Transitive Closure of Vague Soft Set Relations and its Operators

다국어 초록 (Multilingual Abstract)

A vague soft set is a mapping from a parameter set to the collection of vague subsets of the universal set. In this study, a vague soft relation is presented based on the Cartesian product of vague soft sets. The basic properties of these relations are studied to explain the concept of transitive closure of a vague soft relation. The symmetric, reflexive, and transitive closures of a vague soft set are introduced followed by examples to illustrate these relations. The concepts are further extended by proposing some of their properties. The existence and uniqueness of the transitive closure of a vague soft relation are established, and an algorithm to compute the transitive closure of a vague soft relation is also provided.

목차 (Table of Contents)

• Abstract
• 1. Introduction
• 2. Preliminaries
• 3. Transitive Closure of Vague Soft Set
• 4. Properties of Closure
• 5. Conclusion
• References

참고문헌 (Reference)

1 W. Xu, "Vague soft sets and their properties" 59 (59): 787-794, 2010

2 K. Alhazaymeh, "Vague soft set relations and functions" 28 (28): 1205-1212, 2015

3 K. Alhazaymeh, "Vague soft multiset theory" 93 (93): 511-523, 2014

4 W. L. Gau, "Vague sets" 23 (23): 610-614, 1993

5 Reza Ghasemi ; Mohammad Reza Rabiei ; Ahmad Nezakati, "Strong Law of Large Numbers for Fuzzy Random Variables in Fuzzy Metric Space" 한국지능시스템학회 20 (20): 278-289, 2020

6 J. H. Park, "Some properties of equivalence soft set relations" 63 (63): 1079-1088, 2012

7 D. Molodtsov, "Soft set theory: first results" 37 (37): 19-31, 1999

8 K. V. Babitha, "Soft set relations and functions" 60 (60): 1840-1849, 2010

9 M. Agarwal, "Relations in generalized intuitionistic fuzzy soft sets" 2011 : 1-6, 2011

10 Jiˇr´ı Moˇckoˇr, "Powerset Theory of Fuzzy Soft Sets" 한국지능시스템학회 20 (20): 298-315, 2020

11 K. Alhazaymeh, "Possibility intervalvalued vague soft set" 7 (7): 6989-6994, 2013

12 K. T. Atanassov, "Operators over interval valued intuitionistic fuzzy sets" 64 (64): 159-174, 1994

13 Y. Al-Qudah, "Operations on complex multi-fuzzy sets" 33 (33): 1527-1540, 2017

14 박진한, "Operations on Generalized Intuitionistic Fuzzy Soft Sets" 한국지능시스템학회 11 (11): 184-189, 2011

15 M. I. Ali, "On some new operations in soft set theory" 57 (57): 1547-1553, 2009

16 Y. Al-Qudah, "On (2, 2)-regular non-associative ordered semigroups via its semilattices and generated (generalized fuzzy) ideals" 8 (8): 353-362, 2020

17 X. Huang, "Notes on “Vague soft sets and their properties" 64 (64): 2153-2157, 2012

18 P. C. Saxena, "Normalization in type- 2 fuzzy relational data model based on fuzzy functional dependency using fuzzy functions" 20 (20): 99-138, 2012

19 Shawkat Alkhazaleh ; Emad A. Marei, "New Soft Rough Set Approximations" 한국지능시스템학회 21 (21): 123-134, 2021

20 윤상민 ; 이석종, "New Approach to Intuitionistic Fuzzy Rough Sets" 한국지능시스템학회 20 (20): 129-137, 2020

21 Y. Al-Qudah, "Mapping on complex multifuzzy soft expert classes" 1212 : 012019-, 2019

22 P. K. Maji, "Intuitionistic fuzzy soft sets," 9 (9): 677-692, 2001

23 K. T. Atanassov, "Intuitionistic fuzzy sets" 20 (20): 87-96, 1986

24 W. Su, "Intuitionistic fuzzy decision-making with similarity measures and OWA operator" 21 (21): 245-262, 2013

25 H. Garg, "Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multicriteria decision-making" 34 (34): 215-224, 2019

26 K. Alhazaymeh, "Generalized interval-valued vague soft set" 7 (7): 6983-6988, 2013

27 P. K. Maji, "Fuzzy soft sets" 9 (9): 589-602, 2001

28 L. A. Zadeh, "Fuzzy sets" 8 (8): 338-353, 1965

29 N. Hassan, "Fuzzy parameterized complex multi-fuzzy soft set," 1212 : 012016-, 2019

30 Y. Al-Qudah, "Fuzzy parameterized complex multi-fuzzy soft expert sets" 2111 : 020022-, 2019

31 Y. Al-Qudah, "Fuzzy parameterized complex multi-fuzzy soft expert set theory and its application in decision-making" 11 (11): 358-, 2019

32 I. Al-Zuhairi, "Fuzzy parameterized complex multi-fuzzy soft expert set in prediction of coronary artery disease" 16 (16): 3133-3157, 2020

33 Muhammad Ibrar ; Asghar Khan ; Sajjad Khan ; Fatima Abbas, "Fuzzy Parameterized Bipolar Fuzzy Soft Expert Set and Its Application in Decision Making" 한국지능시스템학회 19 (19): 234-241, 2019

34 K. Alhazaymeh, "Cubic vague set and its application in decision making" 22 (22): 963-, 2020

35 A. M. Ibrahim, "Composition of soft set relations and construction of transitive closure" 2 (2): 98-107, 2012

36 Y. Al-Qudah, "Complex multi-fuzzy soft set: its entropy and similarity measure" 6 : 65002-65017, 2018

37 Y. Al-Qudah, "Complex multi-fuzzy soft expert set and its application," 14 (14): 149-176, 2019

38 Y. Al-Qudah, "Complex multi-fuzzy relation for decision making using uncertain periodic data" 7 (7): 2437-2445, 2018

39 K. Alhazaymeh, "Application of generalized vague soft expert set in decision making" 93 (93): 361-367, 2014

40 P. K. Maji, "An application of soft sets in a decision making problem" 44 (44): 1077-1083, 2002

41 M. B. Gorzałczany, "A method of inference in approximate reasoning based on interval-valued fuzzy sets" 21 (21): 1-17, 1987

42 A. R. Roy, "A fuzzy soft set theoretic approach to decision making problems" 203 (203): 412-418, 2007

43 박진한 ; 권영철 ; 손미정, "A Generalized Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems" 한국지능시스템학회 11 (11): 71-76, 2011