By Andreas Junghanns, Jonathan Schaeffer (auth.), Robert E. Mercer, Eric Neufeld (eds.)

ISBN-10: 3540645756

ISBN-13: 9783540645757

This e-book constitutes the refereed lawsuits of the twelfth Biennial convention of the Canadian Society for Computational experiences of Intelligence, AI'98, held in Vancouver, BC, Canada in June 1998.

The 28 revised complete papers provided including 10 prolonged abstracts have been conscientiously reviewed and chosen from a complete of greater than two times as many submissions. The e-book is split in topical sections on making plans, constraints, seek and databases; purposes; genetic algorithms; studying and traditional language; reasoning; uncertainty; and learning.

**Read or Download Advances in Artificial Intelligence: 12th Biennial Conference of the Canadian Society for Computational Studies of Intelligence, AI'98 Vancouver, BC, Canada, June 18–20, 1998 Proceedings PDF**

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**Extra resources for Advances in Artificial Intelligence: 12th Biennial Conference of the Canadian Society for Computational Studies of Intelligence, AI'98 Vancouver, BC, Canada, June 18–20, 1998 Proceedings**

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The midpoint (or mean) of a complex interval number [x ; x ] + i x ; x is de…ned to be m [x ; x ] + i x ; x = m ([x ; x ]) + im x ; x x +x x +x +i = 2 2 . Hence, the midpoint of a point complex interval number is its ordinary complex isomorphic copy, that is (8x ; x 2 R) (m ([x ; x ] + i [x ; x ]) = x + ix ) . We observe that for a complex interval number X +iX with X = [0; 0], the point operations for complex interval numbers are reduced to the corresponding point operations for real interval numbers.

2, we have [z; z] = [x; x] [x; x] = fz 2 Rj (9x 2 [x; x]) z = x2 g = fz 2 Rj (9 x 2 [0; 1]) z = ((x x) z, with respect ito the constraint variable h Optimizing 2 2 2 2 minfx ; x ; 0g; maxfx ; x ; 0g . x x, + x)2 g. we thus get [z; z] = In a manner analogous to the proofs of the above theorems, the following three important results are derivable. 4 (8X 2 c [R]) (X X = [0; 0]). 39 CHAPTER 4. 6 (8X; Y; Z 2 c X = [1; 1]). [R]) (Z (X + Y ) = Z X +Z Y ). Thus, unlike classical interval arithmetic, constraint interval arithmetic has an additive inverse, a multiplicative inverse and satis…es the distributive law.

Thus, the width of a point complex interval number is zero, that is (8x ; x 2 R) (w ([x ; x ] + i [x ; x ]) = 0 + i (0) = 0) . 30 CHAPTER 3. 11 (Complex Interval Radius). The radius of a complex interval number [x ; x ] + i x ; x is de…ned to be r [x ; x ] + i x ; x w [x ; x ] + i x ; x 2 x x (x x ) = +i 2 2 = . 12 (Complex Interval Midpoint). The midpoint (or mean) of a complex interval number [x ; x ] + i x ; x is de…ned to be m [x ; x ] + i x ; x = m ([x ; x ]) + im x ; x x +x x +x +i = 2 2 .

### Advances in Artificial Intelligence: 12th Biennial Conference of the Canadian Society for Computational Studies of Intelligence, AI'98 Vancouver, BC, Canada, June 18–20, 1998 Proceedings by Andreas Junghanns, Jonathan Schaeffer (auth.), Robert E. Mercer, Eric Neufeld (eds.)

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