{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T06:05:56Z","timestamp":1759385156873},"reference-count":182,"publisher":"Elsevier","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1994]]},"DOI":"10.1016\/s0927-0507(05)80099-4","type":"book-chapter","created":{"date-parts":[[2005,4,18]],"date-time":"2005-04-18T19:58:53Z","timestamp":1113854333000},"page":"621-671","source":"Crossref","is-referenced-by-count":17,"title":["Chapter 18 Limitations on conclusions using scales of measurement"],"prefix":"10.1016","author":[{"given":"Fred S.","family":"Roberts","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0927-0507(05)80099-4_bib1","first-page":"226","article-title":"Efficient conversion of non-metric information into metric information","author":"Abelson","year":"1959"},{"key":"10.1016\/S0927-0507(05)80099-4_bib2","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1214\/aoms\/1177703869","article-title":"Efficient utilization of non-numerical information in quantitative analysis: General theory and the case of simple order","volume":"34","author":"Abelson","year":"1963","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0927-0507(05)80099-4_bib3","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1007\/BF02192678","article-title":"On weighted synthesis of judgements","volume":"27","author":"Acz\u00e9l","year":"1984","journal-title":"Aequationes Math."},{"key":"10.1016\/S0927-0507(05)80099-4_bib4","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/0022-247X(90)90193-J","article-title":"Determining merged relative scores","volume":"150","author":"Acz\u00e9l","year":"1990","journal-title":"J. Math. Anal. Applic."},{"key":"10.1016\/S0927-0507(05)80099-4_bib5","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0038-0121(86)90044-3","article-title":"On synthesis of judgements","volume":"20","author":"Acz\u00e9l","year":"1986","journal-title":"Socio-Econom. Planning Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0165-4896(89)90054-1","article-title":"On the possible merging functions","volume":"17","author":"Acz\u00e9l","year":"1989","journal-title":"Math. Social Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib7","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/0022-247X(86)90162-9","article-title":"On scientific laws without dimensional constants","volume":"119","author":"Acz\u00e9l","year":"1986","journal-title":"J. Math. Anal. Applic."},{"key":"10.1016\/S0927-0507(05)80099-4_bib8","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0022-2496(83)90028-7","article-title":"Procedures for synthesizing ratio scale judgements","volume":"27","author":"Acz\u00e9l","year":"1983","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib9","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF02289443","article-title":"A theory of appropriate statistics","volume":"30","author":"Adams","year":"1965","journal-title":"Psychometrika"},{"key":"10.1016\/S0927-0507(05)80099-4_bib10","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0022-2496(85)90019-7","article-title":"A note on real measurement structures of scale type (m, m + 1)","volume":"29","author":"Alper","year":"1985","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib11","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0022-2496(87)90012-5","article-title":"A classification of all order-preserving homeomorphism groups of the reals that satisfy finite uniqueness","volume":"31","author":"Alper","year":"1987","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib12","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0022-2496(78)90034-2","article-title":"Constructing blockmodels: How and why","volume":"17","author":"Arabie","year":"1978","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib13","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1097\/00006199-198101000-00019","article-title":"Parametric statistics and ordinal data: A pervasive misconception","volume":"30","author":"Armstrong","year":"1981","journal-title":"Nursing Res."},{"key":"10.1016\/S0927-0507(05)80099-4_bib14","first-page":"54","article-title":"Letter to the Editor","volume":"33","author":"Armstrong","year":"1984","journal-title":"Nursing Res."},{"key":"10.1016\/S0927-0507(05)80099-4_bib15","first-page":"453","article-title":"The determinateness of the utility function","volume":"49","author":"Armstrong","year":"1939","journal-title":"Econom. J."},{"key":"10.1016\/S0927-0507(05)80099-4_bib16","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/0196-8858(90)90004-I","article-title":"The distribution of clusters in random graphs","volume":"11","author":"Arratia","year":"1990","journal-title":"Adv. Appl. Math."},{"key":"10.1016\/S0927-0507(05)80099-4_bib17","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1080\/00022470.1970.10469453","article-title":"A combined pollution index for measurement of total air pollution","volume":"20","author":"Babcock","year":"1970","journal-title":"J. Air Pollution Control Assoc."},{"key":"10.1016\/S0927-0507(05)80099-4_bib18","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1080\/00022470.1973.10469761","article-title":"Cost effectiveness of emission control","volume":"23","author":"Babcock","year":"1973","journal-title":"J. Air Pollution Control Assoc."