FUZZY SOFT ALPHA-OPEN SETS AND FUZZY SOFT ALPHA-CONTINUOUS FUNCTIONS

Abstract

In real life situation, the problems in Economics, Engineering, Social sciences, Medical science etc. do not always involve crisp data. So, we cannot successfully use the traditional classical methods because of various types of uncertainities presented in these problems. To exceed these uncertainities, some kind of theories were given like theory of fuzzy set, intuitionistic fuzzy set, rough set, bipolar fuzzy set, i.e. which we can use as mathematical tools for dealings with uncertainities. But, all these theories have their inherent difficulities. The reason for these difficulties Molodtsov [1] initiated the concept of soft set theory as a new mathematical tool for dealing with uncertainities which is free from the above difficulties. In [1], Molodtsov successfully applied the soft set theory in several directions, such as smoothness of functions, game theory, operations research, Riemann integration, Perron integration, Probability, theory of measurement, and so on. After presentation of the operations of soft sets [8], the properties and applications of soft set theory have been studied increasingily [7, 2]. Xiao et al [4] and Pei and Miao [5] discussed the relationship between soft sets and information systems.