# Group Verbal Decision Analysis

Alexey Petrovsky (Institute for Systems Analysis – Russian Academy of Sciences, Russia)
DOI: 10.4018/978-1-59904-843-7.ch048

## Abstract

Ordering and classification of objects by their properties are among the typical problems in multiple criteria decision aiding (MCDA). The difficulties of choice problems increase when the same object may exist in several copies with different attributes’ values, and values of different attributes may be repeated within the object description. For example, such situation arises when several experts estimate alternatives upon multiple criteria. In this case, individual expert assessments may be similar, diverse, or contradictory. Various techniques for classification of alternatives or their ranking have been developed. But most of the methods do not pay a serious consideration to contradictions and inconsistencies in decision makers’ (DM) preferences and a problem description. Group verbal decision analysis (GroupVDA) is a new methodological approach in the MCDA area, which enlarges verbal decision analysis (VDA) approach to a group decision. GroupVDA deals with choice problems where preferences of several decision makers may be discordant, and alternatives are described with manifold repeating quantitative and qualitative attributes. New GroupVDA methods are based on the theory of multisets or sets with repeating elements, and represent multi-attribute objects as points in multiset metric spaces.

## Key Terms in this Chapter

Aggregation and Ranking Alternatives nearby the Multi-Attribute Ideal Situations (ARAMIS): ARAMIS is the method for group ordering multi-attribute objects represented as multisets by their closeness to any “ideal” objects in a multiset metric space. The ranking of all objects is found without building many different expert arrangements by many criteria, and without an aggregation them into a common ranking. The object arrangement takes into account various inconsistent and contradictory expert estimates without forcing one to find a compromise among them.

Operations with Multisets: Union A?B, intersection AnB, arithmetic addition A+B, arithmetic subtraction A-B, symmetric difference A?B, complement =Z–A, multiplication by a scalar (reproduction) c•A, arithmetic multiplication ?•?, arithmetic power ??, direct product A×B, direct power (×A)n. In general, arithmetic addition, multiplication by ? scalar, arithmetic multiplication, and raising to an arithmetic power are not defined in the set theory.

Verbal Decision Analysis (VDA): VDA emphasizes ill-structured discrete choice problems, which are represented with quantitative and qualitative attributes. The most important features of VDA are as follows: (1) the problem description with a professional language, which is natural and habitual for a decision maker; (2) a usage of verbal (nominative, ordinal) data on all stages of the problem analysis and solution without transformation into a numerical form; (3) an examination of decision maker’s judgments consistency; (4) a logical and psychological validity of decision rules; and (5) an explanation of intermediate and final results.

Measure of Multiset m: Measure of multiset m is a real-valued non-negative function defined on the algebra of multisets L(Z).

Multiset Metric Space (A,d): Multiset metric space (A,d) is a collection A={A1,...,An} of multisets with any distance d between multisets.

Decision Maker (DM): The DM is a person who is responsible for solution of choice problem.

MASKA (Russian abbreviation for the name: Multi-Attribute Consistent Classification of Alternatives): MASKA is the method for group classifying multi-attribute objects, which are represented as multisets. The method allows us to construct some generalized decision rules for a selection of “good” and “bad” objects from a set of contenders that approximates many inconsistent and contradictory individual sorting rules of several actors with the demanded level of approximation rate.

Group Verbal Decision Analysis (GroupVDA): Group VDA is a new methodological approach in the MCDA area, which enlarges VDA approach to a group decision. GroupVDA deals with choice problems where preferences of several decision makers may be discordant, alternatives are described with manifold repeating quantitative and qualitative attributes, and may exist in several copies.

