Polynomial Conjoint Measurement - Polynomial Conjoint Measurement - Axioms

Axioms

Let, and be non-empty and disjoint sets. Let " " be a simple order. Krantz et al. (1971) argued the quadruple is a polynomial conjoint system if and only if the following axioms hold.

  • WEAK ORDER.
  • SINGLE CANCELLATION. The relation " " satisfies single cancellation upon A whenever if and only if holds for all and . Single cancellation upon P and U is similarly defined.
  • DOUBLE CANCELLATION. The relation " " upon satisfies double cancellation if and only if for all and, and therefore is true for all . The condition holds similarly upon and .
  • JOINT SINGLE CANCELLATION. The relation " " upon satisfies joint single cancellation such that if and only if is true for all and . Joint independence is similarly defined for and .
  • DUAL DISTRIBUTIVE CANCELLATION. Dual distributive cancellation holds upon if and only if

, and implies is true for all and .

  • SOLVABILITY. The relation " " upon is solvable if and only if for all and, there exists and such that .
  • ARCHIMEDEAN CONDITION.

Read more about this topic:  Polynomial Conjoint Measurement, Polynomial Conjoint Measurement

Other articles related to "axioms, axiom":

Brouwer–Hilbert Controversy - Deeper Philosophic Differences - A Philosophical Defeat in The Quest For "truth" in The Choice of Axioms
... And at least with respect to his choice of axioms the case can be made that indeed he does eschew the notion ... The fundamental issue is just how does one choose "the axioms"? Until Hilbert proposed his formalism, the axioms were chosen on an "intuitive" (experiential) basis ... The primitive form of the induction axiom is another – if a predicate P(n) is true for n = 0 and if for all natural numbers n it is true that P(n) => P(n+1 ...
Statistical Proof - Axioms
... There are two kinds of axioms, 1) conventions that are taken as true that should be avoided because they cannot be tested, and 2) hypotheses ... Proof in the theory of probability was built on four axioms developed in the late 17th century The probability of a hypotheses is a non-negative real number The ... The preceding axioms provide the statistical proof and basis for the laws of randomness, or objective chance from where modern statistical theory has advanced ...
Scale-space Axioms
... particular type of scale space representation is to establish a set of scale-space axioms, describing basic properties of the desired scale-space representation and often chosen so as to make the ... Once established, the axioms narrow the possible scale-space representations to a smaller class, typically with only a few free parameters ... A set of standard scale space axioms, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image ...
Tarski's High School Algebra Problem - Statement of The Problem
... Tarski considered the following eleven axioms about addition ('+'), multiplication ('·'), and exponentiation to be standard axioms taught in high school x + y = y + x (x + y) + z = x + (y + z) x · 1 ... These eleven axioms, sometimes called the high school identities, are related to the axioms of an exponential ring ... but that cannot be proved using only the axioms 1–11? ...
Median Algebra
... a median algebra is a set with a ternary operation satisfying a set of axioms which generalise the notion of median or majority function, as a Boolean function ... The axioms are The second and third axioms imply commutativity it is possible (but not easy) to show that in the presence of the other three, axiom (3) is redundant ... The fourth axiom implies associativity ...

Famous quotes containing the word axioms:

    The axioms of physics translate the laws of ethics. Thus, “the whole is greater than its part;” “reaction is equal to action;” “the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;” and many the like propositions, which have an ethical as well as physical sense. These propositions have a much more extensive and universal sense when applied to human life, than when confined to technical use.
    Ralph Waldo Emerson (1803–1882)

    “I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.”
    Henry Brooks Adams (1838–1918)