On rough sets induced by fuzzy relations approach in semigroups

Prasertpong, Rukchart; Siripitukdet, Manoj

doi:10.1515/math-2018-0136

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…He introduced the notion of a rough left (right, two-sided, bi-) ideal in semigroups and gave some properties of such ideals. Furthermore, the theory of rough ideals in other structures has also been studied by many authors, for example, rough ideals of Γ -semigroup studied in [2,7,8], Prasertpong and Siripitukdet [17] introduced a rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation, and some interesting properties were investigated, etc.. A Pythagorean fuzzy set [21,22] is one of generalizations of the fuzzy set. After its existence, several researchers have studied.…”

Section: Introductionmentioning

confidence: 99%

Rough Pythagorean fuzzy ideals in ternary semigroups

Chinram¹,

Panityakul²

2020

J. Math. Computer Sci.

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Section: Introductionmentioning

confidence: 99%

Rough Pythagorean fuzzy ideals in ternary semigroups

Chinram¹,

Panityakul²

2020

J. Math. Computer Sci.

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Roughness of soft sets and fuzzy sets in semigroups based on set-valued picture hesitant fuzzy relations

Prasertpong

2022

MATH

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<abstract><p>In the philosophy of rough set theory, the methodologies of rough soft sets and rough fuzzy sets have been being examined to be efficient mathematical tools to deal with unpredictability. The basic of approximations in rough set theory is based on equivalence relations. In the aftermath, such theory is extended by arbitrary binary relations and fuzzy relations for more wide approximation spaces. In recent years, the notion of picture hesitant fuzzy relations by Mathew et al. can be considered as a novel extension of fuzzy relations. Then this paper proposes extended approximations into rough soft sets and rough fuzzy sets from the viewpoint of its. We give corresponding examples to illustrate the correctness of such approximations. The relationships between the set-valued picture hesitant fuzzy relations with the upper (resp., lower) rough approximations of soft sets and fuzzy sets are investigated. Especially, it is shown that every non-rough soft set and non-rough fuzzy set can be induced by set-valued picture hesitant fuzzy reflexive relations and set-valued picture hesitant fuzzy antisymmetric relations. By processing the approximations and advantages in the new existing tools, some terms and products have been applied to semigroups. Then, we provide attractive results of upper (resp., lower) rough approximations of prime idealistic soft semigroups over semigroups and fuzzy prime ideals of semigroups induced by set-valued picture hesitant fuzzy relations on semigroups.</p></abstract>

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On rough sets induced by fuzzy relations approach in semigroups

Cited by 2 publications

References 18 publications

Rough Pythagorean fuzzy ideals in ternary semigroups

Rough Pythagorean fuzzy ideals in ternary semigroups

Roughness of soft sets and fuzzy sets in semigroups based on set-valued picture hesitant fuzzy relations

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