María Teresa Lamata

A new measure of consistency for positive reciprocal matrices

Abstract The analytic hierarchy process (AHP) provides a decision maker with a way of examining the consistency of entries in a pairwise comparison matrix and the hierarchy as a whole through the consistency ratio measure. It has always seemed to us that this commonly used measure could be improved upon. The purpose of this paper is to present an alternative consistency measure and demonstrate how it might be applied in different types of matrices.

The shortest path problem on networks with fuzzy parameters

Shortest path problem where the costs have vague values is one of the most studied problems in fuzzy sets and systems area. However, due to its high computational complexity, previously published algorithms present peculiarities and problems that need to be addressed (e.g. they find costs without an existing path, they determine a fuzzy solution set but do not give any guidelines to help the decision-maker choose the best path, they can only be applied in graphs with fuzzy non-negative parameters, etc.). In this paper, one proposes an iterative algorithm that assumes a generic ranking index for comparing the fuzzy numbers involved in the problem, in such a way that each time in which the decision-maker wants to solve a concrete problem (s)he can choose (or propose) the ranking index that best suits that problem. This algorithm, that solves the above remarked drawbacks, is based on the Ford-Moore-Bellman algorithm for classical graphs, and in concrete it can be applied in graphs with negative parameters and it can detect whether there are negative circuits. For the sake of illustrating the performance of the algorithm in the paper, it has been here developed using only certain order relations, but it is not restricted at all to use these comparison relations exclusively. The proposed algorithm is easy of understanding as the theoretical base of a decision support system oriented to solving this kind of problems.

The concept of conditional fuzzy measure

In this article a concept of conditional fuzzy measure is presented, which is a generalization of conditional probability measure. Its properties are studied in the general case and in some particular types of fuzzy measures as representable measures, capacities of order two, and belief‐plausibility measures. In the case of capacities of order two it coincides with the concept given by Dempster for representable measures. However, it differs from the Dempsters rule for conditioning belief‐plausibility measures. As it is shown, Dempsters rule of conditioning is based on the idea of combining information and our definition is based on a restriction in the set of possible worlds.

Selection of a cleaning system for engine maintenance based on the analytic hierarchy process

Environmental impact assessment is an intrinsically complex multi-dimensional process which involves multiple criteria and multiple actors. Multi-criteria methods can serve as useful decision aids for carrying out environmental impact assessment. This paper proposes the use of a multi-criteria technique, namely the analytic hierarchy process, as a potential decision-making method for use in management maintenance processes. In this case, our problem concerns the selection of a parts cleaning system for diesel engine maintenance. A hierarchical structure is built for the prequalification of the criteria and the alternatives within the system. By applying the analytic hierarchical process, the criteria can be prioritized and the alternatives can be organized in descending order so that the best parts cleaning system may be selected.

MEASURES OF ENTROPY IN THE THEORY OF EVIDENCE

Abstract This paper considers two measures of entropy for the Theory of Evidence and studies their properties. The first measure is based on the measures of entropy and specificity as defined by Yager. The other one may easily be applied to more general classes of fuzzy measures.

A unified approach to define fuzzy integrals

Recently, the two most general and well-known fuzzy integrals (Sugenos integral and Choquets integral) were characterized. It was also shown how both integrals fitted the same formal model, and they only differed in the operators used. In this paper we try to analyze whether it is possible to improve those characterization theorems, and we also study the possibility of defining other fuzzy integrals following the same model but using other operators. In a recent paper, Campos and Bolafios (6) characterized two general and well-known fuzzy integrals: Sugenos integral (11) and Choquets integral (7), the last one also called monotone expectation (2, 4, 5, 6). The two characterization theorems are based on the same formal model of four properties, which only differ in the operators used: sum and product for Choquets integral, maximum and minimum for Sugenos integral. Two important questions remained open: one involved the characterization theorems of these integrals in an attempt to further refine them; the second question was to investigate the possibility of defining other fuzzy integrals using different operators but following the same model. In this paper we give answers to those problems. Section 2 is devoted to describing fuzzy integrals (defined on Sugenos fuzzy measures), particularly Sugenos and Choquets integrals, and their characterizations. In Section 3, we show how the characterization of Choquets integral can be refined, whereas the same cannot be made for Sugenos integral. Finally, other fuzzy integrals fitting our formal model are obtained in Section 4.

A method for improving the consistency of judgements

The Analytic Hierarchy Process provides the decision maker with a method for improving the consistency of pairwise comparison matrices. Although it is one of the most commonly used method it presents some disadvantages related generally with the consistency problem. The purpose of this paper is to provide an alternative method for improving consistency and show how it can be applied to pairwise comparison matrices. The contribution to this method and also its limitations are shown at the end.

Evaluation of suitable locations for the installation of solar thermoelectric power plants

Evaluation of optimal sites to implant solar thermoelectric power plants.Combination of Soft Computing (SC) and Geographic Information Systems (GIS).Multicriteria Decision Making Method MCDM applied.Analytical Hierarchy Process (AHP) method.TOPSIS method, linguistic labels for qualitative criterion modeled by fuzzy numbers. The aim of the present paper is to determine the best location to host a solar thermoelectric power plant. We will seek to show how Geographic Information Systems (GIS) and Multi Criteria Decision Making (MCDM) such as the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS method) and Analytic Hierarchy Process (AHP), are an excellent combination to solve complex locations problems. The coast of the Region of Murcia in the southeast of Spain has been chosen as the study area to carry out this evaluation.The GIS will be shown to be a very useful tool, since GIS are able to generate a database which serves as a starting point for conducting any decision support system. The posed problem will be resolved using restrictions to reduce the area of study, and the criteria that will influence the decision-making. These criteria will be of different natures; with quantitative criteria (numerical values) coexisting with qualitative criteria (labels and linguistic variables). In this article, AHP will be used to obtain the weights of the criteria, and the fuzzy TOPSIS method for the evaluation of the alternatives. In order to compare the results obtained with TOPSIS, the ELECTRE-TRI methodology will be applied.

Classification of fuzzy measures

The aim of this paper is to study several classes of fuzzy measures and the relationships among them. This classification is based on the one due to Banon, but it has some particularities. First new kinds of fuzzy measures are considered. But the most important feature is that the classification is not directly applied to fuzzy measures but to pairs of dual fuzzy measures.

Decision making problems in a general environment

Abstract A general model for decision problems is presented, based on the consideration of an evidence given by a basic probability assignment, which is the information about states of nature. Decision rules are defined in two steps by means of a composition of functions. Firstly, the lower and upper expected values provide limits to the expected utility value for each decision. The function of the second step reflects the decision makers subjectivity and lets us model it between these two boundaries by means of a convex combination. The relationships between evidences and fuzzy measures are shown in Section 2 and some relevants properties of lower and upper expected values are proved in Section 3. In Section 4, a definition of inclusion relation on the set of evidence is used to study existing relations among results which can be obtained from different basic probability assignments, and, finally, we show the way in which our model includes the most classical criteria, such as min-max or mathematical expectation criteria in uncertainty or risk environments.