The Expansion Of Fuzzy Soft Sets Based On Fuzzy Description Logics

In1999, researcher Molodtsov introduced the definition of soft set theory, which can beused as a genetic mathematical tool for dealing with fuzzy objects and uncertainty. Sincetheories are proposed, more and more scholars have been interested in the soft set theory andits applied research.Later, Maji et al. introduced the concept of fuzzy soft set which is acombination of fuzzy set and soft set.Description logics (DLs for short) are a family of knowledge representation languageswhich can be used to represent the terminological knowledge of an application domain in astructured and formally well-understood way. It have gained considerable attention the lastdecade and have been applied in lots of fields such as software engineering, configuration,conceptual modeling, information integration, query mechanisms, view maintain, softwaremanagement system, canonical system, the layout system and natural language processingand so on. However, with the developing of information technology and intelligencetechnology, a lot of concepts are vague or uncertain data in real life, so Straccia introduced theconcept of fuzzy description logics (FDLs) in order to cope with this, it is the applicationbasis of vague concepts for a new generation of description logic basis.In this paper, firstly, we introduce soft set theory, fuzzy soft set theory, descrption logics,fuzzy description logics and discuss the main part. Secondly, we extend fuzzy soft sets withfuzzy DLs (FDLs), i.e., present an extended fuzzy soft sets theory by using the concepts ofFDLs to act as the parameters of fuzzy soft sets because of the reasoning function of FDLs.Then, we define some operations for the extended fuzzy soft sets. Moreover, we prove threetheorems, including De Morgan’s inclusions and De Morgan’s laws, we prove that thetheorems hold in the extended fuzzy soft set theory with respect to these operations, and wepresent correct proof to prove our definitions are integrated and right. We also believe that theextended fuzzy soft set theory will have more widespread applications on societal or scientificfields.