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A fuzzy ordering on multi-dimensional fuzzy sets induced from convex cones |
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| Authors: | Yuji Yoshida Etienne E. Kerre |
| Affiliation: | a Faculty of Economics and Business Administration, the University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577, Japan;b Department of Applied Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling, Krijgslaan 281 (S9), B-9000, Gent, Belgium |
| Abstract: | A fuzzy ordering for fuzzy sets on is presented by a fuzzy relation on which is induced by closed convex cones. The suitability of the fuzzy order is discussed using the axioms A1–A7 in (Fuzzy Sets and Systems 118 (2001) 375). For fuzzy sets on which are incomparable with respect to the fuzzy order, a method to evaluate the degree of satisfaction regarding the fuzzy order is presented by using a subsethood degree. Approximation by discrete cases is discussed for numerical calculation on the degree of the fuzzy order. Numerical examples are also given to illustrate our idea. |
| Keywords: | Fuzzy partial ordering Fuzzy relation Multi-dimensional fuzzy set Degree of order Convex cone Multi-criteria decision making |
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