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Topological soft algebra and its application. (English) Zbl 0769.03034

Preparata and Yeh introduced the concept of a soft algebra, which is an algebraic system \(\langle K,+,\cdot,-,0,1\rangle\), and which is an algebra based on fuzzy logic. In this paper, the author proposes a soft algebra with closure operation (shortly, a topological soft algebra); some properties of such a system are proved and it is shown that the word problem of topological soft algebra is solvable; finally this result is used to show that a kind of decision problem of a modal fuzzy logic is solvable; furthermore, a solution to this problem is given not only theoretically but also as a procedure.

MSC:

03G25 Other algebras related to logic
03B52 Fuzzy logic; logic of vagueness
03D40 Word problems, etc. in computability and recursion theory
22A30 Other topological algebraic systems and their representations
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References:

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