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

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

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

Consensus building in group decision making based on multiplicative consistency 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.

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

Xu (Int J Approx Reason 36:261---270, 2004) introduced the concepts of incomplete reciprocal relation and additive consistent incomplete reciprocal relation. The aim of this paper is to develop a novel procedure for group decision making with incomplete reciprocal relations. The procedure utilizes each given incomplete reciprocal relation to construct an auxiliary reciprocal relation based on additive transitivity, and then aggregates directly these auxiliary reciprocal relations into a collective auxiliary reciprocal relation. After that, based on the collective auxiliary reciprocal relation, a simple linear system of equations is established for ranking alternatives. Finally, a numerical example is given to illustrate the developed procedure.

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.

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).

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

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.

Monotonicity-based ranking on the basis of multiple partially specified reciprocal relations

Studies in the elderly suggest a reciprocal relation between increased marrow adiposity and bone loss, supporting basic research data indicating that osteoblasts and adipocytes share a common progenitor cell. However, whether this relation represents a preferential differentiation of stromal cells from osteoblasts to adipocytes or whether a passive accumulation of fat as bone is lost and marrow space increases with aging is unknown. To address this question and avoid the confounding effect of bone loss, we examined teenagers and young adults. Using computed tomography, we obtained measurements of bone density and cross-sectional area of the lumbar vertebral bodies and cortical bone area, cross-sectional area, marrow canal area, and fat density in the marrow of the femurs in 255 sexually mature subjects (126 females, 129 males; 15-24.9 yr of age). Additionally, values for total body fat were obtained with dual-energy x-ray absorptiometry. Regardless of gender, reciprocal relations were found between fat density and measures of vertebral bone density and femoral cortical bone area (r = 0.19-0.39; all P values < or = .03). In contrast, there was no relation between marrow canal area and cortical bone area in the femurs, neither between fat density and the cross-sectional dimensions of the bones. We also found no relation between anthropometric or dual-energy x-ray absorptiometry fat values and measures for marrow fat density. Our results indicate an inverse relation between bone marrow adiposity and the amount of bone in the axial and appendicular skeleton and support the notion of a common progenitor cell capable of mutually exclusive differentiation into the cell lineages responsible for bone and fat formation.

The daily reciprocal relations between parental psychological aggression and adolescent anxiety and the heterogeneity, i.e., whether these relations vary across different adolescents, remain unclear. This study examined this issue with a 15-day daily diary study among 326 Chinese adolescents (Mage = 14.53 years, SD = 0.60, 47.2% girls). Dynamic structural equation models revealed that parental psychological aggression co-fluctuated with adolescent anxiety within a day. For lagged associations, only father-driven effects were supported but not mother-driven effects, whereas child-driven effects were supported for both parents. These within-person associations were heterogeneous across adolescents. Moreover, adolescents with more parental psychological aggression reported higher anxiety. This study revealed the reciprocal relations between parental psychological aggression and adolescent anxiety at the micro timescale and also highlighted that the within-person associations were heterogeneous across different adolescents.

A dynamic dual-trust network-based consensus model for individual non-cooperative behaviour management in group decision-making

Workshop report