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The ambiguity in the style of writing a function should not be confused with a multivalued function , which can (and should) be defined in a deterministic and unambiguous way. Several Online Cheap Online Clearance Store Online HEE GRAND Flats Retro Crosstied Sandals Rattan Gladiators Latest Collections For Sale Cheap Discount sIOlJtt0xj
still do not have established notations. Usually, the conversion to another notation requires to scale the argument or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions:

Ambiguous expressions often appear in physical and mathematical texts. It is common practice to omit multiplication signs in mathematical expressions. Also, it is common to give the same name to a variable and a function, for example, f = f ( x ) {\displaystyle f=f(x)} . Then, if one sees f = f ( y + 1 ) {\displaystyle f=f(y+1)} , there is no way to distinguish whether it means f = f ( x ) {\displaystyle f=f(x)} multiplied by ( y + 1 ) {\displaystyle (y+1)} , or function f {\displaystyle f} evaluated at argument equal to ( y + 1 ) {\displaystyle (y+1)} . In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning.

Therefore, for most practical purposes decision-makers are unlikely to need to rank pairs defined on more than two criteria, thereby reducing the burden on decision-makers. For example, approximately 95 explicit pairwise rankings are required for the value model referred to above with eight criteria and four categories each (and 2,047,516,416 undominated pairs to be ranked); 25 pairwise rankings for a model with five criteria and three categories each; and so on. OZZEG 2018 Shoes Platform Slip On Summer Sandals For Women Cheap Sale View uyZHgfaAeD
The real-world applications of PAPRIKA referred to earlier suggest that decision-makers are able to rank comfortably more than 50 and up to at least 100 pairs, and relatively quickly, and that this is sufficient for most applications.

The PAPRIKA method’s closest theoretical antecedent is Pairwise Trade-off Analysis, Active Mesh PU Laces Up 2017 Mens Sport Shoes Lowest Price Sale Online New Pictures Cheap Price New Lower Prices Free Shipping For Sale cFSaOc
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Like the PAPRIKA method, Pairwise Trade-off Analysis is based on the idea that undominated pairs that are explicitly ranked by the decision-maker can be used to implicitly rank other undominated pairs. Pairwise Trade-off Analysis was abandoned in the late 1970s, however, because it lacked a method for systematically identifying implicitly ranked pairs.

The ZAPROS method (from Russian for ‘Closed Procedure Near References Situations’) was also proposed; Official 2018 New Product Mesh Md Sole Breathable Sport Shoes Men Running Sneakers Low Price MQmkB8YPe
however, with respect to pairwise ranking all undominated pairs defined on two criteria “it is not efficient to try to obtain full information”. [72] As explained in the present article, the PAPRIKA method overcomes this efficiency problem.

The PAPRIKA method can be easily demonstrated via the simple example of determining the point values (weights) on the criteria for a value model with just three criteria – denoted by ‘a’, ‘b’ and ‘c’ – and two categories within each criterion – ‘1’ and ‘2’, where 2 is the higher ranked category. Collections Online Clearance With Credit Card 2018 Latest designs elegant women sleeveless sexy plaid dress fashion formal check dress for ladies Pictures Cheap Price 8H2r4KpW

This value model’s six point values (two for each criterion) can be represented by the variables a1, a2, b1, b2, c1, c2 (a2 > a1, b2 > b1, c2 > c1), and the eight possible alternatives (2 3 = 8) as ordered triples of the categories on the criteria (abc): 222, 221, 212, 122, 211, 121, 112, 111. These eight alternatives and their total score equations – derived by simply adding up the variables corresponding to the point values (which are as yet unknown: to be determined by the method being demonstrated here) – are listed in Table 2.

Undominated pairs are represented as ‘221 vs (versus) 212’ or, in terms of the total score equations, as ‘a2 + b2 + c1 vs a2 + b1 + c2’, etc. [Recall, as explained earlier, an ‘undominated pair’ is a pair of alternatives where one is characterized by a higher ranked category for at least one criterion and a lower ranked category for at least one other criterion than the other alternative, and hence a judgement is required for the alternatives to be pairwise ranked. Conversely, the alternatives in a ‘dominated pair’ (e.g. 121 vs 111 – corresponding to a1 + b2 + c1 vs a1 + b1 + c1) are inherently pairwise ranked due to one having a higher category for at least one criterion and none lower for the other criteria (and no matter what the point values are, given a2 > a1, b2 > b1 and c2 > c1, the pairwise ranking will always be the same).]

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