Soft set theory

By Pabitra Kumar Maji, R. Biswas, Akhil Ranjan Roy. 2003

2,646 citations recorded by the source corpus.

Abstract In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.

Subfields: Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/5cee6b7fb97778fb9343a308f5b6982ef9c97135

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In Management Science and Operations Research

Citations in the corpus

Picture fuzzy sets (2015, result): “Now we present a new definition , an example and some results which are the generalization of some propositions given in [1, 12].”
operation and decompositions of some forms of soft continuity in soft topological spaces (2013, background): “In recent years, many interesting applications of soft set theory have been expanded by embedding the ideas of fuzzy sets [1, 2, 5, 9, 10, 11, 12, 13, 15, 20].”
Soft sets and soft rough sets (2011, methodology): “[16] introduced several operations in soft set theory and carried out a detailed theoretical study on soft sets.”
Introduction to fuzzy soft groups (2009, background): “Furthermore Maji, Biswas and Roy worked on soft set theory in [7].”
Soft semirings (2008, background): “[10] introduced and investigated several binary operations such as intersection, union, AND-operation, and OR-operation of soft sets.”
On Soft Topological Spaces (2013, background): “The soft set theory has been applied to many different fields (see, for example, [ 1], [2], [4], [5], [7], [8], [11], [12], [13], [14], [15], [16], [22], [25], [27]).”
On soft linear spaces and soft normed linear spaces (2013, background): “([13],[14]) introduced several operations on soft sets and applied it to decision making problems.”
Soft topology (2011, result): “In this section, we present the basic definitions and results of soft set theory which may be found in earlier studies [45,3,1].”
T-soft equality relation (2020, background): “[1] pointed out the shortcoming that arise from the two definitions of null soft set introduced in [22] and [34], by a counterexample.”
Soft set theory and topology (2014, background): “The soft set theory has been applied to many different fields (see, for example, [1], [2], [4], [5], [7], [8], [10], [12], [13], [14], [15], [21], [23], [25]).”
SOFT GENERALIZED CLOSED SETS IN SOFT TOPOLOGICAL SPACES (2012, methodology): “[7, 8] presented an application of soft sets in decision making problems that is based on the reduction of parameters to keep the optimal choice objects.”
Soft set theory and uni-int decision making (2010, background): “[13] published a detailed theoretical study on soft sets.”
MAPPINGS ON SOFT CLASSES (2010, background): “[10], is not unique in a soft space (X,E) , rather it depends upon A ⊆ E.”
On Fuzzy Soft Sets (2009, background): “In 2005, Pei and Miao [4] and Chen et al. [5] improved the work of Maji et al. [2, 3].”