Abstract
Recently, in computer science, the commuting quantum query language (CQQL) has been introduced for ranking search results in a database (Schmitt I, VLDB Very Large Data Base J 17(1):39–56, 2008). A user is asked to express search conditions and to rank presented samples, then, the CQQL system matches select-conditions with attribute values. Schmitt’s (VLDB Very Large Data Base J 17(1):39–56, 2008) approach is based on von Neumann’s (Grundlagen der Quantenmechanik. Springer, Berlin, 1932) quantum mechanics and quantum logic and is adapted in this paper to the usual conjoint analysis setting in marketing research where respondents are asked to evaluate selected attribute level combinations for choice prediction purposes. The results of an application show that the new approach competes well with the traditional approach.
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Notes
- 1.
1.0 corresponds to true and 0.0 to false.
- 2.
For simplicity, we assume metric attribute values. The corresponding proximity predicates compare the value closeness to a highest or a lowest value. Due to space restriction, we do not discuss here the non-metric case.
- 3.
Recall, that the rules of Boolean algebra hold.
- 4.
For simplicity, the expression \([a\mid b]\) means either a or b. This decision depends on the corresponding minterm.
- 5.
Please notice, that two different minterms differ always in the negation of at least one predicate. Therefore, disjunction of minterms is mapped to a simple sum.
References
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Saretz, S. (2010). Evaluierung und Abgrenzung der Ähnlichkeitsanfragesprache CQQL gegenüber anderen DB-Retrieval-Verfahren. Working paper series, Institute of Computer Science, Information and Media Technology, BTU Cottbus.
Schmitt, I. (2008). QQL: A DB&IR query language. The VLDB (Very Large Data Base) Journal, 17(1), 39–56.
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Schmitt, I., Baier, D. (2013). Logic Based Conjoint Analysis Using the Commuting Quantum Query Language. In: Lausen, B., Van den Poel, D., Ultsch, A. (eds) Algorithms from and for Nature and Life. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-00035-0_49
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DOI: https://doi.org/10.1007/978-3-319-00035-0_49
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