m | number of decision alternatives |

p | number of objectives |

S | set of decision alternatives |

z | objective i |

${z}_{i}^{k}$ | performance measure of alternative k on objective i |

u | marginal utility function for objective i |

g(.) | decision maker’s utility or value function |

lt | lower threshold of objective i |

ut | upper threshold of objective i |

u | marginal utility function for increasing objectives with thresholds and for increasing side of target objective i |

u | marginal utility function for decreasing objectives with threshold and for decreasing side of target objective i |

I | ideal value for objective i |

N | nadir value for objective i |

A | aspiration value for objective i |

${{z}^{\prime}}_{i}^{k}$ | modified value of alternative k on objective i |

m | number of distinct values for objective i between N |

M | index set of alternatives |

w | weight of objective i in the simulated DM preference function |

B | set of out-ranking alternatives to alternative j |

c | maximum allowable normalized difference for objectives where alternative k has better scores than alternative j |

${\alpha}_{i}^{kj}$ | binary function equal 1 if modified value of alternative k is greater than or equal to j with respect to objective i |

${\beta}_{i}^{kj}$ | difference between normalized values of alternative j and k with respect to objective i |