},{"key":"10.1016\/S0927-0507(05)80099-4_bib19","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1177\/001316446602600204","article-title":"Weak measurement vs. strong statistics: An empirical critique of S.S. Stevens' proscriptions on statistics","volume":"26","author":"Baker","year":"1966","journal-title":"Educational Psychological Measurement"},{"key":"10.1016\/S0927-0507(05)80099-4_bib20","series-title":"Applications of Combinatorics and Graph Theory to the Biological and Social Sciences","first-page":"39","article-title":"Social welfare and aggregation procedures: Combinatorial and algorithmic aspects","volume":"Vol. 17","author":"Barth\u00e9lemy","year":"1989"},{"key":"10.1016\/S0927-0507(05)80099-4_bib21","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/0165-4896(81)90041-X","article-title":"The median procedure in cluster analysis and social choice theory","volume":"1","author":"Barth\u00e9lemy","year":"1981","journal-title":"Math. Social Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib22","series-title":"Classification and Related Methods of Data Analysis","article-title":"The median procedure in data analysis: New results and open problems","author":"Barth\u00e9lemy","year":"1988"},{"key":"10.1016\/S0927-0507(05)80099-4_bib23","series-title":"Research Methods in Social Network Analysis","first-page":"89","article-title":"Inferring meaningful global network properties from individual actors' measurement scales","author":"Batchelder","year":"1989"},{"key":"10.1016\/S0927-0507(05)80099-4_bib24","article-title":"Combined pollutant indexes for the San Francisco Bay Area","author":"Bay Area Pollution Control District","year":"1968","journal-title":"Information Bulletin 10-68"},{"key":"10.1016\/S0927-0507(05)80099-4_bib25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0136001","article-title":"Consensus signed digraphs","volume":"36","author":"Bogart","year":"1979","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/S0927-0507(05)80099-4_bib26","article-title":"T-colorings of complete graphs","author":"Bonias","year":"1991"},{"key":"10.1016\/S0927-0507(05)80099-4_bib27","series-title":"Statistical Analysis for Managerial Decisions","author":"Boot","year":"1970"},{"key":"10.1016\/S0927-0507(05)80099-4_bib28","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/0022-2496(75)90028-0","article-title":"An algorithm for clustering relational data, with applications to social network analysis and comparison with multidimensional scaling","volume":"12","author":"Breiger","year":"1975","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib29","series-title":"the Annual Meeting of the Society of Automotive Engineers","article-title":"The assignment of responsibility for air pollution","author":"Caretto","year":"1972"},{"key":"10.1016\/S0927-0507(05)80099-4_bib30","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1287\/mnsc.23.8.789","article-title":"Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms","volume":"23","author":"Cornuejols","year":"1977","journal-title":"Management Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib31","first-page":"191","article-title":"T-colorings of graphs and the channel assignment problem","volume":"35","author":"Cozzens","year":"1982","journal-title":"Congressus Numerantium"},{"key":"10.1016\/S0927-0507(05)80099-4_bib32","first-page":"286","article-title":"Greedy algorithms for T-colorings of complete graphs and the meaningfulness of conclusions about them","volume":"16","author":"Cozzens","year":"1991","journal-title":"J. Comb. Inform. Syst. Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib33","unstructured":"Dalkey, N. (1969). Personal communication."},{"key":"10.1016\/S0927-0507(05)80099-4_bib34","unstructured":"Ebenegger, C. (1988). Personal communication."},{"key":"10.1016\/S0927-0507(05)80099-4_bib35","series-title":"Elements of Psychophysical Theory","author":"Falmagne","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib36","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/BF00485824","article-title":"Scales and meaningfulness of quantitative laws","volume":"55","author":"Falmagne","year":"1983","journal-title":"Synthese"},{"key":"10.1016\/S0927-0507(05)80099-4_bib37","series-title":"Elemente der Psychophysik","author":"Fechner","year":"1860"},{"key":"10.1016\/S0927-0507(05)80099-4_bib38","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0270-0255(83)90026-X","article-title":"Testing for homogeneity of two-dimensional surfaces","volume":"4","author":"Filliben","year":"1983","journal-title":"Math. Modelling"},{"key":"10.1016\/S0927-0507(05)80099-4_bib39","series-title":"Utility Theory for Decision Making","author":"Fishburn","year":"1970"},{"key":"10.1016\/S0927-0507(05)80099-4_bib40","series-title":"Interval Orders and Interval Graphs","author":"Fishburn","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib41","series-title":"Nonlinear Preference and Utility Theory","author":"Fishburn","year":"1988"},{"key":"10.1016\/S0927-0507(05)80099-4_bib42","series-title":"The Making of Index Numbers","author":"Fisher","year":"1923"},{"key":"10.1016\/S0927-0507(05)80099-4_bib43","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1145\/5666.5673","article-title":"How not to lie with statistics: The correct way to summarize benchmark results","volume":"29","author":"Fleming","year":"1986","journal-title":"Commun. ACM"},{"key":"10.1016\/S0927-0507(05)80099-4_bib44","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1037\/0033-2909.87.3.564","article-title":"Measurement scales and statistics: Resurgence of an old misconception","volume":"87","author":"Gaito","year":"1980","journal-title":"Psychol. Bull."