A Novel Characterization of Fuzzy Soft Substructures in Quantales Theory

Saqib Mazher Qurashi; Muhammad Gulzar; Rani Sumaira Kanwal; Dilruba Akter; Muhammad Shawaiz Safdar

doi:10.1155/2023/6087990

A Novel Characterization of Fuzzy Soft Substructures in Quantales Theory

Saqib Mazher Qurashi
, Muhammad Gulzar^*
, Rani Sumaira Kanwal
, Dilruba Akter^*
, Muhammad Shawaiz Safdar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we use an algebraic structure quantale and define the idea of fuzzy soft substructures as a generalization of fuzzy substructures in quantale. These fuzzy soft substructures include fuzzy soft subquantales, fuzzy soft ideals, fuzzy soft prime ideals, fuzzy soft semiprime ideals, and fuzzy soft primary ideals. Furthermore, different characterizations of fuzzy soft substructures in quantales are introduced. Moreover, we extend this ideology to investigate that for each fuzzy soft substructure in quantale, there exists an α-soft substructure in quantales. These fuzzy soft subquantales and fuzzy soft ideals are characterized by their level subquantales and ideals, respectively. Finally, fuzzy soft image and fuzzy soft inverse image of fuzzy soft substructures under quantale homomorphism in quantale are discussed.

Original language	English
Article number	6087990
Journal	Complexity
Volume	2023
DOIs	https://doi.org/10.1155/2023/6087990
State	Published - 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 Saqib Mazher Qurashi et al.

ASJC Scopus subject areas

General Computer Science
General

Access to Document

10.1155/2023/6087990

Cite this

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title = "A Novel Characterization of Fuzzy Soft Substructures in Quantales Theory",

abstract = "In this paper, we use an algebraic structure quantale and define the idea of fuzzy soft substructures as a generalization of fuzzy substructures in quantale. These fuzzy soft substructures include fuzzy soft subquantales, fuzzy soft ideals, fuzzy soft prime ideals, fuzzy soft semiprime ideals, and fuzzy soft primary ideals. Furthermore, different characterizations of fuzzy soft substructures in quantales are introduced. Moreover, we extend this ideology to investigate that for each fuzzy soft substructure in quantale, there exists an α-soft substructure in quantales. These fuzzy soft subquantales and fuzzy soft ideals are characterized by their level subquantales and ideals, respectively. Finally, fuzzy soft image and fuzzy soft inverse image of fuzzy soft substructures under quantale homomorphism in quantale are discussed.",

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T1 - A Novel Characterization of Fuzzy Soft Substructures in Quantales Theory

AU - Mazher Qurashi, Saqib

AU - Gulzar, Muhammad

AU - Sumaira Kanwal, Rani

AU - Akter, Dilruba

AU - Shawaiz Safdar, Muhammad

PY - 2023

Y1 - 2023

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AB - In this paper, we use an algebraic structure quantale and define the idea of fuzzy soft substructures as a generalization of fuzzy substructures in quantale. These fuzzy soft substructures include fuzzy soft subquantales, fuzzy soft ideals, fuzzy soft prime ideals, fuzzy soft semiprime ideals, and fuzzy soft primary ideals. Furthermore, different characterizations of fuzzy soft substructures in quantales are introduced. Moreover, we extend this ideology to investigate that for each fuzzy soft substructure in quantale, there exists an α-soft substructure in quantales. These fuzzy soft subquantales and fuzzy soft ideals are characterized by their level subquantales and ideals, respectively. Finally, fuzzy soft image and fuzzy soft inverse image of fuzzy soft substructures under quantale homomorphism in quantale are discussed.

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