Araştırma Makalesi
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(α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET

Yıl 2023, , 114 - 130, 31.01.2023
https://doi.org/10.33773/jum.1232944

Öz

In this paper, (α,β)-interval valued set is studied. The order relation on (α,β)-interval valued set is defined. It is shown that (α,β)-interval valued set is complete lattice by giving the definitions of infumum and supremum on these sets. Then, negation function on these sets is introduced.
With the help of (α,β)-interval valued set ,(α,β)-interval valued intuitionistic fuzzy sets are defined. The fundamental algebraic properties of these sets are examined. The level subsets of (α,β)-interval valued intuitionistic fuzzy sets are given. Some propositions and examples are studied.

Kaynakça

  • K. T. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR’s Session, Sofia, June, (deposed in Central Sci.-Techn. Library of Bulg. Acad. Of Sci. No. 1697/84 (in Bulgaria), 1983. Reprinted: Int. J. Bioautomation, Vol.20, No.1, pp.S1-S6 (2016).
  • K. T. Atanassov, G. Gargov, Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol.31, No.3, pp.343-349 (1989).
  • K. T. Atanassov, Operators over Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol.64, No.2, pp.159-174 (1994).
  • K. T. Atanassov, Intuitionistic Fuzzy Sets, Springer, Heidelberg, (1999).
  • K. T Atanassov, Intuitionistic Fuzzy Sets and Interval Valued Intuitionistic Fuzzy Sets, Advanced Studies in Contemporary Mathematics, Vol.28, No.2, pp.167-176 (2018).
  • G. Çuvalcıoğlu, A. Bal, M. Çitil, The α-Interval Valued Fuzzy Sets Defined on α-Interval Valued Set, Thermal Science, Vol.26, No.2, pp.665-679 (2022).
  • I. Grattan-Guiness, Fuzzy Membership Mapped onto Interval and Many-valued Quantities, Z. Math. Logik. Grundladen Math, Vol.22, No.1, pp.149-160 (1975).
  • B. Gorzalczany, Approximate Inference with Interval-valued Fuzzy Sets, an Outline, in: Proc. Polish Symp. on Interval and Fuzzy Mathematics, Poznan, pp.89–95 (1983).
  • B.Gorzalczany, A Method of Inference in Approximate Reasoning Based on Interval-valued Fuzzy Set, Fuzzy Sets and Systems, Vol.21, No.1, pp.1-17 (1987).
  • K. U. Jahn, Intervall-wertige Mengen, Math.Nach, Vol.68, No.1, pp.115-132 (1975).
  • T. K. Mondal, S. K. Samanta , Topology of Interval-Valued Fuzzy Sets, Indian J. Pure Applied Math, Vol.30, No.1, pp.20-38 (1999).
  • T. K. Mondal, S. K. Samanta, Topology of Interval-Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol.119, No.3, pp.483-494 (2004).
  • R. Sambuc, Fonctions φ-floues. Application L’aide au Diagnostic en Pathologie Thyroidi- enne, Ph. D. Thesis, Univ. Marseille, France, (1975).
  • I. Turksen, Interval Valued Fuzzy Sets Based on Normal Forms, Fuzzy Sets and Systems, Vol.20, No.2, pp.191–210 (1986).
  • L. A. Zadeh, Fuzzy Sets, Information and Control, Vol.8, No.3, pp.338-353 (1965).
  • L.A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part 1, Infor. Sci., Vol.8, No.3, pp.199-249 (1975).
  • L. A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part 2, Infor. Sci., Vol.8, No.4, pp.301-357 (1975).
  • L. A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part 3, Infor. Sci., Vol.9, No.1, pp.43-80 (1975).
Yıl 2023, , 114 - 130, 31.01.2023
https://doi.org/10.33773/jum.1232944

