Investigation of Order among Some Known T-norms

Shohel Babu; Fatema Tuj Johora; Abdul Alim

doi:doi:10.11648/j.ajam.20150305.14

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Investigation of Order among Some Known T-norms

Shohel Babu, Fatema Tuj Johora, Abdul Alim

Published in American Journal of Applied Mathematics (Volume 3, Issue 5)

Received: 26 August 2015 Accepted: 11 September 2015 Published: 26 September 2015

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Abstract

In this paper, order among some known T-norms is investigated. Firstly, the T-norm which is the strongest or greatest and the T-norm which is the weakest is observed. Comparing two T-norms we establish the relation which is strong or weak. In addition, for parametric T-norms after changing the interval of their parameter a relation has established which is strong or weak. Finally, compared has done among three or more T-norms.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 5)
DOI	10.11648/j.ajam.20150305.14
Page(s)	229-232
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

T-norm Algebraic Product T_P, T-norm Min T_M, T-norm Drastic Product T_D, T-norm Franks Product T_F, T-norm Einstein Product T_E, T-norm Hamacher Product T_H, T-norm Dubois & Prade Product T_DP

References

[1]	Didier Dobois, Prade Henri, FUZZY SET AND SYSTEM, THEORY AND APPLICATIONS, Academic press INC, New York.
[2]	Peter Vicenik, A NOTE TO CONSTRUCTION OF T-NORMS BASED ON PSEUDO-INVERSE OF MONOTONE FUNCTIONS; Department of Mathematics, Slovak Technical University, Radlinskeho 11, 813 68 Bratislava, Slovak Republic Received June 1998.
[3]	George J Klir, Yuan Bo, FUZZY SETS AND FUZZY LOGIC, Theory and Applications, Prentice-Hall Inc. N.J. U.S.A. 1995.
[4]	Lowen, FUZZYSET THEORY, Department of Mathematics and Computer Science, University of Antwerp; Belgium, Basic Concepts, Techniques and Bibliography, Kluwer Academic Publishers Dordeecht/Boston/London.
[5]	Peter Vicenik, A NOTE ON GENERATORS OF T-NORMS; Department of Mathematics, Slovak Technical University, Radlinskeho 11, 813 68 Bratislava, Slovak Republic.
[6]	Matteo Bianchi, The logic of the strongest and the weakest t-norms, Fuzzy Sets Syst. 276 (2015) 31–42, http://dx.doi.org/10.1016/j.fss.2015.01. 13.
[7]	Mirko Navara(2007), “Triangular norms and conforms” Scholarpedia
[8]	Wladyslaw Homenda, TRIANGULAR NORMS, UNI-AND NULLNORMS,BALANCED NORMS,THE CASES OF THE HIERACHY OF ITERATIVE OPERATORS, Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland.
[9]	Mirta N.K., FUZZY SET THEORY RELATIONAL STRUCTURE USING T-NORMS AND MATHLAB, Department of Mathematics, University of Dhaka.
[10]	Klement, Erich Perer; Mesiar, Radko; and Pap, Endre(2000),Triangular Norms. Dordrecht: Kluwer. ISBN 0-7923-6416-3.

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APA Style

Shohel Babu, Fatema Tuj Johora, Abdul Alim. (2015). Investigation of Order among Some Known T-norms. American Journal of Applied Mathematics, 3(5), 229-232. https://doi.org/10.11648/j.ajam.20150305.14

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ACS Style

Shohel Babu; Fatema Tuj Johora; Abdul Alim. Investigation of Order among Some Known T-norms. Am. J. Appl. Math. 2015, 3(5), 229-232. doi: 10.11648/j.ajam.20150305.14

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AMA Style

Shohel Babu, Fatema Tuj Johora, Abdul Alim. Investigation of Order among Some Known T-norms. Am J Appl Math. 2015;3(5):229-232. doi: 10.11648/j.ajam.20150305.14

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@article{10.11648/j.ajam.20150305.14,
  author = {Shohel Babu and Fatema Tuj Johora and Abdul Alim},
  title = {Investigation of Order among Some Known T-norms},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {5},
  pages = {229-232},
  doi = {10.11648/j.ajam.20150305.14},
  url = {https://doi.org/10.11648/j.ajam.20150305.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150305.14},
  abstract = {In this paper, order among some known T-norms is investigated. Firstly, the T-norm which is the strongest or greatest and the T-norm which is the weakest is observed. Comparing two T-norms we establish the relation which is strong or weak. In addition, for parametric T-norms after changing the interval of their parameter a relation has established which is strong or weak. Finally, compared has done among three or more T-norms.},
 year = {2015}
}

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TY  - JOUR
T1  - Investigation of Order among Some Known T-norms
AU  - Shohel Babu
AU  - Fatema Tuj Johora
AU  - Abdul Alim
Y1  - 2015/09/26
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150305.14
DO  - 10.11648/j.ajam.20150305.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 229
EP  - 232
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150305.14
AB  - In this paper, order among some known T-norms is investigated. Firstly, the T-norm which is the strongest or greatest and the T-norm which is the weakest is observed. Comparing two T-norms we establish the relation which is strong or weak. In addition, for parametric T-norms after changing the interval of their parameter a relation has established which is strong or weak. Finally, compared has done among three or more T-norms.
VL  - 3
IS  - 5
ER  -

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Author Information

Shohel Babu

Mathematics, IUBAT-International University of Business Agriculture and Technology, Dhaka, Bangladesh
Fatema Tuj Johora

Mathematics, IUBAT-International University of Business Agriculture and Technology, Dhaka, Bangladesh
Abdul Alim

Mathematics, BGMEA University of Fashion and Technology, Dhaka, Bangladesh

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APA Style

Shohel Babu, Fatema Tuj Johora, Abdul Alim. (2015). Investigation of Order among Some Known T-norms. American Journal of Applied Mathematics, 3(5), 229-232. https://doi.org/10.11648/j.ajam.20150305.14

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ACS Style

Shohel Babu; Fatema Tuj Johora; Abdul Alim. Investigation of Order among Some Known T-norms. Am. J. Appl. Math. 2015, 3(5), 229-232. doi: 10.11648/j.ajam.20150305.14

Copy | Download

AMA Style

Shohel Babu, Fatema Tuj Johora, Abdul Alim. Investigation of Order among Some Known T-norms. Am J Appl Math. 2015;3(5):229-232. doi: 10.11648/j.ajam.20150305.14

Copy | Download

@article{10.11648/j.ajam.20150305.14,
  author = {Shohel Babu and Fatema Tuj Johora and Abdul Alim},
  title = {Investigation of Order among Some Known T-norms},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {5},
  pages = {229-232},
  doi = {10.11648/j.ajam.20150305.14},
  url = {https://doi.org/10.11648/j.ajam.20150305.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150305.14},
  abstract = {In this paper, order among some known T-norms is investigated. Firstly, the T-norm which is the strongest or greatest and the T-norm which is the weakest is observed. Comparing two T-norms we establish the relation which is strong or weak. In addition, for parametric T-norms after changing the interval of their parameter a relation has established which is strong or weak. Finally, compared has done among three or more T-norms.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Investigation of Order among Some Known T-norms
AU  - Shohel Babu
AU  - Fatema Tuj Johora
AU  - Abdul Alim
Y1  - 2015/09/26
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150305.14
DO  - 10.11648/j.ajam.20150305.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 229
EP  - 232
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150305.14
AB  - In this paper, order among some known T-norms is investigated. Firstly, the T-norm which is the strongest or greatest and the T-norm which is the weakest is observed. Comparing two T-norms we establish the relation which is strong or weak. In addition, for parametric T-norms after changing the interval of their parameter a relation has established which is strong or weak. Finally, compared has done among three or more T-norms.
VL  - 3
IS  - 5
ER  -

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