Fuzzy Soft Set And Its Application In Decision Making

Fuzzy set and soft set are important theories and tools, they are applied widely in intelligentinformation processing. Fuzzy soft set is the new concept which has advantages in fuzzy set andsoft set, there has been some research results.The paper mainly discusses research on the new operations of fuzzy soft, fuzzy interval soft、interval-valued fuzzy soft set、soft-rough fuzzy set and their application in decision making. Thespecific work is as follows:(1) The new concept and some relative therom of null fuzzy soft sets are gived; the newcomplement and generalized extended intersection operations of fuzzy soft set are proposed, andrelationship with preexisting operations is discussed;“generalized and” operation and “generalizedor” operation are proposed, and their algebraic properties are dicussed.(2) The notion of fuzzy interval soft set is introduced, basic algebra operations areinvestigated and the relationship among interval-valued soft set, vague soft set and fuzzy intervalsoft set is discussed. Meanwhile, through importing the definitions of interval-valued fuzzy soft setof synthetic operation and interval-valued fuzzy soft set comparison matrix, then a new decisionmethod is proposed, and the method is applied to the decision making case.(3) Through delimiting soft fuzzy decision system and decision classified fuzzy soft setdependent degree, fuzzy knowledge express system is analyzed with soft-rough fuzzy set. Theconcepts of significance of condition bijective soft set with respect to decision classified fuzzy softset, reduction of soft fuzzy decision system, decision rules in soft fuzzy decision system and so onare defined. By these notions, an algorithm of decision making based on soft-rough fuzzy set ispresented, and an example is given to show the feasibility of the method.