Öz

Kaynakça

  • K. T. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR’s Session, Sofia, June, (deposed in Central Sci.-Techn. Library of Bulg. Acad. Of Sci. No. 1697/84 (in Bulgaria), 1983. Reprinted: Int. J. Bioautomation, Vol.20, No.1, pp.S1-S6 (2016).
  • K. T. Atanassov, G. Gargov, Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol.31, No.3, pp.343-349 (1989).
  • K. T. Atanassov, Operators over Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol.64, No.2, pp.159-174 (1994).
  • K. T. Atanassov, Intuitionistic Fuzzy Sets, Springer, Heidelberg, (1999).
  • K. T Atanassov, Intuitionistic Fuzzy Sets and Interval Valued Intuitionistic Fuzzy Sets, Advanced Studies in Contemporary Mathematics, Vol.28, No.2, pp.167-176 (2018).
  • G. Çuvalcıoğlu, A. Bal, M. Çitil, The α-Interval Valued Fuzzy Sets Defined on α-Interval Valued Set, Thermal Science, Vol.26, No.2, pp.665-679 (2022).
  • I. Grattan-Guiness, Fuzzy Membership Mapped onto Interval and Many-valued Quantities, Z. Math. Logik. Grundladen Math, Vol.22, No.1, pp.149-160 (1975).
  • B. Gorzalczany, Approximate Inference with Interval-valued Fuzzy Sets, an Outline, in: Proc. Polish Symp. on Interval and Fuzzy Mathematics, Poznan, pp.89–95 (1983).
  • B.Gorzalczany, A Method of Inference in Approximate Reasoning Based on Interval-valued Fuzzy Set, Fuzzy Sets and Systems, Vol.21, No.1, pp.1-17 (1987).
  • K. U. Jahn, Intervall-wertige Mengen, Math.Nach, Vol.68, No.1, pp.115-132 (1975).
  • T. K. Mondal, S. K. Samanta , Topology of Interval-Valued Fuzzy Sets, Indian J. Pure Applied Math, Vol.30, No.1, pp.20-38 (1999).
  • T. K. Mondal, S. K. Samanta, Topology of Interval-Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol.119, No.3, pp.483-494 (2004).
  • R. Sambuc, Fonctions φ-floues. Application L’aide au Diagnostic en Pathologie Thyroidi- enne, Ph. D. Thesis, Univ. Marseille, France, (1975).
  • I. Turksen, Interval Valued Fuzzy Sets Based on Normal Forms, Fuzzy Sets and Systems, Vol.20, No.2, pp.191–210 (1986).
  • L. A. Zadeh, Fuzzy Sets, Information and Control, Vol.8, No.3, pp.338-353 (1965).
  • L.A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part 1, Infor. Sci., Vol.8, No.3, pp.199-249 (1975).
  • L. A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part 2, Infor. Sci., Vol.8, No.4, pp.301-357 (1975).
  • L. A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part 3, Infor. Sci., Vol.9, No.1, pp.43-80 (1975).
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Arif Bal 0000-0003-4386-7416

Gökhan Çuvalcıoğlu 0000-0001-5451-3336

Cansu Altıncı 0000-0003-0675-9555

Yayımlanma Tarihi 31 Ocak 2023
Gönderilme Tarihi 12 Ocak 2023
Kabul Tarihi 30 Ocak 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Bal, A., Çuvalcıoğlu, G., & Altıncı, C. (2023). (α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET. Journal of Universal Mathematics, 6(1), 114-130. https://doi.org/10.33773/jum.1232944
AMA Bal A, Çuvalcıoğlu G, Altıncı C. (α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET. JUM. Ocak 2023;6(1):114-130. doi:10.33773/jum.1232944
Chicago Bal, Arif, Gökhan Çuvalcıoğlu, ve Cansu Altıncı. “(α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET”. Journal of Universal Mathematics 6, sy. 1 (Ocak 2023): 114-30. https://doi.org/10.33773/jum.1232944.
EndNote Bal A, Çuvalcıoğlu G, Altıncı C (01 Ocak 2023) (α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET. Journal of Universal Mathematics 6 1 114–130.
IEEE A. Bal, G. Çuvalcıoğlu, ve C. Altıncı, “(α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET”, JUM, c. 6, sy. 1, ss. 114–130, 2023, doi: 10.33773/jum.1232944.
ISNAD Bal, Arif vd. “(α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET”. Journal of Universal Mathematics 6/1 (Ocak 2023), 114-130. https://doi.org/10.33773/jum.1232944.
JAMA Bal A, Çuvalcıoğlu G, Altıncı C. (α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET. JUM. 2023;6:114–130.
MLA Bal, Arif vd. “(α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET”. Journal of Universal Mathematics, c. 6, sy. 1, 2023, ss. 114-30, doi:10.33773/jum.1232944.
Vancouver Bal A, Çuvalcıoğlu G, Altıncı C. (α,β)-INTERVAL VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (α,β)-INTERVAL VALUED SET. JUM. 2023;6(1):114-30.