A prototype of a functional approach to personalized menus generation using set operations

  • Eugenio Roanes–Lozano
  • José Luis Galán–García
  • Gabriel Aguilera–VenegasEmail author


The authors developed some time ago a RBES devoted to preparing personalized menus at restaurants according to the allergies, religious constraints, likes, and other diet requirements as well as products availability. This can be specially important when traveling abroad and facing unknown dishes in a menu. Some restaurants include icons in their menu regarding their adequateness for celiacs or vegetarians and vegans, but this is not always a complete information, as it doesn’t consider, for instance, personal dislikes, or uncommon allergies. The tool previously developed uses logic deduction to obtain a personalized menu for each customer, according to the precise recipes of the restaurant and taking into account the data provided by the customer and the ingredients out of stock (if any). That previous work had an impact in Spanish society: news about it were disseminated by different news agencies and appeared in some newspapers. The authors were also interviewed in radio networks and television channels. Now a new approach that uses functions and set operations has been followed and the speed has been increased by three orders of magnitude, allowing to deal with huge menus instantly. Both approaches have been implemented in the computer algebra system Maple and are exemplified using the same recipes in order to compare their performances.


Restaurant menu Automatic deduction Set operations Computer algebra systems 

Mathematics Subject Classification (2010)

03B70 03E75 68T35 


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We would like to thank the anonymous reviewers for their constructive comments and suggestions.

Funding information

This work was partially supported by the research projects TIN2015-66471-P (Government of Spain) and CASI-CAM S2013/ICE-2845 (Comunidad Autónoma de Madrid).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de Matemática Interdisciplinar & Departamento de Didáctica de Ciencias Experimentales, Sociales y Matemáticas, Facultad de EducaciónUniversidad Complutense de MadridMadridSpain
  2. 2.Departamento de Matemática Aplicada, Escuela de Ingenierías IndustrialesUniversidad de MálagaMálagaSpain
  3. 3.Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería InformáticaUniversidad de Málaga, Complejo TecnológicoMálagaSpain

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