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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 special functions 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. New Design OEM black mesh EVA men sneakers air sports shoes for men low price 2018 For Sale Outlet Ebay Low Shipping Fee For Sale Low Cost Cheap Price Hyper Online L2WfZjKq
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, Whensinger 2018 Summer Sandals Women Fashion Genuine Leather Shoes Retro Buckle Strap Design 591 Visa Payment Cheap Online The Cheapest Free Shipping Eastbay Cheap Best Sale Clearance Low Price Fee Shipping OfnlGnz
a precursor to Adaptive Conjoint Analysis in marketing research . [70] 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; [71] however, with respect to pairwise ranking all undominated pairs defined on two criteria “it is not efficient to try to obtain full information”. LANSHITINA 2018 summer style simple ladies slippers trend Great Deals Cheap Online Buy Cheap Marketable plbFRVs2L
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. APRUUK PEEP toes sexy summer wedding shoes bride HS305 Discount Online Cheap Online Limited Edition Cheap Price New Arrival Cheap Price Buy Online Cheap 8NH5gV

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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