Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM

Muhammed Riaz; Filiz Çıtak; Nabeela Wali; Amna Mushtaq

EN

Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM

Abstract

In this paper, we tried to hybrid soft sets with multisets. We define some basic properties of soft multiset and present some important results. We define some binary relations, equivalence relations and an indiscernibility relation on soft multiset with examples. The concept of an approximation space associated with each parameter in a soft multiset is discussed and an approximation space associated with the soft multiset is defined. We introduce the novel concepts of roughness and fuzziness associated with soft multiset. We use soft multiset in multi-valued information system. Furthermore, we present an algorithm to cope with uncertainties in multi-attribute decision making (MADM) problems by utilizing soft multisets and related concepts. The efficiency of the algorithm is verified by a case study to find the optimal choice of the real-world problems having uncertainties.

Keywords

Soft multi-set, roughness and fuzziness, multiu-valued information systems, MADM

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Muhammed Riaz ^*
Pakistan

Filiz Çıtak
Türkiye

Nabeela Wali
Pakistan

Amna Mushtaq
Pakistan

Publication Date

June 30, 2020

Submission Date

January 1, 2020

Acceptance Date

May 14, 2020

Published in Issue

Year 2020 Number: 31

IZ

https://izlik.org/JA84UF35RG

APA

Riaz, M., Çıtak, F., Wali, N., & Mushtaq, A. (2020). Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM. Journal of New Theory, 31, 1-19. https://izlik.org/JA84UF35RG

AMA

1.Riaz M, Çıtak F, Wali N, Mushtaq A. Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM. JNT. 2020;(31):1-19. https://izlik.org/JA84UF35RG

Chicago

Riaz, Muhammed, Filiz Çıtak, Nabeela Wali, and Amna Mushtaq. 2020. “Roughness and Fuzziness Associated With Soft Multi-Sets and Their Application to MADM”. Journal of New Theory, nos. 31: 1-19. https://izlik.org/JA84UF35RG.

EndNote

Riaz M, Çıtak F, Wali N, Mushtaq A (June 1, 2020) Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM. Journal of New Theory 31 1–19.

IEEE

[1]M. Riaz, F. Çıtak, N. Wali, and A. Mushtaq, “Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM”, JNT, no. 31, pp. 1–19, June 2020, [Online]. Available: https://izlik.org/JA84UF35RG

ISNAD

Riaz, Muhammed - Çıtak, Filiz - Wali, Nabeela - Mushtaq, Amna. “Roughness and Fuzziness Associated With Soft Multi-Sets and Their Application to MADM”. Journal of New Theory. 31 (June 1, 2020): 1-19. https://izlik.org/JA84UF35RG.

JAMA

1.Riaz M, Çıtak F, Wali N, Mushtaq A. Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM. JNT. 2020;:1–19.

MLA

Riaz, Muhammed, et al. “Roughness and Fuzziness Associated With Soft Multi-Sets and Their Application to MADM”. Journal of New Theory, no. 31, June 2020, pp. 1-19, https://izlik.org/JA84UF35RG.

Vancouver

1.Muhammed Riaz, Filiz Çıtak, Nabeela Wali, Amna Mushtaq. Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM. JNT [Internet]. 2020 Jun. 1;(31):1-19. Available from: https://izlik.org/JA84UF35RG