Deriving Priorities from Incomplete Fuzzy Reciprocal Preference Relations

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Multiplicative preference relations, also known as pairwise comparisons in AHP, were introduced by Dr. Thomas L. Saaty, with a significant focus on deriving priorities from these comparisons. Various methods have emerged for this purpose, including the fuzzy reciprocal preference relation, which has been adapted for incomplete contexts. The challenge of deriving priorities from incomplete fuzzy reciprocal preference relations is both intriguing and complex. This work systematically explores the theories and methodologies for this derivation, structured into three main parts. The first part covers the fundamental concepts of fuzzy reciprocal preference relations and their incomplete counterparts, introducing two types of consistencies: additive and multiplicative. It also examines the relationships between fuzzy reciprocal elements and weights. The second part presents various priority methods, along with inconsistency repair procedures. Finally, the book addresses priority methods for incomplete hesitant fuzzy reciprocal preference relations. It serves as a valuable reference for researchers in management science, information science, systems engineering, and operations research, and can also function as a textbook for upper-level undergraduate and graduate students.