A sufficient and necessary condition for an OWA bag mapping having the self-identity |
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Authors: | Zhongqiang Yang Xiaoe Zhou |
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Institution: | Department of Mathematics, Shaanxi Normal University, Xi'an, 710062, PR China |
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Abstract: | A mapping ? : n=1∞In → I is called a bag mapping having the self-identity if for every (x1,…,xn) ε i=1∞In we have (1) ?(x1,…,xn) = ?(xi1,…,xin) for any arrangement (i1,…,in) of {1,…,n}; monotonic; (3) ?(x1,…,xn, ?(x1,…,xn)) = ?(x1,…,xn). Let {ωi,n : I = 1,…,n;n = 1,2,…} be a family of non-negative real numbers satisfying Σi=1nωi,n = 1 for every n. Then one calls the mapping ? : i=1∞In → I defined as follows an OWA bag mapping: for every (x1,…,xn) ε i=1∞In, ?(x1,…,xn) = Σi=1nωi,nyi, where yi is the it largest element in the set {x1,…,xn}. In this paper, we give a sufficient and necessary condition for an OWA bag mapping having the self-identity. |
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Keywords: | Bag mapping Self-identity OWA |
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