α-inclusions applied to group theory via soft set and logic

Abstract

Soft set theory, initiated by Molodtsov, is a tool for modeling various types of uncertainty. In this paper, upper and lower-inclusions of a soft set are de…ned. By using these new notions, some analyzes with respect to group theory are made and it is shown that some of the subgroups of a group can be obtained easily with the help of these notions. It is also illustrated that a soft int-group and a soft uni-group can be obtained by its upper-subgroups and lower-subgroups, respectively. Furthermore, soft int-group by its family of upper-subgroups is characterized under a certain equivalence relation. Finally, a new method used to construct a soft int-group with the help of its upper-subgroups are introduced and an application of this method is given.

Set-generated soft subrings of rings

“…Moreover, by using the upper α-inclusion of a soft set, they proposed the idea of upper α-semigroups for the soft sets. In [41], the authors made some analyzes with respect to group theory and showed that some subgroups of a group can be achieved easily by means of the notions of upper and lower α-inclusions of soft sets. They also demonstrated that a soft uni-group and a soft int-group can be derived by its lower α-subgroup and upper α-subgroup, respectively.…”

“…They also demonstrated that a soft uni-group and a soft int-group can be derived by its lower α-subgroup and upper α-subgroup, respectively. In [40,41], the authors focused on the α-oriented subgroup structures of soft sets. However, the α-oriented subring structure of soft sets is a gap in the literature.…”

Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making

“…One of the other state-of-the-art mathematical tools is soft sets defined by Molodstov [4] in 1999 to parameterise the alternative set for the considered problems without employing the specific membership functions. Due to its ease of implementation, it has been applied to a great variety of fields such as algebra [5][6][7], topology [8][9][10], decision-making [11][12][13][14][15], and machine learning [16][17][18]. After that, the hybrid structures of fuzzy sets and soft sets are studied, and fuzzy soft sets [19,20], fuzzy parameterized soft sets [21], and fuzzy parameterized fuzzy soft sets [22] are introduced to model problems containing fuzzy parameters or alternatives.…”

A new classification method using soft decision-making based on an aggregation operator of fuzzy parameterized fuzzy soft matrices

“…Besides the fuzzy sets successfully applied in machine learning as mentioned above, the concept of soft sets [9] has been propounded by Molodtsov to overcome various uncertainties as a new mathematical tool and applied to assorted fields from algebra to medical diagnostics over the last two decades [10][11][12][13][14][15][16][17]. Soft sets have led to the emergence of new fields, including soft algebra [22][23][24], soft topology [25][26][27], soft analysis [28], and soft decision-making (SDM) [29][30][31], which has given birth to their various applications [18][19][20][21]. Moreover, hybrid versions of fuzzy sets and soft sets, such as fuzzy soft sets [32,33], fuzzy parameterized soft sets [34],…”