Flexibility Analysis Of Fuzzy Judgement Information And Decision-making Models

In the 1970 s,the American operational research expert Satty proposed the famous decision making methodology of Analytic Hierarchy Process(AHP).Then the methodology has been widely applied in decision-making.In practical decision-making process,the consistency degree of decision maker's opinions or judgements is very important to make the ranking of alternatives being reasonable.Due to the complexity of decision-making environment and the limitations of decision makers' thinking when faced with a complex decision-making problem,it is difficult to provide precise preference values to express the judgements.Therefore,a feasible approach is using interval numbers or other fuzzy numbers to express decision makers' preference information based on the fuzzy set theory proposed by Zadel.Consistency of preference relations is used to describe the consistent logic of decision makers,and inconsistent preference relations could yield a selfcontradictory result.It is an important problem to study the consistency of fuzzy-valued judgement matrices in decision-making.Moreover,the theory of fuzzy sets considers that everything has some elasticity to some extent.When the decision makers use the interval numbers,triangle fuzzy numbers,trapezoidal fuzzy numbers and other fuzzy numbers to represent their preference information,the decision maker's judgment is often flexible.Then it is worth studying how to quantify the flexibility degree of fuzzy numbers.This thesis studies the flexibility of fuzzy judgement information and the decisionmaking models.The main results are given as follows:(1)The flexibility and consistency of interval-valued judgement matrices are analyzed.The existing consistency definitions of interval-valued judgement matrix have been reviewed.The equivalence theorems for two consistency definitions of interval-valued judgement matrices are obtained and the proof of theorems are also given.The observations reveal that the concept of approximate consistency can be used to characterize the flexibility nature of interval-valued preference relations.(2)The factors of affecting the flexibility degree of fuzzy numbers has been analyzed.A new method of quantifying the flexibility degree of triangular and trapezoidal fuzzy numbers are proposed by considering the ?-cut set.And the definitions of flexibility degree of triangular additive and multiplicative reciprocal matrix are provided by considering the effects of applied scale and reciprocity.(3)The FD-IOWA operator is offered to aggregate individual preference information.A novel group decision-making model based on the flexibility degree of triangular fuzzy numbers is proposed,and a new algorithm for decision making problem with flexibility is presented.The studies show that by considering the idea of decision makers' flexibility degree,the uncertainty of real decision-making problem can be captured reasonably.The proposed models and methods enrich the decision-making theory and methodology.