LEADER 04396nam 22006375 450 001 9910735788803321 005 20240619105242.0 010 $a3-031-33837-5 024 7 $a10.1007/978-3-031-33837-3 035 $a(MiAaPQ)EBC30666746 035 $a(Au-PeEL)EBL30666746 035 $a(DE-He213)978-3-031-33837-3 035 $a(PPN)272250287 035 $a(CKB)27861153400041 035 $a(EXLCZ)9927861153400041 100 $a20230725d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNormalization of Multidimensional Data for Multi-Criteria Decision Making Problems $eInversion, Displacement, Asymmetry /$fby Irik Z. Mukhametzyanov 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (314 pages) 225 1 $aInternational Series in Operations Research & Management Science,$x2214-7934 ;$v348 311 08$aPrint version: Mukhametzyanov, Irik Z. Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems Cham : Springer International Publishing AG,c2023 9783031338366 320 $aIncludes bibliographical references. 327 $aIntroduction -- The MCDM Rank Model -- Normalization and rank model MCDM -- Linear Methods for Multivariate Normalization -- Inversion of normalized values. ReS-algorithm -- Rank Reversal in MCDM Models. Contribution of the normalization -- Coordination of scales of normalized values. IZ-method MS-transformation of Z-Score -- Nonlinear multivariate normalization methods -- Normalization for the case ?Nominal value the best? -- Comparative results of ranking of alternatives using different normalization methods. Computational experiment -- 12 Significant difference of the performance indicator of alternatives -- Conclusion. 330 $aThis book presents a systematic review of multidimensional normalization methods and addresses problems frequently encountered when using various methods and ways to eliminate them. The invariant properties of the linear normalization methods presented here can be used to eliminate simple problems and avoid obvious errors when choosing a normalization method. The book introduces valuable, novel techniques for the multistep normalization of multidimensional data. One of these methods involves inverting the normalized values of cost attributes into profit attributes based on the reverse sorting algorithm (ReS algorithm). Another approach presented is the IZ method, which addresses the issue of shift in normalized attribute values. Additionally, a new method for normalizing the decision matrix is proposed, called the MS method, which ensures the equalization of average values and variances of attributes. Featuring numerous illustrative examples throughout, the book helps readers to understand what difficulties can arise in multidimensional normalization, what to expect from such problems, and how to solve them. It is intended for academics and professionals in various areas of data science, computing in mathematics, and statistics, as well as decision-making and operations. 410 0$aInternational Series in Operations Research & Management Science,$x2214-7934 ;$v348 606 $aOperations research 606 $aManagement science 606 $aComputer science?Mathematics 606 $aOperations Research and Decision Theory 606 $aOperations Research, Management Science 606 $aMathematical Applications in Computer Science 606 $aPresa de decisions multicriteri$2thub 608 $aLlibres electrònics$2thub 615 0$aOperations research. 615 0$aManagement science. 615 0$aComputer science?Mathematics. 615 14$aOperations Research and Decision Theory. 615 24$aOperations Research, Management Science . 615 24$aMathematical Applications in Computer Science. 615 7$aPresa de decisions multicriteri 676 $a705 676 $a519.542 700 $aMukhametzyanov$b Irik Z.$01379165 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910735788803321 996 $aNormalization of Multidimensional Data for Multi-Criteria Decision Making Problems$93418605 997 $aUNINA