# MVNn

AcronymDefinition
MVNnMedial Vestibular Nuclei Neurons
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Let A and B be two MVNNs. The comparision methods can be defined as follows:
Aggregation operators of MVNNs and their application to multi-criteria decision-making problems
In this section, applying the MVNSs operations, we present aggregation operators for MVNNs and propose a method for MCDM by utilizing the aggregation operators.
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a collection of MVNNs, and let
(1) (Idempotency): Let [A.sub.j](j = 1,2, ..., n) be a collection of MVNNs. If all [A.sub.j](j = 1,2, ..., n) are equal, i.e., [A.sub.j] = A, for all j [member of] {1, 2, ..., n}, then
(2) (Boundedness): If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a collection of MVNNs and
(3) (Monotonity): Let [A.sub.j] (j = 1,2, ..., n) a collection of MVNNs. If [A.sub.j] [subset or equal to] [A.sup.*.sub.j], for j [member of] {1, 2, ..., n}, then [SNNWA.sub.w]([A.sub.1], [A.sub.2], ..., [A.sub.n]) [subset or equal to] [SNNWA.sub.w]([A.sup.*.sub.1], [A.sup.*.sub.2], ..., [A.sup.*.sub.n]).
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a collection of MVNNs, W = {[w.sub.1], w, ..., [w.sub.n]) be the weight vector of [A.sub.j] (j = 1, 2, ..., n), with [w.sub.j] [greater than or equal to] 0 (j = 1,2, ..., n) and [n.summation over (j=1)] [w.sub.j] = 1.
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a collection of MVNNs, we have the following result: [MVNNOWG.sub.w] ([A.sub.1], [A.sub.2], ..., [A.sub.n])
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a collection of MVNNs, W = ([w.sub.1,], w, ..., [w.sub.n]) be the weight vector of [A.sub.j] (j = 1, 2, ..., n).
Utilize the MVNNWA operator or the MVNNWG operator or MVNNHOWA operator or the MVNNHOWG to aggregate MVNNs and we can get the individual value of the alternative [a.sub.i] (i = 1, 2, ..., j = 1, 2, ..., m).
The four possible alternatives are to be evaluated under the above three criteria by the form of MVNNs, as shown in the following simplified neutrosophic decision matrix D:
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