## Complete Chapter List

Search this Book:
Reset
Dedication
Contents by Volume
Contents by Keyword
Foreword
Jean-Charles Pomerol
Preface
Acknowledgment
Chapter 1
\$37.50
Chapter 2
Zita Zoltay Paprika
\$37.50
Chapter 3
John Wang, Chandana Chakraborty, Huanyu Ouyang
\$37.50
Chapter 4
Sven A. Carlsson
\$37.50
Chapter 5
Ricardo Colomo Palacios, Juan Miguel Gómez Berbís, Ángel García Crespo
\$37.50
Chapter 6
Maria Eugénia Captivo, João Clímaco, Sérgio Fernandes
\$37.50
Chapter 7
Amit V. Deokar, Omar F. El-Gayar
\$37.50
Chapter 8
Sergio F. Ochoa, José A. Pino
\$37.50
Chapter 9
Malcolm J. Beynon
\$37.50
Chapter 10
Thomas Madritsch, Michael May, Herwig Ostermann, Roland Staudinger
\$37.50
Chapter 11
Alexandre Gachet, Ralph Sprague
\$37.50
Chapter 12
Patrick Brézillon, Jean-Charles Pomerol
\$37.50
Chapter 13
Pascale Zaraté
\$37.50
Chapter 14
Dashboards for Management  (pages 116-123)
Werner Beuschel
\$37.50
Chapter 15
John Wang, James Yao, Qiyang Chen
\$37.50
\$37.50
Chapter 17
Patrick Humphreys
\$37.50
Chapter 18
A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
\$37.50
Chapter 19
A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
\$37.50
Chapter 20
Ivan Bruha
\$37.50
Chapter 21
Viviane Barbosa Diniz, Marcos R.S. Borges, José Orlando Gomes, José H. Canós
\$37.50
Chapter 22
\$37.50
Chapter 23
Hannu Kivijärvi, Markku Tuominen
\$37.50
\$37.50
Chapter 25
Udo Richard Averweg
\$37.50
Chapter 26
Patrick Humphreys
\$37.50
Chapter 27
Daniel J. Power
\$37.50
Chapter 28
James Yao, John Wang, Qiyang Chen, June Lu
\$37.50
Chapter 29
Dina Neiger, Leonid Churilov
\$37.50
Chapter 30
Zhen Chen, Heng Li, Qian Xu, Szu-Li Sun
\$37.50
Chapter 31
Omar F. El-Gayar, Amit V. Deokar
\$37.50
Chapter 32
DS/AHP  (pages 278-285)
Malcolm J. Beynon
\$37.50
Chapter 33
\$37.50
Chapter 34
Ran M. Bittmann, Roy M. Gelbard
\$37.50
Chapter 35
Norman Pendegraft, Mark Rounds
\$37.50
Chapter 36
\$37.50
Chapter 37
Gloria E. Phillips-Wren, Manuel Mora, Guisseppi Forgionne
\$37.50
Chapter 38
Giusseppi Forgionne, Stephen Russell
\$37.50
Chapter 39
Margaret W. Wood, David C. Rine
\$37.50
Chapter 40
David Sammon
\$37.50
Chapter 41
Simon Woodworth, Joe Cunningham
\$37.50
Chapter 42
G. Kouamou, C. Pettang
\$37.50
Chapter 43
Fátima C.C. Dargam
\$37.50
Chapter 44
Fuzzy Decision Trees  (pages 382-390)
Malcolm J. Beynon
\$37.50
Chapter 45
P. Serra, R. A. Ribeiro, R. Marques Pereira, R. Steel, M. Niezette, A. Donati
\$37.50
Chapter 46
Games of Strategy  (pages 402-409)
Geraldine Ryan, Seamus Coffey
\$37.50
Chapter 47
John Wang, Dajin Wang, Aihua Li
\$37.50
Chapter 48
Alexey Petrovsky
\$37.50
Chapter 49
Frédéric Adam, Jean-Charles Pomerol, Patrick Brézillon
\$37.50
Chapter 50
Marcelo Índio dos Reis, Marcos R.S. Borges, José Orlando Gomes
\$37.50
Chapter 51
Fergal Carton
\$37.50
Chapter 52
