A new classification of hemirings through double-framed soft h-ideals

Due to lack of parameterization, various ordinary uncertainty theories like theory of fuzzy sets, and theory of probability cannot solve complicated problems of economics and engineering involving uncertainties. The aim of the present paper was to provide an appropriate mathematical tool for solving such type of complicated problems. For the said purpose, the notion of double-framed soft sets in hemirings is introduced. As h-ideals of hemirings play a central role in the structural theory, therefore, we developed a new type of subsystem of hemirings. Double-framed soft left (right) h-ideal, double-framed soft h-bi-ideals and double-framed soft h-quasi-ideals of hemiring are determined. These concepts are elaborated through suitable examples. Furthermore, we are bridging ordinary h-ideals and double-framed soft h-ideals of hemirings through double-framed soft including sets and characteristic double-framed soft functions. It is also shown that every double-framed soft h-quasi-ideal is double-framed soft h-bi-ideal but the converse inclusion does not hold. A well-known class of hemrings i.e. h-hemiregular hemirings is characterized by the properties of these newly developed double-framed soft h-ideals o