},{"key":"10.1016\/S0927-0507(05)80099-4_bib45","article-title":"Performance measurement and analysis of certain search heuristics","author":"Gaschnig","year":"1979"},{"key":"10.1016\/S0927-0507(05)80099-4_bib46","series-title":"Nonparametric Statistical Inference","author":"Gibbons","year":"1971"},{"key":"10.1016\/S0927-0507(05)80099-4_bib47","series-title":"Graphs as Structural Models","author":"Godehart","year":"1990"},{"key":"10.1016\/S0927-0507(05)80099-4_bib48","series-title":"SIAM Symposium on Applications of Discrete Mathematics","article-title":"Discrete mathematics in government","author":"Goldman","year":"1981"},{"key":"10.1016\/S0927-0507(05)80099-4_bib49","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/MAHC.1985.10011","article-title":"On the history of the minimum spanning tree problem","volume":"7","author":"Graham","year":"1985","journal-title":"Ann. History Comput."},{"key":"10.1016\/S0927-0507(05)80099-4_bib50","series-title":"Computer-Assisted Analysis and Model Simplification","year":"1981"},{"key":"10.1016\/S0927-0507(05)80099-4_bib51","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02616245","article-title":"Efficient algorithms for divisive hierarchical clustering with the diameter criterion","volume":"8","author":"Gu\u00e9noche","year":"1991","journal-title":"J. Classification"},{"key":"10.1016\/S0927-0507(05)80099-4_bib52","first-page":"1497","article-title":"Frequency assignment: Theory and applications","volume":"68","author":"Hale","year":"1980"},{"key":"10.1016\/S0927-0507(05)80099-4_bib53","unstructured":"Hansen, P. (1991). Personal communication."},{"key":"10.1016\/S0927-0507(05)80099-4_bib54","series-title":"Office of Naval Research Workshop on Discrete Structured Classification","article-title":"Recent results in clustering","author":"Hansen","year":"1992"},{"key":"10.1016\/S0927-0507(05)80099-4_bib55","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF01908598","article-title":"Maximum sum of splits clustering","volume":"6","author":"Hansen","year":"1989","journal-title":"J. Classification"},{"key":"10.1016\/S0927-0507(05)80099-4_bib56","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/BF01896987","article-title":"Minimum sum of diameters clustering","volume":"4","author":"Hansen","year":"1987","journal-title":"J. Classification"},{"key":"10.1016\/S0927-0507(05)80099-4_bib57","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1111\/j.1749-6632.1989.tb22456.x","article-title":"On the theory of meaningfulness of ordinal comparisons in measurement II","volume":"555","author":"Harvey","year":"1989","journal-title":"Annals N.Y. Acad. Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib58","first-page":"17","article-title":"Invariant properties of masking phenomena in psychoacoustics and their theoretical consequences","volume":"Vol. 13","author":"Iverson","year":"1981"},{"key":"10.1016\/S0927-0507(05)80099-4_bib59","series-title":"Applications of Combinatorics and Graph Theory to the Biological and Social Sciences","first-page":"169","article-title":"The micro-macro connection: Exact structure and process","volume":"Vol. 17","author":"Johnsen","year":"1989"},{"key":"10.1016\/S0927-0507(05)80099-4_bib60","series-title":"Decisions with Multiple Objectives: Preferences and Value Tradeoffs","author":"Keeney","year":"1976"},{"key":"10.1016\/S0927-0507(05)80099-4_bib61","first-page":"575","article-title":"Mathematics without numbers","volume":"88","author":"Kemeny","year":"1959","journal-title":"Daedalus"},{"key":"10.1016\/S0927-0507(05)80099-4_bib62","series-title":"Mathematical Models in the Social Sciences","author":"Kemeny","year":"1962"},{"key":"10.1016\/S0927-0507(05)80099-4_bib63","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/0165-4896(90)90075-I","article-title":"On the possible scientific laws","volume":"20","author":"Kim","year":"1990","journal-title":"Math. Social Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib64","first-page":"54","article-title":"Letter to the Editor","volume":"33","author":"Knapp","year":"1984","journal-title":"Nursing Res."},{"key":"10.1016\/S0927-0507(05)80099-4_bib65","series-title":"Treating ordinal scales as interval scales: An annotated bibliography of selected references","author":"Knapp","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib66","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1097\/00006199-199003000-00019","article-title":"Treating ordinal scales as interval scales: An attempt to resolve the controversy","volume":"39","author":"Knapp","year":"1990","journal-title":"Nursing Res."},{"key":"10.1016\/S0927-0507(05)80099-4_bib67","series-title":"Machine Learning: A Guide to Current Research","article-title":"Coper: A methodology for learning invariant functional descriptions","author":"Kokar","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib68","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF00114869","article-title":"Determining arguments of invariant functional descriptions","volume":"1","author":"Kokar","year":"1986","journal-title":"Machine Learning"},{"key":"10.1016\/S0927-0507(05)80099-4_bib69","series-title":"Proc. of AAAI-86, Fifth National Conference on Artificial Intelligence","first-page":"455","article-title":"Discovering functional formulas through changing representation base","author":"Kokar","year":"1986"},{"key":"10.1016\/S0927-0507(05)80099-4_bib70","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0167-5060(08)70820-3","article-title":"Approximative algorithms for discrete optimization problems","volume":"4","author":"Korte","year":"1979","journal-title":"Ann. Discrete Math."