Manual Mora, Ovsei Gelman, Guisseppi Forgionne, Francisco Cervantes
\$37.50
Chapter 53
John McAvoy, Tom Butler
\$37.50
Chapter 54
Peter O’Donnell, Rob Meredith
\$37.50
Chapter 55
Cristina Casado Lumbreras, Ricardo Colomo Palacios, Juan Miguel Gómez Berbís
\$37.50
Chapter 56
Ramon Brena, Carlos Chesñevar
\$37.50
Chapter 57
Dina Neiger, Leonid Churilov
\$37.50
Chapter 58
Gloria E. Phillips-Wren
\$37.50
Chapter 59
Ilya Ashikhmin, Eugenia Furems, Alexey Petrovsky, Michael Sternin
\$37.50
Chapter 60
R.A. Ribeiro, I.L. Nunes
\$37.50
Chapter 61
Pandian Vasant, Hrishikesh S. Kale
\$37.50
Chapter 62
Peer-Olaf Siebers, Uwe Aickelin
\$37.50
Chapter 63
Knowledge Based DSS  (pages 565-575)
Michel R. Klein
\$37.50
Chapter 64
James D. Jones
\$37.50
Chapter 65
Camille Rosenthal-Sabroux, Michel Grundstein, Fernando Iafrate
\$37.50
Chapter 66
James D. Jones
\$37.50
Chapter 67
Stephan Scheuerer
\$37.50
Chapter 68
Osvaldo García de la Cerda, Renato Orellana Muermann
\$37.50
\$37.50
Chapter 70
\$37.50
Chapter 71
\$37.50
Chapter 72
Peer-Olaf Siebers, Uwe Aickelin, Helen Celia, Chris Clegg
\$37.50
Chapter 73
Csaba Csáki
\$37.50
Chapter 74
Brad Morantz, Thomas Whalen, G. Peter Zhang
\$37.50
Chapter 75
Chris Schlueter Langdon
\$37.50
Chapter 76
Manual Mora, Francisco Cervantes, Guisseppi Forgionne, Ovsei Gelman
\$37.50
Chapter 77
Tan Yigitcanlar, Jung Hoon Han, Sang Ho Lee
\$37.50
Chapter 78
Tan Yigitcanlar, Omur Saygin
\$37.50
Chapter 79
João Carlos Namorado Clímaco, João Carlos Soares de Mello, Lidia Angulo Meza
\$37.50
Chapter 80
Luis Antunes, Ana Respício, João Balsa, Helder Coelho
\$37.50
Chapter 81
Geraldine Ryan, Edward Shinnick
\$37.50
Chapter 82
N. Chugunov, G. Shepelyov, M. Sternin
\$37.50
Chapter 83
PROMETHEE  (pages 743-750)
Malcolm J. Beynon
\$37.50
Chapter 84
Malcolm J. Beynon
\$37.50
Chapter 85
Todd McElroy
\$37.50
Chapter 86
\$37.50
Chapter 87
Edward Shinnick, Geraldine Ryan
\$37.50
Chapter 88
Rough Set Theory  (pages 783-789)
Malcolm J. Beynon
\$37.50
Chapter 89
Dorrie DeLuca, Joseph S. Valacich
\$37.50
Chapter 90
Software Agents  (pages 798-806)
Stanislaw Stanek, Maciej Gawinecki, Malgorzata Pankowska, Shahram Rahimi
\$37.50
Chapter 91
\$37.50
\$37.50
Chapter 93
Hannu Kivijärvi, Markku Tuominen, Kalle Elfvengren, Kalle Piirainen, Samuli Kortelainen
\$37.50
Chapter 94
C.W. Holsapple
\$37.50
Chapter 95
Mattias Strand, Sven A. Carlsson
\$37.50
Chapter 96
Robert Fitzgerald, John Findlay
\$37.50
Chapter 97
Hanan Yaniv, Susan Crichton
\$37.50
Chapter 98
Hanan Yaniv
\$37.50
Chapter 99
Pat Finnegan, Jeremy Hayes
\$37.50
Chapter 100
Giusseppi Forgionne, Stephen Russell
\$37.50
\$37.50
Chapter 102
David Sammon
\$37.50
Chapter 103
David Sammon
\$37.50
Chapter 104
\$37.50
Chapter 105
\$37.50
Chapter 106
Giusseppi Forgionne, Stephen Russell
\$37.50
Chapter 107