Advances in Multiple Objective and Goal Programming: by Rafael Caballero, Francisco Ruiz, Ralph E. Steuer (auth.),

By Rafael Caballero, Francisco Ruiz, Ralph E. Steuer (auth.), Prof. Rafael Caballero, Prof. Francisco Ruiz, Prof. Ralph Steuer (eds.)

In the box of a number of standards selection making, this quantity covers the newest advances in a number of goal and objective programming as provided on the second overseas convention on Multi-Objective Programming and target Programming, Torremolinos, Spain, could sixteen - 18, 1996. The booklet is an undispensable resource of the most recent examine effects, offered via the prime specialists of the sector.

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Extra info for Advances in Multiple Objective and Goal Programming: Proceedings of the Second International Conference on Multi-Objective Programming and Goal Programming, Torremolinos, Spain, May 16–18, 1996

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It has been observed that such a perfect learning gives a poor generalization ability in many cases. This phenomenon is known as the over learning. In order to avoid the over-learning, in this paper, we suggest methods which do not require the perfect classification for given data, but allow unclassified data. This idea can be performed by applying fuzzy mathematical programming techniques which produce "gray zones". The effectiveness of the modified methods can be proved by several applications to artificial classification problems.

Wagner, H. , 1969. PrinCiples of Operations Research, PrenticeHall, Englewood Cliffs, N1. 24 o~~ __ __ __ ~ ~ ~~ __ __ ~ ~~ __ __ ~ ~~ Jan , Feb. Mar. Apr, May June July Aug. Sept. Oct. Nov_ Dec, Month h~un: I, Smoothmg l'rohkm ~ Monthly Ikmand (iass 19X5) 105 90 75 7 8 9 10 11 12 Months hgun: 2, Smoothing I'mhleITL MinimuJll Surplus Solution ( ia,;,; 19X5) 25 105~~---r---r--~--~--~--r-~r-~---r--~ . l! Total monthly surplus \ '" :rl ~ 45 / ,/ " 1\\ .... - ........ l! ~ 45 30 - / V 15 01 / 2 / ,3 '" I I I Monthly production ,- ....

Another one is to apply the fuzzy programming by which we can get fuzzy discrimination curves with gray zones. In addition, using the suggested methods, the additional learning can be easily made. These features of the methods make the discrimination more realistic. The effectiveness of the methods are shown on the basis of some applications. Keywords. Pattern classification, linear goal programming, fuzzy goal programming 1 Introduction Machine learning for pattern classification is one of most important subjects in artificial intelligence.

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