On the equiponderate equation \(x^a+x^b+x=x^c+x^d+1\) and a representation of weight quadruplets (Q1281344)
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scientific article; zbMATH DE number 1267366
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the equiponderate equation \(x^a+x^b+x=x^c+x^d+1\) and a representation of weight quadruplets |
scientific article; zbMATH DE number 1267366 |
Statements
On the equiponderate equation \(x^a+x^b+x=x^c+x^d+1\) and a representation of weight quadruplets (English)
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22 March 1999
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Summary: The equation \(x^a+ x^b+ x= x^c+ x^d+ 1\) considered in this paper is a particular equiponderate equation. The number and location of the roots (w.r.t. \(x=1\)) of this equation are determined in case \((a,b,c,d)\in ]0,1[^4\). Based on these results, it is shown that any weight quadruplet, a basic tool in fuzzy preference modelling, admits an interesing expression in terms of Frank t-norms with reciprocal parameters.
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weight quadruplet
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equiponderate equation
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fuzzy preference modelling
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Frank t-norms
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