BL-Algebras Based on Soft Set Theory

Abstract

Abstract. Molodtsov introduced the concept of soft sets, which can be seen as a newmathematical tool for dealing with uncertainty. In this paper, we initiate the study ofsoft BL-algebras by using the soft set theory. The notion of lteristic soft BL-algebras isintroduced and some related properties are investigated. 1. IntroductionTo solve complicated problems in economics, engineering, and environment, wecannot successfully use classical methods because of various uncertainties typicalfor those problems. There are three theories: theory of probability, theory of fuzzysets, and the interval mathematics which we can consider as mathematical toolsfor dealing with uncertainties. But all these theories have their own difficulties.Uncertainties cannot be handled using traditional mathematical tools but may bedealt with using a wide range of existing theories such as probability theory, theoryof (intuitionistic) fuzzy sets, theory of vague sets, theory of interval mathematics,and theory of rough sets. However, all of these theories have their own difficultieswhich have been pointed out in [12]. Maji et al. [10] and Molodtsov [12] sug-gested that one reason for these difficulties may be due to the inadequacy of theparametrization tool of the theory. To overcome these difficulties, Molodtsov [12]introduced the concept of soft set as a new mathematical tool for dealing with un-certainties that is free from the difficulties that have troubled the usual theoreticalapproaches. Molodtsov pointed out several directions for the applications of softsets. At present, research on the soft set theory is progressing rapidly. Maji etal. [11] described the application of soft set theory to a decision making problem.They also studied several operations on the theory of soft sets. The most appro-