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Logic Aggregators and Their Implementations

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Modeling Decisions for Artificial Intelligence (MDAI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13890))

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Abstract

In this paper we present necessary properties of logic aggregators and compare their major implementations. If decision making includes the identification of a set of alternatives followed by the evaluation of alternatives and selection of the best alternative, then evaluation must be based on graded logic aggregation. The resulting analytic framework is a graded logic which is a seamless generalization of Boolean logic, based on analytic models of graded simultaneity (various forms of conjunction), graded substitutability (various forms of disjunction) and complementing (negation). These basic logic operations can be implemented in various ways, including means, t-norms/conorms, OWA, and fuzzy integrals. Such mathematical models must be applicable in all regions of the unit hypercube \([0,1]^{n}\). In order to be applicable in various areas of decision making, the logic aggregators must be consistent with observable patterns of human reasoning, supporting both formal logic and semantic aspects of human reasoning. That creates a comprehensive set of logic requirements that logic aggregators must satisfy. Various popular aggregators satisfy these requirements to the extent investigated in this paper. The results of our investigation clearly show the limits of applicability of the analyzed aggregators in the area of decision making.

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Authors and Affiliations

  1. Department of Computer Science, San Francisco State University, San Francisco, CA, USA

    Jozo Dujmović

  2. Department of Computer Sciences, Umeå University, Umeå, Sweden

    Vicenç Torra

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  1. Jozo Dujmović
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  2. Vicenç Torra
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Correspondence to Jozo Dujmović .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Vicenç Torra

  2. Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

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Dujmović, J., Torra, V. (2023). Logic Aggregators and Their Implementations. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2023. Lecture Notes in Computer Science(), vol 13890. Springer, Cham. https://doi.org/10.1007/978-3-031-33498-6_1

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  • DOI: https://doi.org/10.1007/978-3-031-33498-6_1

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