US3628904A — Computer programming

Claim 1

Independent Claim 254 words

A method of operating a general purpose digital computer to perform the measurement known as dimensional synthesis for expressing in terms of quantity, subjective multidimensional concepts known as product values, each defined by N characteristic FACTORS and consisting in: a. representing the objects, individuals or entities to which every product value which it is desired to express in terms of quantity is related, by the elements of a vector space of N dimensions and its reduced punctual space corresponding biunivocally to the N factors defining this value, b. assigning a standard of measurement to the vector space and establishing a hierarchical relationship between the said factors of definition, c. calculating the measurement of the product value on each element when its support is an element of the vector space by the norm of the said element and when its support is an element of the reduCed punctual space, by the distance from this element to a punctual optimum element representing the individual object or entity considered as ideals relatively to the product value concerned, d. calculating the measurement of the product value of any group of elements by the norm of the vector sum in the case of elements of the vector space and by the distance to the optimum point from an imaginary point, the moment of inertia of which would be the same as that of the group, in the case of elements of the reduced punctual space, e. finally classifying the elements on the basis of the measurement values thus calculated.

Claim 2

Independent Claim 254 words

A method of operating a general purpose digital computer to perform the measurement known as dimensional synthesis for expressing in terms of quantity, subjective multidimensional concepts known as product values, each defined by N characteristic FACTORS and consisting in: a. representing the objects, individuals or entities to which every product value which it is desired to express in terms of quantity is related, by the elements of a vector space of N dimensions and its reduced punctual space corresponding biunivocally to the N factors defining this value, b. assigning a standard of measurement to the vector space and establishing a hierarchical relationship between the said factors of definition, c. calculating the measurement of the product value on each element when its support is an element of the vector space by the norm of the said element and when its support is an element of the reduCed punctual space, by the distance from this element to a punctual optimum element representing the individual object or entity considered as ideals relatively to the product value concerned, d. calculating the measurement of the product value of any group of elements by the norm of the vector sum in the case of elements of the vector space and by the distance to the optimum point from an imaginary point, the moment of inertia of which would be the same as that of the group, in the case of elements of the reduced punctual space, e. finally classifying the elements on the basis of the measurement values thus calculated.

Claim 3

Dependent Claim 77 words

A method of measurement as claimed in claim 1, wherein in a first type of application, the measurement known as the imposed standard of measurement is obtained in the vector space and there defines a scalar product such as a parallelepiped constructed on the intervals of variation of the distribution of the factors of the rectangular parallelepiped, the length of the faces of which remain in the same proportion to each other as the homologous hierarchical coefficients.

Claim 4

Dependent Claim 78 words

A method of measurement as claimed in claim 1, wherein in a second type of application, the standard of measurement known as the free standard of measurement is obtained in the vector space and there defines a scalar product such that the parallelepiped constructed on the standard deviation values of the distribution of factors is a rectangular parallelepiped, the lengths of the faces of which remain in the same proportion to each other as the homologous hierarchical coefficients.

Claim 5

Independent Claim 288 words

A method of operating a general purpose digital computer to perform a measurement known as dimensional synthesis, for expressing in terms of quantity, certain subjective multidimensional concepts known as product values each being defined by N characteristic factors, comprising the steps of: a. representing the objects to which each product value desired to be expressed in terms of quantity is related, by the elements of an N-dimensional vector space and its reduced punctual space corresponding to the N factors defining said product value and reading numbers corresponding to these elements into a computer memory. b. assigning a standard of measurement to said vector space, establishing a hierarchical relationship between the said factors and entering numbers representing said relationship into said computer memory, c. using the numbers in said computer memory to calculate the measurement of said product value of each element, when it is an element of said vector space, by the norm of said element, and when it is an element of said reduced punctual space, by the distance from said element to a punctual optimum element representing the individual object considered as an ideal relative to the product value concerned and entering the result in said computer memory, d. using the numbers in said computer memory to calculate the measurement of the product value for any group of elements for the norm of the vector sum in the case of elements of said vector space and for the distance to the optimum point from an imaginary point, the moment of inertia of which would be the same as that of said group, in the case of elements of said reduced punctual space, and e. classifying the elements on the basis of the measurement values thus calculated.

