Deriving Priorities from Incomplete Fuzzy Reciprocal Preference Relations Theories and Methodologies

As we know, multiplicative preference relations (or called pairwise comparisons in AHP) were proposed by Dr. Thomas L Saaty. One important work is to derive its priority from pairwise comparisons. It has been proposed many methods to derive priority for multiplicative preference relation. On the basis of fuzzy sets, the fuzzy reciprocal preference relation is proposed and is extended to the incomplete contexts. However, how to derive the priorities from incomplete fuzzy reciprocal preference relations is an interesting and challenging work. This book systematically presents the theories and methodologies for deriving priorities from incomplete fuzzy reciprocal preference relations. This book can be divided into three parts. In the first part, this book introduces the basic concepts of fuzzy reciprocal preference relations and incomplete fuzzy reciprocal preference relations. Then, two consistencies of complete fuzzy reciprocal preference relations are introduced: additive consistency and multiplicative consistency. Then, the relationships between the fuzzy reciprocal elements and the weights are showed. Afterward, in the second part, different priority methods are presented. The inconsistency repairing procedures are also proposed. Last, the priority method for incomplete hesitant fuzzy reciprocal preference relations is presented. This book can be used as a reference for researchers in the areas of management science, information science, systems engineering, operations research, and other relevant fields. It can also be employed as a textbook for upper-level undergraduate students and graduate students.

Chapter 1. Introduction.- Chapter 2. Normalizing Rank Aggregation-based Method.- Chapter 3. Eigenvector Method.- Chapter 4. Logarithmic Least Squares Method.- Chapter 5. A Chi-Square Method.- Chapter 6. A Least Deviation Method.- Chapter 7. Priorities from Fuzzy Best Worst Method Matrix.- Chapter 8. Weighted Least Square Method.- Chapter 9. Priorities from Incomplete Hesitant Fuzzy Reciprocal Preference Relations.

Yejun XU is currently a professor in the College of Management and Economics, Tianjin University, Tianjin China. He received his MS in 2005 and PhD in 2009 both in Management Science and Engineering from Southeast University, China.

He has authored and coauthored more than 120 articles in professional journals, such as European Journal of Operational Research, IEEE Transactions on Cybernetics, IEEE Transactions on Systems, Man, and Cybernetics: Systems, IEEE Transactions on Fuzzy Systems, Fuzzy Sets and Systems, Information Sciences, International Journal of Approximate Reasoning, Knowledge-Based Systems, etc. His research interests include group decision-making under uncertainty.