VSOP fuzzy numbers and fuzzy comparison relations

A fuzzy (real) number is usually defined as a normal convex and upper semicontinuous fuzzy set on R. However, the conventional fuzzy numbers do not fulfil some useful algebraic properties, such as axioms for a group. The authors introduce a new fuzzy number system called VSOP (vector set of ordered pairs). VSOP is a natural extension of the conventional fuzzy number, and satisfies the axioms for a ring. Fuzzy comparison relations on VSOP are also introduced. VSOP can be usefully applied to various fuzzy systems, such as fuzzy linear regression analysis, fuzzy linear programming, etc.<
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