IDEAS home Printed from https://ideas.repec.org/p/ahh/wpaper/worms2109.html
   My bibliography  Save this paper

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Author

Listed:

Abstract

In this work, we propose a new method for modeling human reasoning about objects’ similarities. We assume that similarity depends on perceived intensities of objects’ attributes expressed by natural language expressions such as low, medium, and high. We show how to find the underlying structure of the matrix with intensities of objects’ similarities in the factor-analysis-like manner. The demonstrated approach is based on fuzzy logic and set-theory principles, and it uses only maximum and minimum operators. Similarly to classic eigenvector decomposition, we aim at representing the initial linguistic-ordinal-scale (LOS) matrix as a max-min product of other LOS matrix and its transpose. We call this reconstructing matrix a neuromatrix because we assume that such a process takes place at the neural level in our brain. We show and discuss on simple, illustrative examples, how the presented way of modeling grasps natural way of reasoning about similarities. The unique characteristics of our approach is treating smaller attribute intensities as less important in making decisions about similarities. This feature is consistent with how the human brain is functioning at a biological level. A neuron fires and passes information further only if input signals are strong enough. The proposal of the heuristic algorithm for finding the decomposition in practice is also introduced and applied to exemplary data from classic psychological studies on perceived similarities between colors and between nations. Finally, we perform a series of simulation experiments showing the effectiveness of the proposed heuristic.

Suggested Citation

  • Jerzy Grobelny & Rafal Michalski & Gerhard-Wilhelm Weber, 2021. "Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic," WORking papers in Management Science (WORMS) WORMS/21/09, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    • Handle: RePEc:ahh:wpaper:worms2109
    DOI: 10.1007/s00521-020-05363-y
    as

