Incomplete pairwise comparison and consistency optimization

This paper proposes a new method for calculating the missing elements of an incomplete matrix of pairwise comparison values for a decision problem. The matrix is completed by minimizing a measure of global inconsistency, thus obtaining a matrix which is optimal from the point of view of consistency with respect to the available judgements. The optimal values are obtained by solving a linear system and unicity of the solution is proved under general assumptions. Some other methods proposed in the literature are discussed and a numerical example is presented.consistency, pairwise comparison matrices

Group decision-making based on heterogeneous preference relations with self-confidence

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Preference relations are very useful to express decision makers’ preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing preference relations. In this study, we define the preference relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the preference relation with self-confidence. Furthermore, we present a two-stage linear programming model for estimating the collective preference vector for the group decision-making based on heterogeneous preference relations with self-confidence. Finally, numerical examples are used to illustrate the two-stage linear programming model, and a comparative analysis is carried out to show how self-confidence levels influence on the group decision-making results

Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods

On the priority vector associated with a fuzzy preference relation and a multiplicative preference relation.

We propose two straightforward methods for deriving the priority vector associated with a fuzzy preference relation. Then, using transformations between multiplicative preference relations and fuzzy preference relations, we study the relationships between the priority vectors associated with these two types of preference relations.pairwise comparison matrix; fuzzy preference relation; priority vector

Modelling Group Decision Making Problems in Changeable Conditions

The aim of this paper is to present a new group decision making model with two important characteristics: i) we apply mobile technologies in the decision process and ii) the set of alternatives is not constant through time.We implement a prototype of a mobile decision support system based on changeable sets of alternatives. Using their mobile devices (as mobile phones or PDAs), experts can provide/receive information in anywhere and anytime. The prototype also incorporates a new system to manage the alternatives and thus, to give more realism to decision processes allowing to manage changeable set of alternatives, focussing the discussion in a subset of them that changes in each stage of the process.FEDER funds in FUZZYLING project (TIN2007-61079)PETRI project (PET2007-0460)Ministry of Public Works (90/07)Excellence Andalusian Project (TIC5299

Group decision making with incomplete reciprocal preference relations based on multiplicative consistency

This paper comprises a new iterative method for multi-person decision making based on multiplicative consistency with incomplete reciprocal preference relations (IRPRs). Additionally, multiplicative transitivity property of reciprocal preference relation (RPR) is used at the first level to estimate the unknown preference values and get the complete preference relation, then it is confirmed to be multiplicative consistent by using transitive closure formula. Following this, expert's weights are evaluated by merging consistency and trust weights. The consistency weights against the experts are evaluated through multiplicative consistency investigation of the preferences given by each expert, while trust weights play the role to measure the level of trust for an expert. The consensus process determines whether the selection procedure should start or not. If it results in negative, the feedback mechanism is used to enhance the consensus degree. At the end, a numerical example is given to demonstrate the efficiency and practicality of the proposed method

On the normalization of a priority vector associated with a reciprocal relation.

In this paper we show that the widely used normalization constraint SUM(i=1,n) wi = 1 does not apply to the priority vectors associated with reciprocal relations, whenever additive transitivity is involved. We show that misleading applications of this type of normalization may lead to unsatisfactory results and we give some examples from the literature. Then, we propose an alternative normalization procedure which is compatible with additive transitivity and leads to better results.reciprocal relation; fuzzy preference relation; priority vector; normalization

A comparative analysis between two statistical deviation–based consensus measures in group decision making problems

The mean absolute deviation and the standard deviation, two statistical measures commonly used in quantifying variability, may become an interesting tool when defining consensus measures. Two consensus indexes which obtain the level of consensus in some problems of Group Decision Making are introduced in this paper by expanding the aforementioned statistical concepts. A comparative analysis reveals that the levels of consensus derived from these indexes are close to those obtained employing distance functions when a fuzzy preference relations frame is considered, so they turn out to be a useful tool in this context. In addition, these indexes are different from each other and with the distance functions considered. Thus, they are applicable tools in the calculation of consensus in our context and are different from those commonly used