},{"key":"10.1016\/S0927-0507(05)80099-4_bib71","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/0022-2496(72)90025-9","article-title":"A theory of magnitude estimation and cross-modality matching","volume":"9","author":"Krantz","year":"1972","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib72","volume":"Vol. 1","author":"Krantz","year":"1971"},{"key":"10.1016\/S0927-0507(05)80099-4_bib73","first-page":"48","article-title":"On the shortest spanning tree of a graph and the traveling salesman problem","volume":"7","author":"Kruskal","year":"1956"},{"key":"10.1016\/S0927-0507(05)80099-4_bib74","series-title":"The Effects of Noise on Man","author":"Kryter","year":"1970"},{"key":"10.1016\/S0927-0507(05)80099-4_bib75","doi-asserted-by":"crossref","first-page":"151","DOI":"10.2307\/2574595","article-title":"Some observations on measurement and statistics","volume":"46","author":"Labovitz","year":"1967","journal-title":"Social Forces"},{"key":"10.1016\/S0927-0507(05)80099-4_bib76","doi-asserted-by":"crossref","first-page":"515","DOI":"10.2307\/2092993","article-title":"The assignment of numbers to rank order categories","volume":"35","author":"Labovitz","year":"1970","journal-title":"Amer. Sociological Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib77","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1515\/jbnst-1871-0124","article-title":"Die Berechnung einer Mittleren Warrenpreissteigerung","volume":"16","author":"Laspeyres","year":"1871","journal-title":"Jahrb. National\u00f6konom. Statist."},{"key":"10.1016\/S0927-0507(05)80099-4_bib78","series-title":"The use of structural modeling for technology assessment","year":"1978"},{"key":"10.1016\/S0927-0507(05)80099-4_bib79","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0040-1625(79)90032-5","article-title":"The use of structural modeling for technology assessment","volume":"14","author":"Linstone","year":"1979","journal-title":"Tech. Forecasting Social Change"},{"key":"10.1016\/S0927-0507(05)80099-4_bib80","article-title":"Graph homomorphisms and the channel assignment problem","author":"Liu","year":"1991"},{"key":"10.1016\/S0927-0507(05)80099-4_bib81","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1037\/h0063675","article-title":"On the statistical treatment of football numbers","volume":"8","author":"Lord","year":"1953","journal-title":"Amer. Psychologist"},{"key":"10.1016\/S0927-0507(05)80099-4_bib82","doi-asserted-by":"crossref","first-page":"178","DOI":"10.2307\/1905751","article-title":"Semiorders and a theory of utility discrimination","volume":"24","author":"Luce","year":"1956","journal-title":"Econometrica"},{"key":"10.1016\/S0927-0507(05)80099-4_bib83","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1037\/h0043178","article-title":"On the possible psychophysical laws","volume":"66","author":"Luce","year":"1959","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib84","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1037\/h0040415","article-title":"Comments on Rozeboom's criticisms of \u2018On the possible psychophysical laws\u2019","volume":"69","author":"Luce","year":"1962","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib85","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/0022-2496(64)90004-5","article-title":"A generalization of a theorem of dimensional Analysis","volume":"1","author":"Luce","year":"1964","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib86","series-title":"Les Mod\u00e8les et la Formalisation du Compartment","first-page":"27","article-title":"Remarks on the theory of measurement and its relation to psychology","author":"Luce","year":"1967"},{"key":"10.1016\/S0927-0507(05)80099-4_bib87","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1086\/288776","article-title":"Dimensionally invariant numerical laws correspond to meaningful qualitative relations","volume":"45","author":"Luce","year":"1978","journal-title":"Philos. Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib88","unstructured":"Luce, R.D. (1985). Personal communication, August 20."},{"key":"10.1016\/S0927-0507(05)80099-4_bib89","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/0022-2496(86)90017-9","article-title":"Uniqueness and homogeneity of ordered relational structures","volume":"30","author":"Luce","year":"1986","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib90","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/BF00337695","article-title":"Measurement structures with Archimedean ordered translation groups","volume":"4","author":"Luce","year":"1987","journal-title":"Order"},{"key":"10.1016\/S0927-0507(05)80099-4_bib91","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1037\/0033-295X.97.1.66","article-title":"\u2018On the possible psychophysical laws\u2019 revisited: Remarks on cross-modal matching","volume":"97","author":"Luce","year":"1990","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib92","volume":"Vol. III","author":"Luce","year":"1990"},{"key":"10.1016\/S0927-0507(05)80099-4_bib93","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/0022-2496(83)90026-3","article-title":"Symmetry scale types, and generalizations of classical physical measurement","volume":"27","author":"Luce","year":"1983","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib94","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0263-2241(84)90022-8","article-title":"Classification of real measurement representations by scale type","volume":"2","author":"Luce","year":"1984","journal-title":"Measurement"},{"key":"10.1016\/S0927-0507(05)80099-4_bib95","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-2496(85)90018-5","article-title":"Classification of concatenation measurement structures according to scale type","volume":"29","author":"Luce","year":"1985","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib96","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1037\/0033-2909.99.2.166","article-title":"Measurement: The theory of numerical assignments","volume":"99","author":"Luce","year":"1986","journal-title":"Psychol. Bull."},{"key":"10.1016\/S0927-0507(05)80099-4_bib97","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1126\/science.236.4808.1527","article-title":"Measurement scales on the continuum","volume":"236","author":"Luce","year":"1987","journal-title":"Science"},{"key":"10.1016\/S0927-0507(05)80099-4_bib98","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/trsc.18.1.1","article-title":"Network design and transportation planning: Models and algorithms","volume":"18","author":"Magnanti","year":"1984","journal-title":"Transportation Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib99","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2307\/1165056","article-title":"Meaningless statistics","volume":"12","author":"Marcus-Roberts","year":"1987","journal-title":"J. Educ. Statist."},{"key":"10.1016\/S0927-0507(05)80099-4_bib100","article-title":"Clustering and multidimensional scaling in Russia (1960\u20131990)","author":"Mirkin","year":"1991"},{"key":"10.1016\/S0927-0507(05)80099-4_bib101","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1037\/0033-2909.100.3.398","article-title":"Measurement scales and statistics: A clash of paradigms","volume":"100","author":"Mitchell","year":"1986","journal-title":"Psychol. Bull."},{"key":"10.1016\/S0927-0507(05)80099-4_bib102","series-title":"An Introduction to the Logic of Psychological Measurement","author":"Mitchell","year":"1990"},{"key":"10.1016\/S0927-0507(05)80099-4_bib103","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1002\/mana.19510060303","article-title":"Bemerkungen zur Dimensionsanalysis","volume":"6","author":"Mohr","year":"1951","journal-title":"Math. Nachr."},{"key":"10.1016\/S0927-0507(05)80099-4_bib104","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/BF00485942","article-title":"On the general theory of meaningful representation","volume":"67","author":"Mundy","year":"1986","journal-title":"Synthese"},{"key":"10.1016\/S0927-0507(05)80099-4_bib105","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02342603","article-title":"A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness","volume":"13","author":"Narens","year":"1981","journal-title":"Theory Decision"},{"key":"10.1016\/S0927-0507(05)80099-4_bib106","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0022-2496(81)90045-6","article-title":"On the scales of measurement","volume":"24","author":"Narens","year":"1981","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib107","series-title":"Abstract Measurement Theory","author":"Narens","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib108","first-page":"61","article-title":"Meaningfulness and the Erlanger Program of Felix Klein","volume":"101","author":"Narens","year":"1988","journal-title":"Math. Inform. Sci. Humaines"},{"key":"10.1016\/S0927-0507(05)80099-4_bib109","series-title":"Structural Theories in Progress, II","first-page":"358","article-title":"A measure of relative balance for social structures","author":"Norman","year":"1972"},{"key":"10.1016\/S0927-0507(05)80099-4_bib110","doi-asserted-by":"crossref","first-page":"851","DOI":"10.2307\/2094532","article-title":"The use of Pearson's r with ordinal data","volume":"44","author":"O'Brien","year":"1979","journal-title":"Amer. Sociological Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib111","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/0022-2496(70)90046-5","article-title":"Further extensions of a theorem of dimensional analysis","volume":"7","author":"Osborne","year":"1970","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib112","series-title":"Combinatorial Optimization: Algorithms and Complexity","author":"Papadimitriou","year":"1982"},{"key":"10.1016\/S0927-0507(05)80099-4_bib113","article-title":"Homogeneity in complete and partial masking","author":"Pavel","year":"1980"},{"key":"10.1016\/S0927-0507(05)80099-4_bib114","series-title":"Theory of Measurement","author":"Pfanzagl","year":"1968"},{"key":"10.1016\/S0927-0507(05)80099-4_bib115","doi-asserted-by":"crossref","first-page":"43","DOI":"10.2307\/2344420","article-title":"Identification and measurement of consumer confidence: Methodology and some preliminary results","author":"Pickering","year":"1973","journal-title":"J. Roy. Statist. Soc. A"},{"key":"10.1016\/S0927-0507(05)80099-4_bib116","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1037\/h0041492","article-title":"Effect of spacing and range of stimuli on magnitude estimation judgments","volume":"66","author":"Pradhan","year":"1963","journal-title":"J. Exp. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib117","article-title":"Intersection assignments, T-coloring, and powers of Graphs","author":"Raychaudhuri","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib118","series-title":"Proof Techniques in Graph Theory","first-page":"139","article-title":"Indifference graphs","author":"Roberts","year":"1969"},{"key":"10.1016\/S0927-0507(05)80099-4_bib119","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1068\/a030395","article-title":"Signed digraphs and the growing demand for energy","volume":"3","author":"Roberts","year":"1971","journal-title":"Environment Planning"},{"key":"10.1016\/S0927-0507(05)80099-4_bib120","article-title":"Building an energy demand signed digraph I: Choosing the Nodes","author":"Roberts","year":"1972"},{"key":"10.1016\/S0927-0507(05)80099-4_bib121","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1068\/a050199","article-title":"Building and analyzing an energy demand signed digraph","volume":"5","author":"Roberts","year":"1973","journal-title":"Environment Planning"},{"key":"10.1016\/S0927-0507(05)80099-4_bib122","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1068\/a070703","article-title":"Weighted digraph models for the assessment of energy use and air pollution in transportation systems","volume":"7","author":"Roberts","year":"1975","journal-title":"Environment Planning"},{"key":"10.1016\/S0927-0507(05)80099-4_bib123","series-title":"Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems","author":"Roberts","year":"1976"},{"key":"10.1016\/S0927-0507(05)80099-4_bib124","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970401","article-title":"Graph Theory and its Applications to Problems of Society","author":"Roberts","year":"1978"},{"key":"10.1016\/S0927-0507(05)80099-4_bib125","series-title":"Measurement Theory, with Applications to Decisionmaking, Utility, and the Social Sciences","author":"Roberts","year":"1979"},{"key":"10.1016\/S0927-0507(05)80099-4_bib126","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/0040-1625(79)90034-9","article-title":"Structural modeling and measurement theory","volume":"14","author":"Roberts","year":"1979","journal-title":"Tech. Forecasting Social Change"},{"key":"10.1016\/S0927-0507(05)80099-4_bib127","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1086\/288945","article-title":"On Luce's theory of meaningfulness","volume":"47","author":"Roberts","year":"1980","journal-title":"Philos. Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib128","series-title":"Trends in Mathematical Psychology","first-page":"283","article-title":"Applications of the theory of meaningfulness to order and matching experiments","author":"Roberts","year":"1984"},{"key":"10.1016\/S0927-0507(05)80099-4_bib129","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0263-2241(84)90021-6","article-title":"On the theory of ordinal comparisons in measurement","volume":"2","author":"Roberts","year":"1984","journal-title":"Measurement"},{"key":"10.1016\/S0927-0507(05)80099-4_bib130","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/0022-2496(85)90011-2","article-title":"Applications of the theory of meaningfulness to psychology","volume":"29","author":"Roberts","year":"1985","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib131","series-title":"Applications of Combinatorics and Graph Theory to the Biological and Social Sciences","first-page":"1","article-title":"Applications of combinatorics and graph theory to the biological and social sciences: Seven fundamental ideas","author":"Roberts","year":"1989"},{"key":"10.1016\/S0927-0507(05)80099-4_bib132","series-title":"Applications of Combinatorics and Graph Theory to the Biological and Social Sciences","first-page":"277","article-title":"Meaningless statements, matching experiments, and colored digraphs (applications of graph theory and combinatorics to the theory of measurement)","author":"Roberts","year":"1989"},{"key":"10.1016\/S0927-0507(05)80099-4_bib133","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/0166-218X(90)90146-4","article-title":"Meaningfulness of conclusions from combinatorial optimization","volume":"29","author":"Roberts","year":"1990","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/S0927-0507(05)80099-4_bib134","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0022-247X(90)90382-P","article-title":"Merging relative scores","volume":"147","author":"Roberts","year":"1990","journal-title":"J. Math. Anal. Applic."},{"key":"10.1016\/S0927-0507(05)80099-4_bib135","first-page":"1031","article-title":"From garbage to rainbows: Generalizations of graph coloring and their applications","volume":"Vol. 2","author":"Roberts","year":"1991"},{"key":"10.1016\/S0927-0507(05)80099-4_bib136","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0012-365X(91)90258-4","article-title":"T-Colorings of graphs: Recent results and open problems","volume":"93","author":"Roberts","year":"1991","journal-title":"Discrete Math."