinary orness level constraints are used in the constraint equations as a special case. We define an orness function for monotonic OWA operators, which measures the closeness of the aggregation value to the maximum value, and a medianness function for symmetric OWA operators, which measures the closeness of the aggregation value to the median value. We also extend the commonly used models for determining OWA operators under given orness values to determine monotonic OWA operators with given orness function values and symmetric OWA operators with given medianness function values. Analytical solutions and properties of these models are discussed. We also provide analytical solutions of the maximum entropy and minimum variance problems with given linear medianness values. By setting different forms of the objective function and constraints, the parameterized OWA operator family elements can achieve various distributions in any desired shape. Two examples are given to show the OWA operator elements distributed in quadratic and Gaussian distribution function shapes.