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α-Interval Valued Fuzzy Sets and α-Interval Valued Fuzzy Subgroups

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New Directions on Hybrid Intelligent Systems Based on Neural Networks, Fuzzy Logic, and Optimization Algorithms

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1146))

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Abstract

α-interval valued sets are studied in the paper. The members of these sets are sub-closed intervals that include α of unit interval. Basic characteristics are researched. The definition of order relation and negation function on these sets are given. α-interval valued fuzzy sets that the degree of membership is sub-closed interval of unit interval including α, are given. The basis algebraic features are viewed. The connection between classical sets and defined sets in the paper is studied. α-interval valued fuzzy subgroups is defined. Typical properties of groups are studied. Main definition and propositions about that structure are examined.

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Author information

Authors and Affiliations

  1. Department of Motor Vehicles and Transportation Technologies, Vocational School of Technical Sciences, Mersin University, Mersin, Turkey

    Arif Bal

  2. Faculty of Science, Department of Mathematics, Mersin University, Mersin, Turkey

    Gökhan Çuvalcıoğlu

  3. Faculty of Science, Department of Mathematics, Kahramanmaraş Sütçü İmam University, Kahramanmaraş, Turkey

    Feride Tuğrul

Authors
  1. Arif Bal
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  2. Gökhan Çuvalcıoğlu
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  3. Feride Tuğrul
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Corresponding author

Correspondence to Arif Bal .

Editor information

Editors and Affiliations

  1. Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico

    Patricia Melin

  2. Division of Graduate Studies &Research, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

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Bal, A., Çuvalcıoğlu, G., Tuğrul, F. (2024). α-Interval Valued Fuzzy Sets and α-Interval Valued Fuzzy Subgroups. In: Melin, P., Castillo, O. (eds) New Directions on Hybrid Intelligent Systems Based on Neural Networks, Fuzzy Logic, and Optimization Algorithms. Studies in Computational Intelligence, vol 1146. Springer, Cham. https://doi.org/10.1007/978-3-031-53713-4_4

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