},{"key":"10.1016\/S0927-0507(05)80099-4_bib137","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0022-2496(76)90002-X","article-title":"On the theory of uniqueness in measurement","volume":"14","author":"Roberts","year":"1976","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib138","series-title":"Graph Theory and its Applications to Algorithms and Computer Science","first-page":"659","article-title":"Some results on automorphisms of ordered relational systems and the theory of scale type in measurement","author":"Roberts","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib139","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0165-4896(86)90048-X","article-title":"Scale type, meaningfulness, and the possible psychophysical laws","volume":"12","author":"Roberts","year":"1986","journal-title":"Math. Social Sci."},{"key":"10.1016\/S0927-0507(05)80099-4_bib140","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0166-218X(88)90123-0","article-title":"Tight and loose value automorphisms","volume":"22","author":"Roberts","year":"1988","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/S0927-0507(05)80099-4_bib141","first-page":"251","article-title":"The meaningfulness of ordinal comparisons for general order relational systems","volume":"Vol. 2","author":"Roberts","year":"1994"},{"key":"10.1016\/S0927-0507(05)80099-4_bib142","article-title":"A set-theoretical approach to empirical meaningfulness of empirical statements","author":"Robinson","year":"1963"},{"key":"10.1016\/S0927-0507(05)80099-4_bib143","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1037\/h0041419","article-title":"The untenability of Luce's principle","volume":"69","author":"Rozeboom","year":"1962","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib144","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1037\/h0039715","article-title":"Comment","volume":"69","author":"Rozeboom","year":"1962","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib145","series-title":"Air improvement recommendations for the San Francisco Bay Area, The Stanford-Ames NASA\/ASEE Summer Faculty Systems Design Workshop","year":"1970"},{"key":"10.1016\/S0927-0507(05)80099-4_bib146","series-title":"Measurement of Sensation","author":"Savage","year":"1970"},{"key":"10.1016\/S0927-0507(05)80099-4_bib147","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0022-2496(64)90002-1","article-title":"Measurement models and linear inequalities","volume":"1","author":"Scott","year":"1964","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib148","doi-asserted-by":"crossref","first-page":"113","DOI":"10.2307\/2964389","article-title":"Foundational aspects of theories of measurement","volume":"23","author":"Scott","year":"1958","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S0927-0507(05)80099-4_bib149","series-title":"Measurement and Statistics","author":"Senders","year":"1958"},{"key":"10.1016\/S0927-0507(05)80099-4_bib150","first-page":"441","article-title":"On the status of \u2018direct\u2019 psychophysical measurement","volume":"Vol. 9","author":"Shepard","year":"1978"},{"key":"10.1016\/S0927-0507(05)80099-4_bib151","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0022-2496(81)90034-1","article-title":"Psychological relations and psychophysical scales: On the status of \u2018direct\u2019 psychophysical measurement","volume":"24","author":"Shepard","year":"1981","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib152","first-page":"273","article-title":"Testing for homogeneity using minimum spanning trees","volume":"3","author":"Shier","year":"1982","journal-title":"UMAP J."},{"key":"10.1016\/S0927-0507(05)80099-4_bib153","series-title":"Nonparametric Statistics for the Behavioral Sciences","author":"Siegel","year":"1956"},{"key":"10.1016\/S0927-0507(05)80099-4_bib154","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1145\/63039.63043","article-title":"Characterizing computer performance with a single number","volume":"31","author":"Smith","year":"1988","journal-title":"Commun. ACM"},{"key":"10.1016\/S0927-0507(05)80099-4_bib155","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1126\/science.103.2684.677","article-title":"On the theory of scales of measurement","volume":"103","author":"Stevens","year":"1946","journal-title":"Science"},{"key":"10.1016\/S0927-0507(05)80099-4_bib156","series-title":"Handbook of Experimental Psychology","first-page":"1","article-title":"Mathematics, measurement, and psychophysics","author":"Stevens","year":"1951"},{"key":"10.1016\/S0927-0507(05)80099-4_bib157","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1121\/1.1908048","article-title":"The measurement of loudness","volume":"27","author":"Stevens","year":"1955","journal-title":"J. Acoust. Soc. Amer."