Modeling action-interdependence in multiple criteria decision making

A problem of subset selection when actions are interdependent is formulated within a multiple criteria framework. More specifically, a novel definition and characterization of interdependence of actions applicable to Multiple Criteria Decision Making (MCDM) are presented. The effects of interdependence of actions on the modeling and resolution of a subset choice problem are shown, and the importance of taking interdependence of actions into account is discussed. Most of the discussion is generalized to independence and interdependence of sets of actions, which are then compared to the case of individual actions. A general approach to evaluate a combination of interdependent actions is proposed and the use of the multiple criteria structure to eliminate some difficulties in evaluating a set of interdependent actions is explained.     

On redundancy in multi criteria decision making

The concept of redundancy is accepted in Operations Research and Information Theory. In Linear Programming, a constraint is said to be redundant if the feasible decision space is identical with or without the constraint. In Information Theory, redundancy is used as a measure of the stability against noise in transmission. Analogies with Multi Criteria Decision Making (MCDM) are indicated and it is argued that the redundancy concept should be used as a regular feature in conditioning and analysis of Multi Criteria Programs. Properties of a proposed conflict-based characterisation are stated and some existence results are derived. Redundancy is here intended for interactive methods, when the efficient set is progressively explored. A new redundancy test for the linear case is formulated from the framework. A probabilistic method based on correlation is proposed and tested for the non-linear case. Finally, some general guidelines are given concerning the redundancy problem.     

Multiple criteria decision making with interactive over-achievement programming

Whereas in goal programming the under-achievement with respect to (usually) unattainable goals are minimized, we propose the maximization of the over-achievements with respect to feasible goals or required values. An interactive algorithm, in which the over-achievements are maximized via a barrier function, is presented to implement the proposed approach.     

Hesitant fuzzy Bonferroni means for multi-criteria decision making

Due to the desirable characteristic of the Bonferroni mean (BM) that it can capture the interrelationship between input arguments, and in order to provide the properties and the modelling capability of the BMs under hesitant fuzzy environment, we explore some new hesitant fuzzy Bonferroni means (HFBMs). The properties and the special cases of HFBMs are studied in detail. We specially define a concept of hesitant Bonferroni element (HBE), which is considered as a ‘bonding satisfaction’ factor used as a calculation unit in the HFBM. The HBE can reflect the correlation between hesitant fuzzy arguments, which makes the HFBM have particular advantages in aggregating arguments. In addition, the weighted hesitant fuzzy Bonferroni mean (WHFBM) is also proposed considering different importance degrees of input arguments. Furthermore, the procedure of multi-criteria decision making based on the WHFBM is given under hesitant fuzzy environment as typical applications, which has much sense in theory and practice for the BM.     

Preference relations on actions and criteria in multicriteria decision making

Let A be a finite set of feasible actions which are judged following several criteria. An outranking relation is defined on A by considering preference of the decision maker as a weak order on each criterion and the relation among criteria as a semi-order on the given set of criteria.Several ways of constructing outranking relations have been proposed. One of the most popular, introduced by B. Roy, for instance ELECTRE(s), is based on the use of weights related to criteria. In our approach, the knowledge of weights is replaced by the existence of a semi-order.A case study is developed. It deals with a computer selection problem.     

Multiple criteria decision making combined with finance: A categorized bibliographic study

This paper provides a categorized bibliography on the application of the techniques of multiple criteria decision making (MCDM) to problems and issues in finance. A total of 265 references have been compiled and classified according to the methodological approaches of goal programming, multiple objective programming, the analytic hierarchy process, etc., and to the application areas of capital budgeting, working capital management, portfolio analysis, etc. The bibliography provides an overview of the literature on “MCDM combined with finance,” shows how contributions to the area have come from all over the world, facilitates access to the entirety of this heretofore fragmented literature, and underscores the often multiple criterion nature of many problems in finance.     

Planning federal public investment in Mexico using multiobjective decision making

The scope of this article is showing how multicriteria decision making can be anefficient tool to manage public investment planning in complex situations. Forthis aim, we will analyse the problem in all its aspects: building the modelfrom data using econometrical tools, solving the resulting highly complex modelusing modern efficient techniques (multiobjective meta-heuristics) and helpingthe decision maker to introduce his preferences in order to achieve the mostpreferred solution. This holistic approach let us provide an efficient solutionto a complex public investment planning situation, improving the current stateof the country relating not only economical aspects, but also social and humandevelopment aspects. The real situation studied is focused on Mexico, where, inrecent decades, has undergone remarkable improvements in terms of economicgrowth, which has not been matched by significant improvements in several otherbasic aspects of human development, nor by reductions in regional inequalities.This suggests the need to establish policies aimed at improving these aspectsand reducing inequalities. Federal public investment is an important tool inregional policy to promote and improve these aspects; so we introduce amultiobjective programming problem for planning federal public investment inMexico. This model will focus on improving national levels in four maindimensions of human development (economic growth, education, health andhousing), and on reducing regional inequalities for those dimensions.     

Complete intersections and rational equivalence

A new criterion for rational equivalence of cycles on a projective variety over an algebraically closed field is given, and some consequences considered.     

Regularized estimation for preference disaggregation in multiple criteria decision making

Disaggregation methods have been extensively used in multiple criteria decision making to infer preferential information from reference examples, using linear programming techniques. This paper proposes simple extensions of existing formulations, based on the concept of regularization which has been introduced within the context of the statistical learning theory. The properties of the resulting new formulations are analyzed for both ranking and classification problems and experimental results are presented demonstrating the improved performance of the proposed formulations over the ones traditionally used in preference disaggregation analysis.     

