This book provides in-depth coverage of the most important results about fuzzy logic including negations, conjunctions, disjunctions, implications and gives the interrelations between those different connectives. The work brings together multiple resultsabout valued binary relations satisfying diverse transitivity-type conditions.The authors propose the first sound introduction to valued preference modelling through the systematic use of fuzzy set theory and functional equations and derive the possible foundations for multicriteria decision aid using aggregation, ranking and choice procedures on the basis of axiomatic results. The text presents a unified view of various multicriteria decision making tools that have been independently derived in the past, dealing with pairwise comparisons. The monograph is mathematically oriented but the results will be of the greatest interest for engineers and economists who design and implement decision support systems in practice. It is also supplied with a sufficient number of examples to make it attractive to nonspecialists.