Claim 6

Independent Claim 288 words

A method of operating a general purpose digital computer to perform a measurement known as dimensional synthesis, for expressing in terms of quantity, certain subjective multidimensional concepts known as product values each being defined by N characteristic factors, comprising the steps of: a. representing the objects to which each product value desired to be expressed in terms of quantity is related, by the elements of an N-dimensional vector space and its reduced punctual space corresponding to the N factors defining said product value and reading numbers corresponding to these elements into a computer memory. b. assigning a standard of measurement to said vector space, establishing a hierarchical relationship between the said factors and entering numbers representing said relationship into said computer memory, c. using the numbers in said computer memory to calculate the measurement of said product value of each element, when it is an element of said vector space, by the norm of said element, and when it is an element of said reduced punctual space, by the distance from said element to a punctual optimum element representing the individual object considered as an ideal relative to the product value concerned and entering the result in said computer memory, d. using the numbers in said computer memory to calculate the measurement of the product value for any group of elements for the norm of the vector sum in the case of elements of said vector space and for the distance to the optimum point from an imaginary point, the moment of inertia of which would be the same as that of said group, in the case of elements of said reduced punctual space, and e. classifying the elements on the basis of the measurement values thus calculated.

Claim 7

Dependent Claim 260 words

An information-processing system for dimensional synthesis, wherein a plurality of entities is defined by a plurality of criteria organized in a balanced tree, of which initially only the extreme criteria, called characteristic factors, are quantified from said plurality of entities, so that all other criteria of the tree, called product values are not qualified; and wherein each characteristic factor is defined by an interval of variation, and a hierarchical coefficient indicative of the relative importance of the factor in relation to the other factors, and wherein the entities are represented by the elements of an N-dimensional vectoral space, the exact positional relation of these in each dimension of the vectoral space being associated with a characteristic factor, and wherein this vectoral space is measured by a product value such that each unitary vector of the vectoral position is the quotient of the interval of variation divided by the hierarchical coefficient of the corresponding characteristic factor, comprising the steps of: a. quantifying the product value of each entity concerned by calculating from it, when its image is in a vector, the NORM of the former, and, when its image is a point, the DISTANCE from the original point to this point, b. calculating, for all of a plurality of entities, when their image is a vector, the norm of the vector sum, and, when their image is a point, the distance from an origin point to an imaginary point at which the moment of inertia is equal to that of the plurality of entities, and c. classifying the values so derived.

Claim 8

Dependent Claim 260 words

An information-processing system for dimensional synthesis, wherein a plurality of entities is defined by a plurality of criteria organized in a balanced tree, of which initially only the extreme criteria, called characteristic factors, are quantified from said plurality of entities, so that all other criteria of the tree, called product values are not qualified; and wherein each characteristic factor is defined by an interval of variation, and a hierarchical coefficient indicative of the relative importance of the factor in relation to the other factors, and wherein the entities are represented by the elements of an N-dimensional vectoral space, the exact positional relation of these in each dimension of the vectoral space being associated with a characteristic factor, and wherein this vectoral space is measured by a product value such that each unitary vector of the vectoral position is the quotient of the interval of variation divided by the hierarchical coefficient of the corresponding characteristic factor, comprising the steps of: a. quantifying the product value of each entity concerned by calculating from it, when its image is in a vector, the NORM of the former, and, when its image is a point, the DISTANCE from the original point to this point, b. calculating, for all of a plurality of entities, when their image is a vector, the norm of the vector sum, and, when their image is a point, the distance from an origin point to an imaginary point at which the moment of inertia is equal to that of the plurality of entities, and c. classifying the values so derived.

