By Professor George J. Klir, Professor Mark J. Wierman (auth.)
Information is helpful. It reduces our uncertainty in making judgements. wisdom concerning the final result of an doubtful occasion offers the possessor a bonus. It alterations the process lives, international locations, and background itself. info is the meals of Maxwell's demon. His energy comes from recognize ing which debris are sizzling and which debris are chilly. His life was once paradoxical to classical physics and merely the belief that details too used to be a resource of strength resulted in his taming. info has lately turn into a commodity, traded and bought like or ange juice or hog bellies. schools supply levels in details technology and knowledge administration. know-how of the pc age has supplied entry to info in overwhelming volume. info has develop into whatever worthy learning in its personal correct. the aim of this quantity is to introduce key advancements and leads to the world of generalized details concept, a concept that offers with uncertainty-based info inside of mathematical frameworks which are broader than classical set thought and likelihood idea. the quantity is geared up as follows.
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Extra info for Uncertainty-Based Information: Elements of Generalized Information Theory
Example text
The theorem also shows that the emerging single measure is a probability measure since it satisfies the condition of additivity. 1 A belief measure Bel on a finite power set P(X) is a probability measure if and only if its basic assignment m is given by m( {x}} = Bel( {x}) and m(A) = 0 for all subsets A of X that are not singletons. Proof. Assume that Bel is a probability measure. For the empty set 0, the theorem trivially holds, since m(0) = 0 by the definition of m. Let A I: 0 and assume A = {Xl, X2, ...
Not only is its interpretation unclear, but above all, it does not satisfy Eq. 89), which is an essential property of necessity measures. Dubois and Prade [1987a) suggested to resolve the problem by keeping the function N eCF, but replacing Eq. 87) with the equation NeCF(A) = h(F) - PosF(A). 118) Clearly Eq. 118) reduces to Eq. 87) when F is normal. Moreover, function NecF, defined by Eq. 118) satisfies both Eqs. 92) 38 2. UNCERTAINTY FORMALIZATIONS for every fuzzy subset F of X. Hence, this suggestion is more reasonable.
37) This formula may also be adopted for calculating the nonspecificity of F. 32) when F is subnormal. 38) does not involve any modification of F. 132) between subnormal fuzzy sets and possibility distributions, as discussed in Sec. 6. 32) should be adopted to measure the uncertainty of fuzzy sets. When a possibility distribution r is derived from a subnormal fuzzy set, then rl < 1 and L~I mi = rl. J i=2 . 40) i=2 respectively. Consider now two universal sets, X and Y, and a joint possibility distribution r defined on X x Y.