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

Year 2023, Volume: 6 Issue: 1, 114 - 130, 31.01.2023

Arif Bal , Gökhan Çuvalcıoğlu , Cansu Altıncı

https://doi.org/10.33773/jum.1232944

Abstract

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.

Keywords

Interval Valued Intuitionistic Fuzzy Sets, (alpha, beta)-Interval Valued Set, (alpha, beta)-Interval Valued Intuitionistic Fuzzy Sets

References

• 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).