Fuzzy Implications: Some Recently Solved Problems

In this chapter we discuss some open problems related to fuzzy implications, which have either been completely solved or those for which partial answers are known. In fact, this chapter also contains the answer for one of the open problems, which is hitherto unpublished. The recently solved problems are so chosen to reflect the importance of the problem or the significance of the solution. Finally, some other problems that still remain unsolved are stated for quick reference

Revealed fuzzy preferences

Bondareva O. Revealed fuzzy preferences. Working Papers. Institute of Mathematical Economics. Vol 183. Bielefeld: Center for Mathematical Economics; 1990

Choice procedures in Pairwise Comparison - Multiple-attribute Decision Making Methods

We consider extensions of some classical rational axioms introduced in conventional choice theory to valued preference relations. The concept of kernel is revisited using two ways: one proposes to determine kernels with a degree of qualification and the other presents a fuzzy kernel where every element of the support belongs to the rational choice set with a membership degree. Links between the two approaches is emphasized. We exploit these results in Multiple-attribute Decision Aid to determine the good and bad choices. All the results are valid if the valued preference relations are evaluated on a finite ordinal scale.