Abstract
Let ( L, ≤, ∨, ∧) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by ∨ and ∧ respectively, is studied. We obtain: (i) the necessary and sufficient conditions for S( A,b) ≠ θ; (ii) the necessary conditions for | S( A,b)| = 1. We also obtain the vector x ˜ ∈ L n and prove that it is the largest element of S( A,b) if S( A,b) ≠ θ.
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