TOPOLOGICAL SOFT ALGEBRA AND ITS APPLICATION

A soft algebra is an algebraic system <K, +, ., -, 0, 1> defined by Preparata and Yeh. This is an algebra based on fuzzy logic. In this paper, we introduce the closure operation C of a topological space to this <K, +, ., -, 0, 1> and we define a topological soft algebra <K, +, ., -, C, 0, 1>. The main purpose of this paper is to give a positive solution of the word problem in this topological soft algebra. By making use of this result, it is also shown that a kind of decision problem of a modal fuzzy logic is solvable. Furthermore, a solution of this problem is given not only theoretically but as a procedure.