Incomplete Fuzzy Preference Research Articles

A new group decision making approach based on incomplete probabilistic dual hesitant fuzzy preference relations

As an enhanced version of probabilistic hesitant fuzzy sets and dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets (PDHFSs) combine probabilistic information with the membership degree and non-membership degree, which can describe decision making information more reasonably and comprehensively. Based on PDHFSs, this paper investigates the approach to group decision making (GDM) based on incomplete probabilistic dual hesitant fuzzy preference relations (PDHFPRs). First, the definitions of order consistency and multiplicative consistency of PDHFPRs are given. Then, for the problem that decision makers (DMs) cannot provide the reasonable associated probabilities of probabilistic dual hesitant fuzzy elements (PDHFEs), the calculation method of the associated probability is given by using an optimal programming model. Furthermore, the consistency level for PDHFPRs is tested according to the weighted consistency index defined by the risk attitude of DMs. In addition, a convergent iterative algorithm is proposed to enhance the unacceptable consistent PDHFPRs’ consistency level. Finally, a GDM approach with incomplete PDHFPRs is established to obtain the ranking of the alternatives. The availability and rationality of the proposed decision making approach are demonstrated by analyzing the impact factors of haze weather.

Two new methods for decision-making with incomplete reciprocal fuzzy preference relations based on additive consistency

ABSTRACT In this paper, we propose two new methods to solve the problem of incomplete reciprocal fuzzy preference relations. Sometimes decision-maker(s) might not be able to provide complete information about their preferences on the alternatives. In general, an incomplete preference relation can be completed if at least a set of nonleading diagonal preference values are known and each one of the alternatives is compared directly or indirectly at least once. However, this is not always the case. Sometimes, the decision-maker(s) might not be able to provide any information with regards to at least one of the alternatives, which is called the ignorance situation. We propose two new methods based on additive consistency for solving these two problems in a multi-attributes/group decision-making environment. The first method is based on a system of equations, which is suitable for estimating missing information in the general case. The second method, which is an extension of the system of equations, utilizes a goal programming model to address the ignorance situations. Our validation of these two methods shows that the proposed methods generate a high consistency level irrespective of the nature of the problem under study. The proposed methods outperform other comparable methods without a need to modify or change the original decision-maker(s) preferences.

An Interactive Consensus Model for Group Decision-Making with Incomplete Multi-Granular 2-Tuple Fuzzy Linguistic Preference Relations

As a result of the heterogeneity of decision-makers, it is more suitable to use multi-granular linguistic information to express assessing information over alternatives for decision-makers. Decision-makers may only provide partial preference information as the limitation of knowledge over the alternatives. Thus, the incomplete multi-granular 2-tuple fuzzy linguistic preference relations (IMGFLPRs) can be applied to manage the GDM problems in complex environments. In this paper, we propose a novel group decision-making (GDM) model based on mathematical programming with IMGFLPRs. It is more important that the proposed mathematical programming can directly deal with IMGFLPRs and does not need to be converted into a uniform form. By this means, we construct a consensus reaching process based on IMGFLPRs, considering simultaneously dynamic adjustment of experts’ weight. Finally, an emergency plan selection problem is solved by the proposed model, which shows the result of GDM is effectiveness.

Addressing consistency and consensus with group decision support model based on incomplete hesitant fuzzy linguistic preference relations

Addressing consistency and consensus with group decision support model based on incomplete hesitant fuzzy linguistic preference relations

Some methods to deal with unacceptable incomplete 2-tuple fuzzy linguistic preference relations in group decision making

In this paper, we first propose a four-way procedure to estimate missing preference values when dealing with acceptable incomplete 2-tuple fuzzy linguistic preference relations (FLPRs). The proposed revised procedure can estimate more missing elements in the first iteration and also has more advantages than the existing methods. Then, we address situations in which an expert do not provide any comparison information for a particular alternative with other alternatives, and thus provides an unacceptable incomplete 2-tuple FLPR. We propose some methods to deal with the unacceptable situations. The main idea of these methods is to set some seed values for the unknown alternative and then to complete the unacceptable incomplete 2-tuple FLPRs by the revised procedure. We also give a simple algorithm to select the best alternative for the group decision making (GDM) problem with incomplete 2-tuple FLPRs. The analysis of advantages and drawbacks for each method are also presented.

A GOAL PROGRAMMING APPROACH TO GROUP DECISION MAKING WITH INCOMPLETE FUZZY AND INTERVAL PREFERENCE RELATIONS

In order to solve group decision making (GDM) problems where the preference relations are provided by decision makers with incomplete fuzzy and interval numbers, this paper develops a GDM approach on the basis of multiple objective optimization and goal programming methods. The proposed approach first analyzes the two types of preference relations and then builds their respective optimization models. Subsequently, an integrated programming model combining the two preference relations is developed to minimize the inconsistency among the decision makers' opinions. By solving the programming model, the ranking of alternatives or selection of the most desirable alternative can be obtained using the intermediate priority vector. Two numerical examples including incomplete fuzzy and interval preference relations are examined to illustrate and show the applicability of the proposed approach.

Incomplete interval-valued intuitionistic fuzzy preference relations

The aim of this paper is to investigate decision making problems with interval-valued intuitionistic fuzzy preference information, in which the preferences provided by the decision maker over alternatives are incomplete or uncertain. We define some new preference relations, including additive consistent incomplete interval-valued intuitionistic fuzzy preference relation, multiplicative consistent incomplete interval-valued intuitionistic fuzzy preference relation and acceptable incomplete interval-valued intuitionistic fuzzy preference relation. Based on the arithmetic average and the geometric mean, respectively, we give two procedures for extending the acceptable incomplete interval-valued intuitionistic fuzzy preference relations to the complete interval-valued intuitionistic fuzzy preference relations. Then, by using the interval-valued intuitionistic fuzzy averaging operator or the interval-valued intuitionistic fuzzy geometric operator, an approach is given to decision making based on the incomplete interval-valued intuitionistic fuzzy preference relation, and the developed approach is applied to a practical problem. It is worth pointing out that if the interval-valued intuitionistic fuzzy preference relation is reduced to the real-valued intuitionistic fuzzy preference relation, then all the above results are also reduced to the counterparts, which can be applied to solve the decision making problems with incomplete intuitionistic fuzzy preference information.