Abstract
In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double‐framed soft sets is introduced, and applications in BCK/BCI‐algebras are discussed. The notions of double‐framed soft algebras in BCK/BCI‐algebras are introduced, and related properties are investigated. Characterizations of double‐framed soft algebras are considered. Product and int‐uni structure of double‐framed soft algebras are discussed, and several examples are provided.
Highlights
The real world is inherently uncertain, imprecise, and vague
There are three theories: theory of probability, theory of fuzzy sets, and the interval mathematics which we can consider as mathematical tools for dealing with uncertainties
Aktasand Cagman 7 studied the basic concepts of soft set theory and compared soft sets to fuzzy and rough sets, providing examples to clarify their differences
Summary
The real world is inherently uncertain, imprecise, and vague. Various problems in system identification involve characteristics which are essentially nonprobabilistic in nature 1. Uncertainties cannot be handled using traditional mathematical tools but may be dealt with using a wide range of existing theories such as probability theory, theory of intuitionistic fuzzy sets, theory of vague sets, theory of interval mathematics, and theory of rough sets. All of these theories have their own difficulties which. Aktasand Cagman 7 studied the basic concepts of soft set theory and compared soft sets to fuzzy and rough sets, providing examples to clarify their differences They discussed the notion of soft groups.
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