Novel concepts of soft sets with applications

다국어 초록 (Multilingual Abstract)

We introduce different concepts of soft sets, including soft $\sigma$-ring, soft algebra, and soft $\sigma$-algebra. We present different types of set functions, including soft finitely sub-additive, soft countably sub-additive, soft finitely additive, soft countably additive and soft monotone. We study the concept of soft outer measure and soft Lebesgue outer measure. We also describe interesting applications of soft mappings to decision-making.

참고문헌 (Reference)

1 D. Chen, "The parametrization reduction of soft sets and its applications" 49 : 757-763, 2005

2 W. Rong, "The countabilities of soft topological spaces, World Accedmy of Science" 6 : 784-787, 2012

3 N. Cagman, "Soft topology" 62 : 351-358, 2011

4 F. Feng, "Soft sets combined with fuzzy sets and rough sets: a tentative approach" 14 (14): 899-911, 2010

5 F. Feng, "Soft sets and soft rough sets" 181 : 1125-1137, 2011

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

7 P. K. Maji, "Soft set theory" 45 : 555-562, 2003

8 S. Das, "Soft real sets, soft real numbers and their properties" 20 (20): 551-576, 2012

9 S. Das, "Soft metric" 6 (6): 77-94, 2013

10 M. Akram, "Soft intersection Lie algebras" 21 : 11-18, 2013

11 S. Abdullah, "Semigroups characterized by the properties of (α, β)*-fuzzy ideals" 9 (9): 43-63, 2015

12 M. Akram, "Representation of labeling tree based on m- polar fuzzy sets" 2016

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

14 A. Z. Khameneh, "On soft σ-algebras" 7 (7): 17-29, 2013

15 M. Shabir, "On soft topological spaces" 61 : 1786-1799, 2011

16 S. Das, "On soft metric spaces" 21 (21): 707-734, 2013

17 P. Majumdar, "On soft mappings" 60 : 2666-2672, 2010

18 I. Zorlutuna, "On continuity of soft mappings" 9 (9): 403-409, 2015

19 A. Mukherjee, "Measurable soft sets" 8 (8): 1-14, 2015

20 M. Riaz, "Measurable Soft Mappings" 48 (48): 19-34, 2016

21 A. Kharal, "Mappings on soft classes" 7 (7): 471-482, 2011

22 허걸, "Fuzzzy Functions and Fuzzy Partially Ordered set" 한국지능시스템학회 9 (9): 285-293, 2009

23 S. Abdullah, "Fuzzy soft set over a fuzzy topological space" 7 (7): 491-499, 2016

24 허걸, "FUZZY EQUIVALENCE RELATIONS AND FUZZY PARTITIONS" 호남수학회 28 (28): 291-315, 2006

25 N. Cagman, "FP-soft set theory and its applications" 2 (2): 219-226, 2011

26 M. Riaz, "Certain properties of soft metric spaces" 2016

27 F. Feng, "Attribute analysis of information systems based on elementary soft implications" 70 : 281-292, 2014

28 N. O. Alshehri, "Applications of soft sets in-algebras" 3 (3): 1-8, 2013

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

30 F. Feng, "An adjustable approach to fuzzy soft set based decision making" 234 (234): 10-20, 2010

31 S. Roy, "A note on a soft topological space" 46 (46): 19-24, 2014

32 V. Cetkin, "A new approach in handling soft decision making problems" 9 : 231-239, 2016