Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

Decision making and Atanassov's approach to fuzzy sets

In this paper we stress the role that decision making, and therefore an underlying binary (bipolar) approach, plays in Atanassov's intuitionistic view of fuzzy sets. Moreover, we point out that such a bipolar view can be found in classical multicriteria models

Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches

Multi-criteria decision analysis studies decision problems in which the alternatives are evaluated on several dimensions or viewpoints. In the problems we consider in this paper, the scales used for assessing the alternatives with respect to a viewpoint are bipolar and univariate or unipolar and bivariate. In the former case, the scale is divided in two zones by a neutral point; a positive feeling is associated to the zone above the neutral point and a negative feeling to the zone below this point. On unipolar bivariate scales, an alternative can receive both a positive and a negative evaluation, reflecting contradictory feelings or stimuli. The paper discusses procedures and models that have been proposed to aggregate multi-criteria evaluations when the scale of each criterion is of one of the two types above. We present both a constructive and a descriptive view on this question; the descriptive approach is concerned with characterizations of models of preference, while the constructive approach aims at building preferences by questioning the decision maker. We show that these views are complementary.Multiple criteria, Decision analysis, Preference, Bipolarmodels, Choquet integral

Modelling multicriteria value interactions with Reasoning Maps

Idiographic causal maps are extensively employed in Operational Research to support problem structuring and complex decision making processes. They model means-end or causal discourses as a network of concepts connected by links denoting influence, thus enabling the representation of chains of arguments made by decision-makers. There have been proposals to employ such structures to support the structuring of multicriteria evaluation models, within an additive value measurement framework. However, a drawback of this multi-methodological modelling is the loss of richness of interactions along the means-end chains when evaluating options. This has led to the development of methods that make use of the structure of the map itself to evaluate options, such as the Reasoning Maps method, which employs ordinal scales and ordinal operators for such evaluation. However, despite their potential, Reasoning Maps cannot model explicitly value interactions nor perform a quantitative ranking of options, limiting their applicability and usefulness. In this article we propose extending the Reasoning Maps approach through a multilinear evaluation model structure, built with the MACBETH multicriteria method. The model explicitly captures the value interactions between concepts along the map and employs the MACBETH protocol of questioning to assess the strength of influence for each means-end link. The feasibility of the proposed approach to evaluate options and to deal with multicriteria interactions is tested in a real-world application to support the construction of a population health index

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences

Network Analysis, Creative System Modelling and Decision Support: The NetSyMoD Approach

This paper presents the NetSyMoD approach – where NetSyMod stands for Network Analysis – Creative System Modelling – Decision Support. It represents the outcome of several years of research at FEEM in the field of natural resources management, environmental evaluation and decision-making, within the Natural Resources Management Research Programme. NetSyMoD is a flexible and comprehensive methodological framework, which uses a suite of support tools, aimed at facilitating the involvement of stakeholders or experts in decision-making processes. The main phases envisaged for the process are: (i) the identification of relevant actors, (ii) the analysis of social networks, (iii) the creative system modelling and modelling of the reality being considered (i.e. the local socio-economic and environmental system), and (iv) the analysis of alternative options available for the management of the specific case (e.g. alternative projects, plans, strategies). The strategies for participation are necessarily context-dependent, and thus not all the NetSyMod phases may be needed in every application. Furthermore, the practical solutions for their implementation may significantly differ from one case to another, depending not only on the context, but also on the available resources (human and financial). The various applications of NetSyMoD have nonetheless in common the same approach for problem analysis and communication within a group of actors, based upon the use of creative thinking techniques, the formalisation of human-environment relationships through the DPSIR framework, and the use of multi-criteria analysis through the mDSS software.Social Network, Integrated Analysis, Participatory Modelling, Decision Support

The Encyclopedia of Neutrosophic Researchers - vol. 3

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements