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001472158 003__ OCoLC
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001472158 019__ $$a1391435610$$a1394924661
001472158 020__ $$a9783031338373
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001472158 0247_ $$a10.1007/978-3-031-33837-3$$2doi
001472158 035__ $$aSP(OCoLC)1391441593
001472158 040__ $$aEBLCP$$beng$$cEBLCP$$dYDX$$dGW5XE$$dEBLCP$$dSFB
001472158 049__ $$aISEA
001472158 050_4 $$aT57.95
001472158 08204 $$a519.542$$223/eng/20230731
001472158 1001_ $$aMukhametzyanov, Irik Z.
001472158 24510 $$aNormalization of multidimensional data for multi-criteria decision making problems :$$binversion, displacement, asymmetry /$$cIrik Z. Mukhametzyanov.
001472158 260__ $$aCham :$$bSpringer,$$c2023.
001472158 300__ $$a1 online resource (314 p.).
001472158 336__ $$atext$$btxt$$2rdacontent
001472158 337__ $$acomputer$$bc$$2rdamedia
001472158 338__ $$aonline resource$$bcr$$2rdacarrier
001472158 4901_ $$aInternational series in operations research and management science series ;$$vvolume 348
001472158 504__ $$aIncludes bibliographical references.
001472158 5050_ $$aIntro -- Preface -- Contents -- About the Author -- List of Abbreviations -- List of Figures -- List of Tables -- Chapter 1: Introduction -- 1.1 The Problem of Multi-criteria Decision-Making -- 1.2 Multidimensional Normalization in the Context of Decision Problems -- References -- Chapter 2: The MCDM Rank Model -- 2.1 MCDM Rank Model -- 2.2 The Target Value of Attributes -- 2.3 Significance of Criteria: Multivariate Assessment -- 2.3.1 Subjective Weighting Methods: Pairwise Comparisons and AHP Process -- 2.3.2 Subjective Weighting Methods: Best-Worst Method
001472158 5058_ $$a2.3.3 Objective Weighting Methods: Entropy, CRITIC, SD -- Entropy Weighting Method (EWM) [26, 27, 37] -- CRiteria Importance Through Inter-criteria Correlation (CRITIC) [28] -- Standard Deviation (SD) -- 2.4 Aggregation of the Attributes: An Overview of Some Methods -- 2.4.1 Value Measurement Methods -- Simple Additive Weighting (SAW) or Weighted Sum Method (WSM) [1] -- Weighted Product Method (WPM) [39] -- Weighted Aggregated Sum Product Assessment (WASPAS) [39] -- Multi-Attributive Border Approximation Area Comparison (MABAC) [45] -- Complex Proportional Assessment (COPRAS) Method [46]
001472158 5058_ $$a2.4.2 Goal or Reference Level Models -- Distance Metric -- Reference Point (RP) Method [47] -- COmbinative Distance-based ASsessment (CODAS) -- Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [1] -- VIsekriterijumsko KOmpromisno Rangiranje (VIKOR) [40] -- Gray Relation Analysis (GRA) [49, 50] -- 2.4.3 Outranking Techniques -- Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) [41] -- Organisazion, RangEment ot SynTEze de donnecs relationnelles (ORESTE) [43, 44] -- 2.4.4 Rank Reversal Problem
001472158 5058_ $$a2.4.5 Distinguishability of the Performance Indicator of Alternatives -- 2.5 Design of the MCDM Model -- 2.6 Conclusions -- References -- Chapter 3: Normalization and MCDM Rank Model -- 3.1 General Principles for Normalizing Multidimensional Data -- 3.1.1 Preserving the Ordering Values of Attributes -- 3.1.2 Scale Invariance of Normalized Values of Attributes -- 3.1.3 Principle of Additive Significance of Attributes -- 3.1.4 Interpretation of Normalized Values of Attributes -- 3.2 Linear Multivariate Normalization Methods -- 3.2.1 How Is the Shift Factor Determined?
001472158 5058_ $$a3.2.2 How Is Scaling Determined? -- 3.2.3 Disadvantages of Data Standardization -- 3.3 Asymmetry in the Distribution of Features -- 3.3.1 Measures of Asymmetry -- 3.4 The Outlier Detection -- 3.5 Non-linear Normalization: General Principles -- 3.6 Target Inversion in Multivariate Normalization -- 3.7 Isotropy of Scales of Normalized Values -- 3.8 Impact of the Choice of Normalization Method on the Rating -- 3.9 Conclusions -- References -- Chapter 4: Linear Methods for Multivariate Normalization -- 4.1 Basic Linear Methods for Multivariate Normalization -- 4.2 Scaling Factor Ratios
001472158 506__ $$aAccess limited to authorized users.
001472158 520__ $$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.
001472158 588__ $$aDescription based upon print version of record.
001472158 650_0 $$aMultiple criteria decision making.
001472158 655_0 $$aElectronic books.
001472158 77608 $$iPrint version:$$aMukhametzyanov, Irik Z.$$tNormalization of Multidimensional Data for Multi-Criteria Decision Making Problems$$dCham : Springer International Publishing AG,c2023$$z9783031338366
001472158 830_0 $$aInternational series in operations research & management science ;$$v348.
001472158 852__ $$bebk
001472158 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-33837-3$$zOnline Access$$91397441.1
001472158 909CO $$ooai:library.usi.edu:1472158$$pGLOBAL_SET
001472158 980__ $$aBIB
001472158 980__ $$aEBOOK
001472158 982__ $$aEbook
001472158 983__ $$aOnline
001472158 994__ $$a92$$bISE