Fuzzy Duplex UP-Algebras

Iampan, Aiyared; Songsaeng, Metawee; Muhiuddin, G.

doi:10.29020/nybg.ejpam.v13i3.3752

Cited by 14 publications

(9 citation statements)

References 13 publications

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“…For more examples of UP-algebras, see [1,2,11,14,[21][22][23][24]. For a nonempty subset S of a UP-algebra X = (X, •, 0) which satisfies the following condition:…”

Section: Basic Results On Up-algebrasmentioning

confidence: 99%

Picture fuzzy sets in UP-algebras by means of a special type

Yuphaphin¹,

Kankaew²,

Lapo³

et al. 2021

J. Math. Computer Sci.

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The concept of picture fuzzy sets was first introduced by Cuong and Kreinovich [B. C. Cuong, V. Kreinovich, Proceedings of the Third World Congress on Information and Communication Technologies WIICT, (2013), 1-6] in 2013, which is direct extensions of the fuzzy sets and the intuitionistic fuzzy sets. In this paper, we applied the concept of picture fuzzy sets in UP-algebras to introduce the eight new concepts of picture fuzzy sets by means of a special type: special picture fuzzy UPsubalgebras, special picture fuzzy near UP-filters, special picture fuzzy UP-filters, special picture fuzzy implicative UP-filters, special picture fuzzy comparative UP-filters, special picture fuzzy shift UP-filters, special picture fuzzy UP-ideals, and special picture fuzzy strong UP-ideals. Also, we discuss the relationship between the eight new concepts of picture fuzzy sets in UPalgebras. This idea is extended to the lower and upper level subsets of picture fuzzy sets in UP-algebras. Moreover, we define a picture fuzzy set in the same way as a characteristic function and study its characterizations from the related subset.

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“…For more examples of UP-algebras, see [1,2,11,14,[21][22][23][24]. For a nonempty subset S of a UP-algebra X = (X, •, 0) which satisfies the following condition:…”

Section: Basic Results On Up-algebrasmentioning

confidence: 99%

Picture fuzzy sets in UP-algebras by means of a special type

Yuphaphin¹,

Kankaew²,

Lapo³

et al. 2021

J. Math. Computer Sci.

Self Cite

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“…For more examples of UP-algebras, see [3,4,8,12,14,[25][26][27][28]. According to [11], we know that the concept of UP-algebras is a generalization of KU-algebras (see [21]).…”

Section: Definition 11 ([11]mentioning

confidence: 99%

“…(14) a rough Pythagorean fuzzy UP-ideal (RPFUPI) of U if it is both an UpRPFUPI and a LoRPFUPI of U; and (15) a rough Pythagorean fuzzy strong UP-ideal (RPFSUPI) of U if it is both an UpRPFSUPI and a LoRPF-SUPI of U. Definition 2.4.…”

mentioning

confidence: 99%

New types of rough Pythagorean fuzzy UP-filters of UP-algebras

Satirad¹,

Chinram²,

Julatha³

et al. 2022

J. Math. Computer Sci.

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The aim of this paper is to introduce nine types of rough Pythagorean fuzzy sets in UP-algebras and nine types of rough sets in UP-algebras. Then we study relation of these rough Pythagorean fuzzy sets and new types of Pythagorean fuzzy UPfilter under equivalence (congruence) relation. Moreover, we will also discuss t-level subsets of rough Pythagorean fuzzy sets in UP-algebras to study the relationships between rough Pythagorean fuzzy sets and rough sets in UP-algebras which we defined them above. Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets.

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“…For more examples of UP-algebras, see [3,4,8,12,14,[22][23][24][25]. According to [11], we know that the concept of UP-algebras is a generalization of KU-algebras (see [19]).…”

Section: Introductionmentioning

confidence: 99%