By George J. Klir
Take care of info and uncertainty thoroughly and successfully utilizing instruments rising from generalized info theory
Uncertainty and knowledge: Foundations of Generalized info concept comprises accomplished and updated insurance of effects that experience emerged from a examine application started by way of the writer within the early Nineteen Nineties lower than the identify "generalized info concept" (GIT). This ongoing learn application goals to strengthen a proper mathematical therapy of the interrelated recommendations of uncertainty and data in all their types. In GIT, as in classical info concept, uncertainty (predictive, retrodictive, diagnostic, prescriptive, and so forth) is seen as a manifestation of knowledge deficiency, whereas details is seen as something able to lowering the uncertainty. A extensive conceptual framework for GIT is bought by way of increasing the formalized language of classical set thought to incorporate extra expressive formalized languages in accordance with fuzzy units of varied varieties, and by means of increasing classical conception of additive measures to incorporate extra expressive non-additive measures of varied types.
This landmark publication examines every one of numerous theories for facing specific sorts of uncertainty on the following 4 levels:
* Mathematical formalization of the conceived form of uncertainty
* Calculus for manipulating this actual form of uncertainty
* Justifiable methods of measuring the quantity of uncertainty in any state of affairs formalizable within the theory
* Methodological elements of the theory
With huge use of examples and illustrations to elucidate advanced fabric and show sensible purposes, beneficiant ancient and bibliographical notes, end-of-chapter routines to check readers' newfound wisdom, glossaries, and an Instructor's guide, this is often a superb graduate-level textbook, in addition to an exceptional reference for researchers and practitioners who take care of a number of the difficulties regarding uncertainty and data. An Instructor's guide offering specific recommendations to the entire difficulties within the e-book is on the market from the Wiley editorial division.
Read Online or Download Uncertainty and information: foundations of generalized information theory PDF
Best information theory books
This specific quantity offers a brand new technique - the overall concept of knowledge - to medical figuring out of knowledge phenomena. in accordance with an intensive research of knowledge strategies in nature, know-how, and society, in addition to at the major instructions in details conception, this thought synthesizes present instructions right into a unified process.
Managing Economies, Trade and International Business
The present section of globalization and the elevated interconnectedness of economies via exchange have motivated the administration and progress premiums of economies and in addition the aggressive and managerial concerns for corporations. This publication specializes in 3 major matters – fiscal development and sustainable improvement; exchange, legislation and legislation; and aggressive and managerial matters in foreign company – from a multidisciplinary, transversal and eclectic viewpoint.
Efficient Secure Two-Party Protocols: Techniques and Constructions
The authors current a finished examine of effective protocols and methods for safe two-party computation – either normal buildings that may be used to soundly compute any performance, and protocols for particular difficulties of curiosity. The booklet specializes in thoughts for developing effective protocols and proving them safe.
Information Theory and Best Practices in the IT Industry
The significance of benchmarking within the provider zone is definitely famous because it is helping in non-stop development in items and paintings tactics. via benchmarking, businesses have strived to enforce most sensible practices with a view to stay aggressive within the product- marketplace during which they function. in spite of the fact that experiences on benchmarking, rather within the software program improvement area, have ignored utilizing a number of variables and for that reason haven't been as finished.
Extra resources for Uncertainty and information: foundations of generalized information theory
Sample text
Rotation of set A in ޒ2. m ( A1 ) = a1 cos q + a2 sin q m ( A2 ) = a1 sin q + a2 cos q . Then under the new coordinate system, 2 2 ’ [1 + m ( A )] + m ( A) - ’ m ( A ) it i =1 it i =1 = 1 + a1 cos q + a2 sin q + a1 sin q + a2 cos q + (a1 cos q + a2 sin q )(a1 sin q + a2 cos q ) + a1a2 ≥ 1 + a1 cos 2q + a2 sin 2q + a1 sin 2q + a2 cos 2q + (a1 cos 2q + a2 sin 2q )(a1 sin 2q + a2 cos 2q ) + a1a2 ≥ (1 + a1 )(1 + a2 ). Therefore, in the 2-dimensional case the measure is additive. The Three-Dimensional Case To prove the additivity in the 3-dimensional space, we only need to prove that for any rotation of set A Œ C, m ( A1 )m ( A2 ) + m ( A1 )m ( A3 ) + m ( A2 )m ( A3 ) ≥ a1a2 + a1a3 + a2 a2 .
This means that H ( X ¥ Y ) - H (Y ) = 0, H ( X ¥ Y ) - H ( X ) = 0, and, hence, H ( X ¥ Y ) = H ( X ) = H (Y ). This implies that |R| = |RX| = |RY|. These equalities can be satisfied only for |R| = 1, 2, . . , min{|X|,|Y|} Clearly, the largest value of information transmission is obtained for R = RX = RY = min{ X , Y }. Hence, TˆH ( X , Y ) = min{log 2 X ,log 2 Y }. 2. HARTLEY MEASURE OF UNCERTAINTY FOR FINITE SETS The normalized information transmission, NTH, is then defined by the formula NTH ( X , Y ) = TH ( X , Y ) TˆH ( X , Y ) .
St +n St ) = Hˆ (St ¥ St +1 ¥ . . ¥ St +n ) - H (Sn ) = log 24 n +1 - log 24 = 2 n, and consequently, I H (St +1 ¥ St + 2 ¥ . . ¥ St +n St ) = 2 n - H (St +1 ¥ St + 2 ¥ . . ¥ St +n St ). 2. 57. When only one state, si, is possible at time t, the number of possible sequences of states of length n in the face of total ignorance is equal to 4n, which means that Hˆ (S t +1 ¥ S t + 2 ¥ . . ¥ S n {si}) = Hˆ ({si} ¥ S t +1 ¥ S t + 2 ¥ . . ¥ S t + n ) - H ({si}) = Hˆ ({si} ¥ S t +1 ¥ . . ¥ S t + n ) = log 4 n = 2 n.