Geo-uninorm consistency control module for preference similarity network hierarchical clustering based consensus model

A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures

A least deviation method for priority derivation in group decision making with incomplete reciprocal preference relations

The consistency of reciprocal preference relations is studied. Consistency is related with rationality, which is associated with the transitivity property. For fuzzy preference relations many properties have been suggested to model transitivity and, consequently, consistency may be measured according to which of these different properties is required to be satisfied. However, we will show that many of them are not appropriate for reciprocal preference relations. We put forward a functional equation to model consistency of reciprocal preference relations, and show that self-dual uninorms operators are the solutions to it. In particular, Tanino's multiplicative transitivity property being an example of such type of uninorms seems to be an appropriate consistency property for fuzzy reciprocal preferences.

Consensus building in group decision making based on multiplicative consistency with incomplete reciprocal preference relations

In the former chapters, we have introduced several priority methods for incomplete fuzzy reciprocal preference relations. In this chapter, we introduce another preference relation called hesitant fuzzy reciprocal preference relation and present how to derive the priority weights from incomplete hesitant fuzzy reciprocal preference relations.

A consensus model for group decision making under additive reciprocal matrices with flexibility

Consistency analysis and group decision making based on triangular fuzzy additive reciprocal preference relations

In group decision-making (GDM) model, experts often evaluate their opinion by using triangular fuzzy numbers. The preference relations with triangular fuzzy numbers are in consistent in nature, so we turned to neutrosophic in this paper. It is very important to take into account consistency of expert opinion and consensus degree in GDM. In order to distinguish the typical consistency, the concept of additive approximation consistency is proposed for triangular neutrosophic additive reciprocal matrices. The properties of triangular neutrosophic additive reciprocal matrices with additive approximation consistency are studied in detail. Second, by using $$(n-1)$$ restricted preference values, a triangular neutrosophic additive reciprocal preference relation with additive approximation consistency is constructed. The differences among expert’s opinions are measured using consensus degree. For generating a collective triangular neutrosophic additive reciprocal matrix with additive approximation consistency, the neutrosophic triangular weighted aggregation operator is used. Finally, a novel algorithm for the group decision-making problem with triangular neutrosophic additive reciprocal preference relations is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm.

In this chapter, we propose the eigenvector method (EM) for priority from an incomplete fuzzy reciprocal preference relation. EM is well known for multiplicative preference relation, which was proposed by Saaty (1980). Lipovetsky and Conklin (2002) and Wang and Parkan (2005) investigated the eigenvector problem for complete fuzzy reciprocal preference relation. In the following, we show that the EM can also be used to derive the weights for incomplete fuzzy reciprocal preference relation.

Dynamics of choice during estimation of subjective value

Fuzzy preference relations (Orlovsky 1978) (also known as reciprocal preference relation (Baets et al. 2006; Xu 2007b,f; Xu and Chen 2008b)) and multiplicative preference relations (Saaty 1980) are the most common tools to express the DMs’ preferences over alternatives in decision making. However, sometimes, to get a more reasonable decision result, a decision organization, which contains a lot of DMs (or experts), is authorized to provide the preferences by comparing each pair of alternatives using 0-1 scale, and when providing the degrees to which an alternative is superior to another, it is not very sure about a value but has hesitancy between several possible values. In such cases, these several possible values can be considered as a HFE, and a hesitant fuzzy preference relation is constructed when all the preferences over a set of alternatives are provided (Xia and Xu 2013).

In multiple-attribute decision making, fuzzy theory is very helpful for dealing with the fuzziness widely existing human judgments. Usually, decision makers obtain their subjective opinions by comparing each pair of decision alternatives and then constructing a rational (consistent) judgment matrix, known as a preference relation (PR) (Saaty, 1980; Xu, 1988) to deal with the ranking of alternatives X = {x 1, x 2 ,..., x n } .

Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations

Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making

Group decision making based on the modified probability calculation method and DEA cross-efficiency with probabilistic hesitant fuzzy preference relations