THERMAL SCIENCE

International Scientific Journal

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Gokhan Cuvalcioglu

,

Arif Bal

,

Mehmet Citil

THE α-INTERVAL VALUED FUZZY SETS DEFINED ON α-INTERVAL VALUED SET

ABSTRACT
In this study, α-interval valued set is defined whose elements are closed sub-intervals including α of unit interval that is I = [0, 1]. With different order relation on this set, the properties of α-interval valued set are examined. By the help of this order relation, it is shown that α-interval valued set is complete lattice. Negation function on α-interval valued set is given in order to study the theoretical properties of this set. By means of discussions on α-interval valued set, the fundamental features of α-interval valued set are studied. By the help of α-interval valued set, α-interval valued fuzzy sets are defined. The fundamental algebraic properties of these sets are examined. The level subsets of α-interval valued fuzzy sets are defined to give the relations between α-interval valued sets and crisp sets. With the help of this definition, some propositions and examples are given.
KEYWORDS
fuzzy sets, interval valued fuzzy sets, α-interval valued set, α-interval valued fuzzy sets
PAPER SUBMITTED: 2022-08-12
PAPER REVISED: 2022-09-10
PAPER ACCEPTED: 2022-09-25
PUBLISHED ONLINE: 2023-01-29
DOI REFERENCE: https://doi.org/10.2298/TSCI22S2665C
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THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 2, PAGES [665 - 679]
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The α-interval valued fuzzy sets defined on α-interval valued set

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence