Bipolar fuzzy soft algebraic structures and their actions on certain fields

Abstract

We have applied the concept of soft set theory into bipolar fuzzy soft newlinesubstructures of G - near ring and study their properties. We have also newlineconstructed the bipolar fuzzy soft product, bipolar fuzzy soft characteristic newlinefunction, bipolar fuzzy soft G - ideals of G - near ring and also the newlineinterrelations of them has been presented. Certain kind of G - near ring are newlinecharacterized in terms of the bipolar fuzzy soft ideals of G - near ring. Thus, newlinethe bipolar fuzzy soft normal G - near ring is being defined and some newlinecharacterizations of the G - near ring with soft normality are being given. newlineWe study bipolar smooth fuzzy soft subgroups and investigate relations newlinewith bipolar smooth fuzzy soft cosets and normal soft subgroups. Then we newlinedefine normalizer and give some theorems relative to these concepts. newlineWe define a new kind of fuzzy set which bipolar smooth fuzzy soft set newlineby combining the fuzzy star shaped set and bipolar smooth fuzzy soft set. By newlinethe basic definition of bipolar smooth fuzzy soft star shaped set, we discuss the newlinerelationships among these different types of star shapedness and obtain some newlineproperties. Finally, we investigate (a,b ) -level bipolar smooth fuzzy soft set newlineand its properties. newlineThe notion of bipolar fuzzy soft sets, the idea of a bipolar d - fuzzy newlinesoft groupoid in a given set d and related properties are investigated. Bipolar newlinefuzzy soft groupoid is also constructed by using bipolar fuzzy soft groupoid. newlineConversely bipolar d - fuzzy soft groupoid is established by the way of bipolar newlinefuzzy soft groupoid. The characterisations of bipolar d - fuzzy soft groupoid is newlineprovided and normal bipolar d - fuzzy soft groupoid are discussed. Finally the newlinedecision making approach for bipolar d - fuzzy soft set is to be analysed with newlinea suitable example. newlineThe Bipolar fuzzy soft techniques represent the recruitment of Assistant newlineProfessor as a multi-criteria group decision making process which involves newlinesubjectivity, imprecision and fuzziness. newline