Statistical classification

Proaftn

Proaftn is a fuzzy classification method that belongs to the class of supervised learning algorithms. The acronym Proaftn stands for: (PROcรฉdure d'Affectation Floue pour la problรฉmatique du Tri Nominal), which means in English: Fuzzy Assignment Procedure for Nominal Sorting. The method enables to determine the fuzzy indifference relations by generalizing the indices (concordance and discordance) used in the ELECTRE III method. To determine the fuzzy indifference relations, PROAFTN uses the general scheme of the discretization technique described in, that establishes a set of pre-classified cases called a training set. To resolve the classification problems, Proaftn proceeds by the following stages: Stage 1. Modeling of classes: In this stage, the prototypes of the classes are conceived using the two following steps: * Step 1. Structuring: The prototypes and their parameters (thresholds, weights, etc.) are established using the available knowledge given by the expert. * Step 2. Validation: We use one of the two following techniques in order to validate or adjust the parameters obtained in the first step through the assignment examples known as a training set. Direct technique: It consists in adjusting the parameters through the training set and with the expert intervention. Indirect technique: It consists in fitting the parameters without the expert intervention as used in machine learning approaches. In multicriteria classification problem, the indirect technique is known as preference disaggregation analysis. This technique requires less cognitive effort than the former technique; it uses an automatic method to determine the optimal parameters, which minimize the classification errors. Furthermore, several heuristics and metaheuristics were used to learn the multicriteria classification method Proaftn. Stage 2. Assignment: After conceiving the prototypes, Proaftn proceeds to assign the new objects to specific classes. (Wikipedia).

Video thumbnail

Learn the basics for simplifying an expression using the rules of exponents

๐Ÿ‘‰ Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

Video thumbnail

Simplify rational expression using the rules of exponents

๐Ÿ‘‰ Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

Video thumbnail

how to simplify an expression raised to a negative power

๐Ÿ‘‰ Learn how to simplify expressions using the power rule and the negative exponent rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the p

From playlist Simplify Using the Rules of Exponents

Video thumbnail

How to simplify a rational exponent raised to a negative power

๐Ÿ‘‰ Learn how to simplify rational powers using the power rule. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the power rule which states that when an expression with an exponent is raised to another exponent tha

From playlist Raise an Exponent to a Fraction

Video thumbnail

Applying the power rule of exponents to an expressions

๐Ÿ‘‰ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Using the reciprocal of a fraction to rewrite an expression with a positive power

๐Ÿ‘‰ Learn how to simplify expressions using the power rule and the negative exponent rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the p

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Simplify an expression using power to product and power to quotient rule

๐Ÿ‘‰ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Applying the power rule to simplify an expression with a rational power

๐Ÿ‘‰ Learn how to simplify rational powers using the power rule. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the power rule which states that when an expression with an exponent is raised to another exponent tha

From playlist Raise an Exponent to a Fraction

Video thumbnail

Learn how to simplify a monomial by applying quotient rule of exponents

๐Ÿ‘‰ Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

Video thumbnail

How to use the power rule of exponents

๐Ÿ‘‰ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac

From playlist Simplify Using the Rules of Exponents

Related pages

Sorting | Fuzzy classification | Multicriteria classification | Discretization of continuous features | Fuzzy logic