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

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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.

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  • 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
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    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

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