Abstract
We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution depending on the number of zero elements. According to the computerized experiment we perform, the lower bounds can affect the solution types, thereby affecting the optimal solution of the three-dimensional constrained OWA aggregation problem with lower bounded variables.
Highlights
An ordered weighted averaging (OWA) operator, proposed by Yager [1], is a general class of parametric aggregation operators that appears in many applications such as control, decision making, expert systems, fuzzy system, neural networks, regression analysis and risk analysis [2,3,4,5,6].A citation-based survey of the literature in all types of optimization problems associated to OWA operators can be found in [7]
To evaluate the optimal solution behaviors of the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present some numerical experiments
The optimal solution type is I for w1 = max wi and w1 > max wi, and types I, II, III and IV for w2 = max wi, w3 = max wi, i =1,2,3 i =2,3 i =1,2,3 i =1,2,3
Summary
An ordered weighted averaging (OWA) operator, proposed by Yager [1], is a general class of parametric aggregation operators that appears in many applications such as control, decision making, expert systems, fuzzy system, neural networks, regression analysis and risk analysis [2,3,4,5,6]. For the constrained OWA aggregation problem with a single constraint on the sum of all variables, Yager [8] presented the optimal solutions for the three-dimensional case. The constrained OWA aggregation problem with a single constraint on the sum of all variables is as follows: s.t.I T X ≤ 1. To reduce the multiple solutions of the MIP (4), we introduce the following constraints: Zi+1 ≤ Zi , i = 1, 2, .
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