Claim 9

Dependent Claim 115 words

A general purpose digital computer system having stored in the memory thereof a group of program subroutines comprising, a first subroutine, FREMEASURE, for causing the system to calculate the expression of the FREE form of dimensional synthesis which defines the intrinsic measurement in the vectoral space of the problem, associated by a given product value, said system calculating for all the values of the index n: the significant deviation of factor fn, that is to say, in the case of deviation value sigma n of the distribution factor fn, the step Pn of factor fn, the term gn of the scalar product value, and the length of the pave-type diagonal, according to the following expressions:

Claim 10

Dependent Claim 115 words

A general purpose digital computer system having stored in the memory thereof a group of program subroutines comprising, a first subroutine, FREMEASURE, for causing the system to calculate the expression of the FREE form of dimensional synthesis which defines the intrinsic measurement in the vectoral space of the problem, associated by a given product value, said system calculating for all the values of the index n: the significant deviation of factor fn, that is to say, in the case of deviation value sigma n of the distribution factor fn, the step Pn of factor fn, the term gn of the scalar product value, and the length of the pave-type diagonal, according to the following expressions:

Claim 11

Independent Claim 273 words

A method of operating a general purpose digital computer system for treating input information comprising the steps of: a. defining a group of objects by the criteria, organized according to a balanced branching structure, of which initially only the elementary criteria are provided as input information while all the other related criteria (called ''''composed criteria'''') are not provided as input information, wherein each elementary criterion is defined by: a significant variation epsilon n defining a unit of information which is chosen equal to the interval of variation, and a hierarchical coefficient kn defining relative importance of each elementary criterion in relation to the other criteria; b. representiNg the objects by the vector elements of a vectorial space of N dimensions, each dimension of the vectorial space being associated with an elementary criterion, wherein the vectorial space is defined by a scale such that each single vector of the vectorial space is the quotient of the significant variation epsilon n divided by the hierarchical coefficient Kn of the elementary criterion; and c. determining the composed criteria by calculating the norm of the vector of each object whose image is a vector Z (with the components zn), by calculating for each object, whose image is a point X, (of coordinates xn), the distance from said point to an original point Omega (of coordinates wn), and by utilization of mathematical terms for the norm of a vector and for the distance between two points, in a space at N orthogonal dimensions, as follows: where, the parameters An and Bn receive the following values: An Kn2/ epsilon n2 Bn 1 in the case of a relative value.

Claim 12

Independent Claim 273 words

A method of operating a general purpose digital computer system for treating input information comprising the steps of: a. defining a group of objects by the criteria, organized according to a balanced branching structure, of which initially only the elementary criteria are provided as input information while all the other related criteria (called ''''composed criteria'''') are not provided as input information, wherein each elementary criterion is defined by: a significant variation epsilon n defining a unit of information which is chosen equal to the interval of variation, and a hierarchical coefficient kn defining relative importance of each elementary criterion in relation to the other criteria; b. representiNg the objects by the vector elements of a vectorial space of N dimensions, each dimension of the vectorial space being associated with an elementary criterion, wherein the vectorial space is defined by a scale such that each single vector of the vectorial space is the quotient of the significant variation epsilon n divided by the hierarchical coefficient Kn of the elementary criterion; and c. determining the composed criteria by calculating the norm of the vector of each object whose image is a vector Z (with the components zn), by calculating for each object, whose image is a point X, (of coordinates xn), the distance from said point to an original point Omega (of coordinates wn), and by utilization of mathematical terms for the norm of a vector and for the distance between two points, in a space at N orthogonal dimensions, as follows: where, the parameters An and Bn receive the following values: An Kn2/ epsilon n2 Bn 1 in the case of a relative value.

Claim 13

Dependent Claim 180 words

A method according to claim 7 further comprising the steps of: a. calculating the composed criteria by calculating, according to a pyramidal value procedure, the norm of the vector sum according to the procedure for the entire subgroup of objects whose images are the vectors; and b. calculating, for the entire subgroup of objects whose images are points, the distance Gamma from a point of origin to an imaginary point, of which the amount of inertia is equal to that of the subgroup, by utilization of the following term, from the norm of the vector, in a space of N orthogonal dimensions: norm Bn Sigma An(zns)2 whereby the parameters An and Bn receive the values such that the variable zns receives the value Zns Sigma ezne where e is the index of the individual vector objects, and, in which, the following term is used: where Ve is the value that each object possesses for the criterion to be measured, and Ue is the norm of the defined vector by the original point and the image point of the object considered.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1974-12-20	1975-06-21	1975-12-21	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1978-12-20	1979-06-21	1979-12-21	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	1982-12-20	1983-06-21	1983-12-21	$7700.00	Window Closed / Lapsed

Computer programming

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