A detailed perspective on restricted and extended intersection, union and difference soft set operations

Inthisthesis, restrictedandextendedintersection, restrictedandextendedunion, andrestrictedandextendeddifferenceoperations, thebasicsoft set operations, areinvestigated in detailbyaddingmanynewpropertiestotheexistingones in the literatüre. Byhandlingthedistributions of theseoperationsoverallothersoft set operations, includingallnewlydefinedsoft set operations. it is examinedin fulldetailwhichalgebaricstructurestheseoperationsalongwithsoftsets form in the set of softsetsovertheuniverseUand in the set of softsetswith a fixedparameterset. Also,somemathematicalerrors in somestudies in theliteratüre regardingthesetopicsarecorrected. Thisthesisconsists of sixsections. Inthefirstsection, a detailedliteraturereview is made on softsets, soft set operations, andsomealgebraicstructures. Inthesecondsection, basicconceptsaboutclassical set operations, algebraicstructuresandsoftsetswhichareusedthroughoutthisthesisarepresented. Inthethirdsection, alltheproperties of therestrictedandextendedintersectionoperations; in thefourthsection, therestrictedandextendedunionoperations; in thefifthsection, therestrictedandextendeddifferenceoperationareexaminedandconsideringthequestion of theproperties of intersection, unionanddifferenceoperations in classicalsetshaveanalogy on thesoft set operations, manynewpropertiesaregivenregardingthesesoft set operationsandpresentedwithdetailedproofs. Inaddition, in ordertoseewhichalgebraicstructuresthesebasicsoft set operations formtogetherwithsoftsets, thedistribution of eachoperationtoallothersoft set operationsareexamined, and itisobservedthatthesoftsets as alongwiththesesoft setoperationscreate a widevariety of algebaricstructures in the set of softsetsovertheuniverseUand in the set of softsetswith a fixedparameterset,such as monoid, bounded semi-lattice, group, semi ring, hemiring, zero-symmetricright semi-near-ring, boundeddistributivelattice, Boolean ring Boolalgebra, De Morgan Algebra, KleeneAlgebra, Stone algebra, MV-algebra, BCK-algebra, whicharegivencollectively in theconclusionsection of thisthesis.Since there is nocomprehensivestudy in theexistingliterature, whichincludesallotherstudiesmade in thisfield, webelievethatthisthesiswillserve as a handbookforthosewho start tostudysoft set theoryandwillfillthisgap in theliteratüre in thisregard.