The SIR method: A superiority and inferiority ranking method for multiple criteria decision making

In this paper, a superiority and inferiority ranking (SIR) method is proposed. This new method uses two types of information, the superiority and the inferiority information, to derive two types of flows, the superiority flow and the inferiority flow, by which the set of alternatives are ranked partially or completely. Relationships between the SIR method and some of the classical multiple criteria decision making (MCDM) methods (such as SAW, TOPSIS and PROMETHEE) are explored. It is proved that the SIR method is a significant extension of the well-known PROMETHEE method.     

Decision-aid for discrete multiple criteria decision making problems with imprecise data

We describe ways of aiding decision making with a discrete set of alternatives. In many decision situations, it is not possible to obtain explicit preference information from the decision makers. Instead, useful decision-aid can be provided to the decision makers by describing what kind of weighting of the criteria result in certain choices of the alternatives. The suggested treatment is based on the basic ideas of the ELECTRE III method. The modelling of the preferences by pseudo-criteria is especially helpful in case the data, that is, the criterion values are imprecise. Unlike ELECTRE III, no ranking of the alternatives is produced. Based on a minimum-procedure in the exploitation of the outranking relations, we provide information about the weights of the criteria that make a certain alternative the best. We also present an interactive searching procedure in the weighting space. The auxiliary optimization problems to be solved are nondifferentiable. Cases with both single and multiple decision makers are considered.     

An action learning evaluation procedure for multiple criteria decision making problems

In this paper we focus on an extension of the Analytic Hierarchy Process (AHP) that accommodates ambiguity on the part of the decision maker (DM), and facilitates the exploration of the decision domain. We propose a systematic action learning process that builds confidence as it converges from numeric interval estimates to numeric point estimates. Our Multiple Criteria Decision Making (MCDM) problem procedure structures the problem as a hierarchy, evaluates all objects using pairwise comparisons that accommodate vagueness and ambiguity, uses interval prioritization techniques, and does synthesis using the linear additive value function. This action learning process facilitates the understanding of key stakeholders, which is imperative for the successful implementation of the subsequent decision.     

Using interdependent information on the relative importance of criteria in decision making

A multicriteria choice problem is considered. The Edgeworth-Pareto principle is established under the assumption that certain axioms hold true. Quantitative interdependent information on the relative importance of two groups of criteria is used to derive upper bounds for the unknown set of selected vectors.     

Revising the OWA operator for multi criteria decision making problems under uncertainty

Multi criteria decision making (MCDM) problems are usually under uncertainty. One of these uncertain parameters is the decision maker (DM)’s degree of optimism, which has an important effect on the results. Fuzzy linguistic quantifiers are used to obtain the assessments of this parameter from DM and then, because of its uncertainty it is assumed to have stochastic nature. A new approach, entitled FSROWA, is introduced to combine the Fuzzy and Stochastic features into a Revised OWA operator.     

An integrated multiple criteria decision making model applying axiomatic fuzzy set theory

This article presents a hybrid model for the multiple criteria decision making problems. The proposed decision model consists of three parts: (i) DEA (data envelopment analysis) is used to provide the best combination on the performance parameters of original data; (ii) By the application of AFS (axiomatic fuzzy set) theory and AHP (analytic hierarchy process) method, the weight of each attribute is calculated and (iii) TOPSIS (technique for order preference by similarity to ideal solution) is applied to provide the ranking order of that best combination based on the weights of attributes. In addition, we also provide the definitely semantic interpretations for the decision results by AFS theory. Specially, the model not only employs the performance parameters from raw data, but also considers the preferences from decision-makers that can make the decision results more reasonable. The proposed model is used for robot selection to verify the proposed model. Using the selection index, the evaluation of alternative robots and the selection of the most appropriate are eventually feasible. Moreover, a numerical example for supplier selection is included to illustrate the application of the model for the newly developed problems.     

Conditional identity calculus and conditioned rational equivalence

We construct a conditional identity calculus (similar to the Birkhoff identity calculus), which complies with the concept of truth for a conditional identity on a universal algebra. The relationship is studied between the isomorphism of embedding categories of conditional varieties and the conditioned rational equivalence of these varieties. As applications, we describe invariants for the relations ‘is conditional rational equivalent’ and ‘is similar’ on finite universal algebras. Supported by RFFR grant No. 93-01-01520. Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 432–459, July–August, 1998.     

Dynamic multiple criteria decision making in changeable spaces: from habitual domains to innovation dynamics

Human behaviors involve dynamic, evolving, interactive and adaptive processes. Important decision makings usually are dynamic, involving multiple criteria in changeable spaces. This article introduces the behavior mechanism that integrates the findings of neural science, psychology, system science, optimization theory and multiple criteria decision making. It shows how our brain and mind operate and describes our behaviors and decision making as dynamic processes of multiple criteria decision making in changeable spaces. Unless extraordinary events occur or special effort exerted, the dynamic processes will be stabilized in certain domains, known as Habitual Domains. Habitual Domains, which play a vital role in upgrading the quality of our decision making and lives, will be explored. In addition, as important consequential derivatives, concepts of Competence Set Analysis and Innovation Dynamics will also be discussed. Note that these concepts involve transitions between dynamic and static states.