},{"key":"10.1016\/S0927-0507(05)80099-4_bib158","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1037\/h0046162","article-title":"On the psychophysical law","volume":"64","author":"Stevens","year":"1957","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0927-0507(05)80099-4_bib159","series-title":"Measurement: Definitions and Theories","first-page":"18","article-title":"Measurement, psychophysics, and utility","author":"Stevens","year":"1959"},{"key":"10.1016\/S0927-0507(05)80099-4_bib160","first-page":"226","article-title":"The psychophysics of sensory function","volume":"48","author":"Stevens","year":"1960","journal-title":"Amer. Scientist"},{"key":"10.1016\/S0927-0507(05)80099-4_bib161","series-title":"Sensory Communication","first-page":"1","article-title":"The psychophysics of sensory function","author":"Stevens","year":"1961"},{"key":"10.1016\/S0927-0507(05)80099-4_bib162","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1126\/science.133.3446.80","article-title":"To honor Fechner and repeal his law","volume":"133","author":"Stevens","year":"1961","journal-title":"Science"},{"key":"10.1016\/S0927-0507(05)80099-4_bib163","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF02289683","article-title":"Toward a resolution of the Fechner-Thurstone legacy","volume":"26","author":"Stevens","year":"1961","journal-title":"Psychometrika"},{"key":"10.1016\/S0927-0507(05)80099-4_bib164","series-title":"Handbook of Measurement and Assessment in Behavioral Sciences","article-title":"Ratio scales of opinion","author":"Stevens","year":"1968"},{"key":"10.1016\/S0927-0507(05)80099-4_bib165","article-title":"Assessment of noise: Calculation procedure mark VII","author":"Stevens","year":"1969"},{"key":"10.1016\/S0927-0507(05)80099-4_bib166","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1037\/0033-2909.105.1.147","article-title":"Meaningful inference: The role of measurement in statistics","volume":"105","author":"Stine","year":"1989","journal-title":"Psychol. Bull."},{"key":"10.1016\/S0927-0507(05)80099-4_bib167","series-title":"Measurement: Definitions and Theories","first-page":"129","article-title":"Measurement, empirical meaningfulness and three-valued logic","author":"Suppes","year":"1959"},{"key":"10.1016\/S0927-0507(05)80099-4_bib168","series-title":"Patrick Suppes","first-page":"207","article-title":"Repplies","author":"Suppes","year":"1979"},{"key":"10.1016\/S0927-0507(05)80099-4_bib169","volume":"Vol. II","author":"Suppes","year":"1989"},{"key":"10.1016\/S0927-0507(05)80099-4_bib170","first-page":"1","article-title":"Basic measurement theory","volume":"Vol. 1","author":"Suppes","year":"1963"},{"key":"10.1016\/S0927-0507(05)80099-4_bib171","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0024-3795(87)90290-4","article-title":"The sensitivity of eigenvalues under elementary matrix perturbations","volume":"86","author":"Tanny","year":"1987","journal-title":"Lin. Alg. Applic."},{"key":"10.1016\/S0927-0507(05)80099-4_bib172","series-title":"A further look at stability notions for pulse processes on weighted digraphs","author":"Tanny","year":"1988"},{"key":"10.1016\/S0927-0507(05)80099-4_bib173","article-title":"T-colorings, list T-colorings, and set T-colorings of graphs","author":"Tesman","year":"1989"},{"key":"10.1016\/S0927-0507(05)80099-4_bib174","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1037\/0033-2909.91.1.198","article-title":"IQ, interval scales and normal distributions","volume":"91","author":"Thomas","year":"1982","journal-title":"Psychol. Bull."},{"key":"10.1016\/S0927-0507(05)80099-4_bib175","first-page":"381","article-title":"Measurement structures and statistics","volume":"Vol. 5","author":"Thomas","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib176","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1037\/0033-2909.96.2.394","article-title":"Measurement scales and statistics: The misconception misconceived","volume":"96","author":"Townsend","year":"1984","journal-title":"Psychol. Bull."},{"key":"10.1016\/S0927-0507(05)80099-4_bib177","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/00221309.1978.9920901","article-title":"On the assumptions concerning the assumptions of a t test","volume":"99","author":"Trachtman","year":"1978","journal-title":"J. Gen. Psychol."},{"key":"10.1016\/S0927-0507(05)80099-4_bib178","series-title":"Applications of Discrete Mathematics","first-page":"45","article-title":"Interval graphs, interval orders and their generalizations","author":"Trotter","year":"1988"},{"key":"10.1016\/S0927-0507(05)80099-4_bib179","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1080\/00022470.1972.10469645","article-title":"A rating of the major air pollutants and their sources by effect","volume":"22","author":"Walther","year":"1972","journal-title":"J. Air Pollution Control Assoc."},{"key":"10.1016\/S0927-0507(05)80099-4_bib180","article-title":"The channel assignment problem and closed neigborhood containment graphs","author":"Wang","year":"1985"},{"key":"10.1016\/S0927-0507(05)80099-4_bib181","series-title":"Computer-Assisted Analysis and Model Simplification","first-page":"69","article-title":"Learning through model building","author":"Warfield","year":"1981"},{"key":"10.1016\/S0927-0507(05)80099-4_bib182","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1287\/moor.6.3.319","article-title":"Measuring the quality of approximate solutions to zero-one programming problems","volume":"6","author":"Zemel","year":"1981","journal-title":"Math. Oper. Res."}],"container-title":["Handbooks in Operations Research and Management Science","Operations Research and The Public Sector"],"original-title":[],"deposited":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T03:40:26Z","timestamp":1625802026000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0927050705800994"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994]]},"references-count":182,"URL":"https:\/\/doi.org\/10.1016\/s0927-0507(05)80099-4","relation":{},"ISSN":["0927-0507"],"issn-type":[{"value":"0927-0507","type":"print"}],"subject":[],"published":{"date-parts":[[1994]]}}}