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Interval-valued intuitionistic fuzzy subgroups based on interval-valued double t-norm

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Abstract

In this paper, the interval-valued double t-norm \(\widetilde{T}\) induced by an interval t-norm \(\overline{T}\) and an interval t-conorm \(\overline{S}\) is defined. The interval-valued intuitionistic fuzzy subgroup and the interval-valued intuitionistic fuzzy normal subgroup based on the interval-valued double t-norm \(\widetilde{T}\) are introduced. In the meantime, some of its basic properties and structural characteristics are studied. Furthermore, the theorems of the homomorphic image and the inverse image are given.

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References

  1. Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349

    Article  MathSciNet  MATH  Google Scholar 

  2. Biswas R (1994) Rosenfeld’s fuzzy subgroup with interval-valued membership functions. Fuzzy Sets Syst 63:87–90

    Article  MATH  Google Scholar 

  3. Ϊbrahimoğlu Ϊ, Çoker D (1997) On intuitionistic fuzzy subgroup and their products. BUSEFAL 70:16–21

    Google Scholar 

  4. Gujin W, Xiapping L (1996) Interval-valued fuzzy subgroups induced by T-triangular norms. BUSEFAL 65:80–84

    Google Scholar 

  5. Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer, Dordrecht

    MATH  Google Scholar 

  6. Mondal TK, Samantha SK (1999) Topology of interval-valued fuzzy sets. Ind J Pure Appl Math 30(1):23–38

    MATH  Google Scholar 

  7. Mondal TK, Samantha SK (2004) Topology of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 119:483–494

    Article  Google Scholar 

  8. Rosenfeld A (1971) Fuzzy groups. J Math Appl 35:512–517

    MathSciNet  MATH  Google Scholar 

  9. Xiapping L, Gujin W (1996) T H interval-valued fuzzy subgroups. J Lanzhou Univ 32:96–99

    Google Scholar 

  10. Xiapping L (2000) The intuitionistic normal fuzzy subgroup and its some equivalent propositions. BUSEFAL 82:40–44

    Google Scholar 

  11. Xiapping L, Gujin W (2000) The S H interval-valued fuzzy subgroups. Fuzzy Sets Syst 112:319–325

    Article  Google Scholar 

  12. Xiapping L (2001) Homomorphism and isomorphism of the intuitionistic fuzzy normal subgroups. BUSEFAL 85:162–175

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Kocaeli University, Umuttepe Campus, 41380, Kocaeli, Turkey

    A. Aygünoğlu, B. Pazar Varol, V. Çetkin & H. Aygün

Authors
  1. A. Aygünoğlu
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  2. B. Pazar Varol
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  3. V. Çetkin
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  4. H. Aygün
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Corresponding author

Correspondence to B. Pazar Varol.

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Aygünoğlu, A., Varol, B.P., Çetkin, V. et al. Interval-valued intuitionistic fuzzy subgroups based on interval-valued double t-norm. Neural Comput & Applic 21 (Suppl 1), 207–214 (2012). https://doi.org/10.1007/s00521-011-0773-5

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  • DOI: https://doi.org/10.1007/s00521-011-0773-5

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