Some classes of binary operations in approximate reasoning

József Tick, J. Fodor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

The aim of this paper is to study some binary operations in approximate reasoning. In the first part we summarize a former practical investigation of the applicability of the implication function based on the nilpotent minimum in that framework [1]. We also present some numerical examples to illustrate the results. In the second part we recall a constructive approach to the axiomatics of generalized modus ponens (GMP) published in [4]. As a consequence, a system of functional equations is obtained. Idempotent as well as non-idempotent conjunctions fulfilling this system are studied. The obtained results support the use of non-commutative and non-associative conjunctions and the corresponding implications in approximate reasoning.

Original languageEnglish
Title of host publicationINES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings
Pages123-128
Number of pages6
Volume2005
DOIs
Publication statusPublished - 2005
EventINES'05: IEEE 9th International Conference on Intelligent Engineering Systems -
Duration: Sep 16 2005Sep 19 2005

Other

OtherINES'05: IEEE 9th International Conference on Intelligent Engineering Systems
Period9/16/059/19/05

Keywords

  • Approximate reasoning
  • Conjunctions
  • Generalized modus ponens
  • Nilpotent minimum and the related implication
  • R-and S-implications

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Tick, J., & Fodor, J. (2005). Some classes of binary operations in approximate reasoning. In INES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings (Vol. 2005, pp. 123-128). [1555143] https://doi.org/10.1109/INES.2005.1555143

Some classes of binary operations in approximate reasoning. / Tick, József; Fodor, J.

INES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings. Vol. 2005 2005. p. 123-128 1555143.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tick, J & Fodor, J 2005, Some classes of binary operations in approximate reasoning. in INES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings. vol. 2005, 1555143, pp. 123-128, INES'05: IEEE 9th International Conference on Intelligent Engineering Systems, 9/16/05. https://doi.org/10.1109/INES.2005.1555143
Tick J, Fodor J. Some classes of binary operations in approximate reasoning. In INES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings. Vol. 2005. 2005. p. 123-128. 1555143 https://doi.org/10.1109/INES.2005.1555143
Tick, József ; Fodor, J. / Some classes of binary operations in approximate reasoning. INES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings. Vol. 2005 2005. pp. 123-128
@inproceedings{782db5b9caac414eab002d23f0fa4f7b,
title = "Some classes of binary operations in approximate reasoning",
abstract = "The aim of this paper is to study some binary operations in approximate reasoning. In the first part we summarize a former practical investigation of the applicability of the implication function based on the nilpotent minimum in that framework [1]. We also present some numerical examples to illustrate the results. In the second part we recall a constructive approach to the axiomatics of generalized modus ponens (GMP) published in [4]. As a consequence, a system of functional equations is obtained. Idempotent as well as non-idempotent conjunctions fulfilling this system are studied. The obtained results support the use of non-commutative and non-associative conjunctions and the corresponding implications in approximate reasoning.",
keywords = "Approximate reasoning, Conjunctions, Generalized modus ponens, Nilpotent minimum and the related implication, R-and S-implications",
author = "J{\'o}zsef Tick and J. Fodor",
year = "2005",
doi = "10.1109/INES.2005.1555143",
language = "English",
isbn = "0780394747",
volume = "2005",
pages = "123--128",
booktitle = "INES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings",

}

TY - GEN

T1 - Some classes of binary operations in approximate reasoning

AU - Tick, József

AU - Fodor, J.

PY - 2005

Y1 - 2005

N2 - The aim of this paper is to study some binary operations in approximate reasoning. In the first part we summarize a former practical investigation of the applicability of the implication function based on the nilpotent minimum in that framework [1]. We also present some numerical examples to illustrate the results. In the second part we recall a constructive approach to the axiomatics of generalized modus ponens (GMP) published in [4]. As a consequence, a system of functional equations is obtained. Idempotent as well as non-idempotent conjunctions fulfilling this system are studied. The obtained results support the use of non-commutative and non-associative conjunctions and the corresponding implications in approximate reasoning.

AB - The aim of this paper is to study some binary operations in approximate reasoning. In the first part we summarize a former practical investigation of the applicability of the implication function based on the nilpotent minimum in that framework [1]. We also present some numerical examples to illustrate the results. In the second part we recall a constructive approach to the axiomatics of generalized modus ponens (GMP) published in [4]. As a consequence, a system of functional equations is obtained. Idempotent as well as non-idempotent conjunctions fulfilling this system are studied. The obtained results support the use of non-commutative and non-associative conjunctions and the corresponding implications in approximate reasoning.

KW - Approximate reasoning

KW - Conjunctions

KW - Generalized modus ponens

KW - Nilpotent minimum and the related implication

KW - R-and S-implications

UR - http://www.scopus.com/inward/record.url?scp=33845503688&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845503688&partnerID=8YFLogxK

U2 - 10.1109/INES.2005.1555143

DO - 10.1109/INES.2005.1555143

M3 - Conference contribution

SN - 0780394747

SN - 9780780394742

VL - 2005

SP - 123

EP - 128

BT - INES'05: IEEE 9th International Conference on Intelligent Engineering Systems - Proceedings

ER -