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Compensatory Fuzzy Logic: A Frame for Reasoning and Modeling Preference Knowledge in Intelligent Systems

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Soft Computing for Business Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 537))

Abstract

This paper presents a new approach to designing multivalued logic systems, called Compensatory Fuzzy Logic that besides constituting a formal system with logic properties of remarkable interest represents a bridge between Logic and Decision-Making. The main aim of this proposal is to use the language as key element of communication in the construction of semantic models that make easier the evaluation, decision-making and knowledge discovery. The axioms that constitute the base of this proposal gather actual characteristics of the decision-making processes, and the way of reasoning of people who intervene in them. Some of these axioms are inspired by approaches that adopt a descriptive position in supporting decision-making. Most axioms contain elements of a rational thought. Hence, this logical approach for decision-making may be considered as a third position that combines normative and descriptive components. This approach enters to make part of the arsenal of methods for multicriteria evaluation, adapting itself especially to those situations in which a decision-maker can verbally describe, often in an ambiguous way, the heuristic it uses when executing actions of multicriteria evaluation/classification. Principal kind of operators of Fuzzy Logic are studied according the introduced axioms. Quasi-Arithmetic Based Compensatory Logic is introduced and its particular case, the Geometric Mean Based Compensatory Logic too. The Universal and Existential quantifiers are defined according the definition of this last logic, for discrete and continues sets. An illustration example using Geometric Mean Based Compensatory Logic is used to explain the Compensatory Fuzzy Logic properties.

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Author information

Authors and Affiliations

  1. “Jose Antonio Echeverria” Higher Technical Institute, Havana, Cuba

    Rafael Alejandro Espín Andrade & Erick González

  2. Autonomous University of Sinaloa, Sinaloa, Mexico

    Eduardo Fernández

Authors
  1. Rafael Alejandro Espín Andrade
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  2. Eduardo Fernández
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  3. Erick González
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Correspondence to Rafael Alejandro Espín Andrade .

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Editors and Affiliations

  1. Centro de Estudios de Técnicas de Dirección, Instituto Superior Politécnico José Antonio Echeverría, La Habana, Cuba

    Rafael Espin

  2. Centro de Estudios de Informática Carretera a Camajuani, Universidad Central Marta Abreu de Las Villas, Santa Clara, Cuba

    Rafael Bello Pérez

  3. Department of Applied Mathematics and Computer Science, Universidad de Cantabria, Santander, Spain

    Angel Cobo

  4. Department für Informatik, Carl Von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Jorge Marx

  5. Instituto Superior Politécnico José Antonio Echeverría, La Habana, Cuba

    Ariel Racet Valdés

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Andrade, R.A.E., Fernández, E., González, E. (2014). Compensatory Fuzzy Logic: A Frame for Reasoning and Modeling Preference Knowledge in Intelligent Systems. In: Espin, R., Pérez, R., Cobo, A., Marx, J., Valdés, A. (eds) Soft Computing for Business Intelligence. Studies in Computational Intelligence, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53737-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-53737-0_1

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