    Download full text from publisher

    File URL: https://worms.pwr.edu.pl/RePEc/ahh/wpaper/WORMS_21_09.pdf
    File Function: Final version, 2021
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00521-020-05363-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Si-Tong Lu & Miao Zhang & Qing-Na Li, 2020. "Feasibility and a fast algorithm for Euclidean distance matrix optimization with ordinal constraints," Computational Optimization and Applications, Springer, vol. 76(2), pages 535-569, June.
    2. Erik Kropat & Ruben A. Tikidji-Hamburyan & Gerhard-Wilhelm Weber, 2017. "Operations research in neuroscience," Annals of Operations Research, Springer, vol. 258(1), pages 1-4, November.
    3. Roger Shepard, 1974. "Representation of structure in similarity data: Problems and prospects," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 373-421, December.
    4. Tom Wilderjans & E. Ceulemans & I. Mechelen, 2012. "The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 724-740, October.
    5. Michael C Hout & Stephen D Goldinger & Kyle J Brady, 2014. "MM-MDS: A Multidimensional Scaling Database with Similarity Ratings for 240 Object Categories from the Massive Memory Picture Database," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-11, November.
    6. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. II," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 219-246, September.
    7. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    8. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    9. Myrsini Katsikatsou & Irini Moustaki, 2016. "Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1046-1068, December.
    10. Joseph Kruskal & Roger Shepard, 1974. "A nonmetric variety of linear factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 39(2), pages 123-157, June.
    11. Emel Savku & Gerhard-Wilhelm Weber, 2018. "A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 696-721, November.
    12. Berna Haktanirlar Ulutas & N. Fırat Özkan & Rafał Michalski, 2020. "Application of hidden Markov models to eye tracking data analysis of visual quality inspection operations," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 761-777, June.
    13. Iwin Leenen & Iven Mechelen & Paul Boeck, 2001. "Models for ordinal hierarchical classes analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 389-403, September.
    14. Tom Wilderjans & Eva Ceulemans & Iven Mechelen, 2008. "The CHIC Model: A Global Model for Coupled Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 729-751, December.
    15. Katsikatsou, Myrsini & Moustaki, Irini & Yang-Wallentin, Fan & Jöreskog, Karl G., 2012. "Pairwise likelihood estimation for factor analysis models with ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4243-4258.
    16. Jerzy Grobelny & Rafal Michalski, 2017. "Applying hidden Markov models to visual activity analysis for simple digital control panel operations," WORking papers in Management Science (WORMS) WORMS/17/06, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    17. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. I," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 125-140, June.
    18. Jerzy Grobelny & Rafal Michalski, 2021. "Hidden Markov models for visual processing of marketing leaflets," WORking papers in Management Science (WORMS) WORMS/21/08, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    19. Paul Boeck & Seymour Rosenberg, 1988. "Hierarchical classes: Model and data analysis," Psychometrika, Springer;The Psychometric Society, vol. 53(3), pages 361-381, September.
    20. Louis Guttman, 1968. "A general nonmetric technique for finding the smallest coordinate space for a configuration of points," Psychometrika, Springer;The Psychometric Society, vol. 33(4), pages 469-506, December.
    21. Papageorgiou, Ioulia & Moustaki, Irini, 2019. "Sampling of pairs in pairwise likelihood estimation for latent variable models with categorical observed variables," LSE Research Online Documents on Economics 87592, London School of Economics and Political Science, LSE Library.
    22. Yerim Choi & Jonghun Park & Dongmin Shin, 2017. "A semi-supervised inattention detection method using biological signal," Annals of Operations Research, Springer, vol. 258(1), pages 59-78, November.
    23. Jerzy Grobelny & Rafal Michalski, 2020. "Investigating human visual behavior by hidden Markov models in the design of marketing information," WORking papers in Management Science (WORMS) WORMS/20/09, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    24. V. Rasoulzadeh & E. C. Erkus & T. A. Yogurt & I. Ulusoy & S. Aykan Zergeroğlu, 2017. "A comparative stationarity analysis of EEG signals," Annals of Operations Research, Springer, vol. 258(1), pages 133-157, November.
    25. Katsikatsou, Myrsini & Moustaki, Irini & Yang-Wallentin, Fan & Jöreskog, Karl G., 2012. "Pairwise likelihood estimation for factor analysis models with ordinal data," LSE Research Online Documents on Economics 43182, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaogeng Ren & Chunwang Li & Xiaojun Ma & Fuxiang Chen & Haoyu Wang & Ashutosh Sharma & Gurjot Singh Gaba & Mehedi Masud, 2021. "Design of Multi-Information Fusion Based Intelligent Electrical Fire Detection System for Green Buildings," Sustainability, MDPI, vol. 13(6), pages 1-15, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. Carroll, 1985. "Review," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 133-140, March.
    2. Jacqueline Meulman, 1992. "The integration of multidimensional scaling and multivariate analysis with optimal transformations," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 539-565, December.
    3. Jacqueline Meulman & Peter Verboon, 1993. "Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 7-35, March.
    4. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    5. Venera Tomaselli, 1996. "Multivariate statistical techniques and sociological research," Quality & Quantity: International Journal of Methodology, Springer, vol. 30(3), pages 253-276, August.
    6. Aurea Grané & Rosario Romera, 2018. "On Visualizing Mixed-Type Data," Sociological Methods & Research, , vol. 47(2), pages 207-239, March.
    7. Ulf Lundberg & Gösta Ekman, 1973. "Subjective geographic distance: A multidimensional comparison," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 113-122, March.
    8. Martin Young & Wayne DeSarbo, 1995. "A parametric procedure for ultrametric tree estimation from conditional rank order proximity data," Psychometrika, Springer;The Psychometric Society, vol. 60(1), pages 47-75, March.
    9. Abe, Makoto, 1998. "Error structure and identification condition in maximum likelihood nonmetric multidimensional scaling," European Journal of Operational Research, Elsevier, vol. 111(2), pages 216-227, December.
    10. Lucia Reis Peixoto Roselli & Leydiana de Sousa Pereira & Anderson Lucas Carneiro de Lima Silva & Adiel Teixeira Almeida & Danielle Costa Morais & Ana Paula Cabral Seixas Costa, 2020. "Neuroscience experiment applied to investigate decision-maker behavior in the tradeoff elicitation procedure," Annals of Operations Research, Springer, vol. 289(1), pages 67-84, June.
    11. Giovanni De Luca & Paola Zuccolotto, 2011. "A tail dependence-based dissimilarity measure for financial time series clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 323-340, December.
    12. Groenen, P.J.F. & Borg, I., 2013. "The Past, Present, and Future of Multidimensional Scaling," Econometric Institute Research Papers EI 2013-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Hossein Safizadeh, M. & McKenna, David R., 1996. "Application of multidimensional scaling techniques to facilities layout," European Journal of Operational Research, Elsevier, vol. 92(1), pages 54-62, July.
    14. Patrick Groenen & Willem Heiser, 1996. "The tunneling method for global optimization in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 529-550, September.
    15. Gruenhage, Gina & Opper, Manfred & Barthelme, Simon, 2016. "Visualizing the effects of a changing distance on data using continuous embeddings," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 51-65.
    16. Verniest, Fabien & Greulich, Sabine, 2019. "Methods for assessing the effects of environmental parameters on biological communities in long-term ecological studies - A literature review," Ecological Modelling, Elsevier, vol. 414(C).
    17. Wayne DeSarbo & Ajay Manrai & Raymond Burke, 1990. "A nonspatial methodology for the analysis of two-way proximity data incorporating the distance-density hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 229-253, June.
    18. Roger Shepard, 1974. "Representation of structure in similarity data: Problems and prospects," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 373-421, December.
    19. H. Micko, 1970. "A “halo”-model for multidimensional ratio scaling," Psychometrika, Springer;The Psychometric Society, vol. 35(2), pages 199-227, June.
    20. Gert Storms, 1995. "On the robustness of maximum likelihood scaling for violations of the error model," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 247-258, June.

    More about this item

    Keywords

    Similarity perception; fuzzy logic; similarity matrix decomposition; neuromatrices; linguistic ordinal scales (LOS); reconstructing similarity matrix;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D87 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Neuroeconomics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ahh:wpaper:worms2109. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Anna Kowalska-Pyzalska (email available below). General contact details of provider: https://edirc.repec.org/data/kbpwrpl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.