Aggregation of fuzzy preference relations to multicriteria decision making

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed fuzzy preference relation includes t-norms and t-conorms to take into account the relation between the criteria importance. Properties of the composition and new relation, giving a possibility to make a consistent choice or to rank the alternatives, are proved. An illustrative numerical study and comparative examples are presented.     

How to treat strict preference information in multicriteria decision analysis

This paper addresses the use of incomplete information on both multi-criteria alternative values and importance weights in evaluating decision alternatives. Incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds. En route to prioritizing alternatives, the majority of previous studies have replaced these strict inequalities with weak inequalities, by employing a small positive number. As this replacement closes the feasible region of decision parameters, it circumvents certain troubling questions that arise when utilizing a mathematical programming approach to evaluate alternatives. However, there are no hard and fast rules for selecting the factual small value and, even if the choice is possible, the resultant prioritizations depend profoundly on that choice. The method developed herein addresses and overcomes this drawback, and allows for dominance and potential optimality among alternatives, without selecting any small value for the strict preference information. Given strict information on criterion weights alone, we form a linear program and solve it via a two-stage method. When both alternative values and weights are provided in the form of strict inequalities, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve this linear program via the same two-stage method. One application of this methodology to a market entry decision, a salient subject in the area of international marketing, is demonstrated in detail herein.     

On finding compromise solutions in multicriteria problems using the fuzzy min-operator

This paper presents an application of fuzzy approaches to the linear vectormaximum problem. It shows that using the fuzzy min-operator together with linear as well as special nonlinear membership functions the obtained solutions are always compromise solutions of the original multicriteria problem.     

Arcwise cone-quasiconvex multicriteria optimization

The aim of this paper is to study the structure of the efficient sets within a special class of multicriteria optimization problems, involving objective functions which are continuous and arcwise quasiconvex with respect to a certain family of cones. In particular, it is shown that such a problem is Pareto reducible and its efficient outcome set is strongly contractible.     

An approximate solution of linear multicriteria control problems through the multicriteria simplex method

This paper deals with multicriteria, linear, continuous optimal control problems through the application of the multicriteria simplex method. Since the system is linear, the state variables at a given time can be expressed in terms of definite integrals. Upon using standard numerical integration formulas, the definite integrals are approximately expressed by means of weighted sums of the integrands. Then, after introducing some suitable auxiliary variables, approximate linear multicriteria programming problems are formulated. Illustrative numerical examples are provided to indicate the efficiency of the proposed method.The author is indebted to Professor Y. Sawaragi of Kyoto University for his constant encouragement. The author also wishes to thank T. Suwa for his cooperation in preparing the programming for the digital computer.     

Management of multicriteria inventory classification

The most common method that materials managers use for classifying inventory items for planning and control purposes is the annual-dollar-usage ranking method (ABC classification). Recently, it has been suggested that multiple criteria ABC classification can provide a more comprehensive managerial approach, allowing consideration of other criteria such as lead time and criticality. This paper proposes the use of the Analytical Hierarchy Process (AHP) to reduce these multiple criteria to a univariate and consistent measure to consider multiple inventory management objectives.     

Implementing stochastic multicriteria acceptability analysis

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with inaccurate, uncertain, or missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision.     

Developments in fuzzy multicriteria analysis

Selecting or ranking available alternatives (observations/objects) with respect to multiple, often conflicting criteria in a fuzzy environment usually referred to as fuzzy multicriteria analysis is a problem of a major interest in information and engineering. Methodologies for addressing this problem have been developed from a variety of research disciplines, including statistics, econometrics, artificial intelligent, and operations research. This paper presents an overview of the developments in fuzzy multicriteria analysis. It discusses the complexity of fuzzy multicriteria analysis and analyses the existing approaches from four different perspectives for facilitating a better understanding of the recent development in this domain. Finally, the paper elaborates on the future research areas in fuzzy multicriteria analysis.     

Insoluble multicriteria linear programming problems

This note concerns a method for analyzing insoluble multicriteria linear programming problems.     

Model choice in multicriteria decision aid

The purpose of this paper is to illustrate, using a real case study, one of the points stressed in the “Manifesto of the new Multi Criteria Decision Aid (MCDA) era” (Bouyssou et al., 1993) regarding the application of the basic theory of MCDA procedures. Although the great diversity of MCDA procedures may be seen as a strong point, it can be a weakness, and a systematic analysis of decision procedures if one method makes more sense than another for a specific problem is necessary. The problem of selecting the most appropriate (MCDA) technique for a particular application is in itself a MCDA problem since the decision making criteria used for the selection are different and conflicting in nature. In this paper three selection models are implemented to assist the system analyst, when confronted with a multi-objective decision problem, to select the most appropriate MCDA technique for application to the problem of optimal ranking of water development projects in an arid country. These models are developed by Deason (1984), Gershon (1981), and Tecle (1988). Results indicated that PROMETHEE was the most preferred method for this problem.     

State-dependent weights in multicriteria value functions

In this paper, the concept of state-dependent weights is studied. This offers the flexibility to approximate the changing weights of the decision maker. The relationship between state-dependent weights and value functions is discussed.     

Postoptimal analysis in multicriteria linear programming

The aim of the paper is to present the postoptimal analysis of a chosen extreme efficient point in multicriteria linear programming. There are three cases considered: one objective function coefficient change, objective function addition and objective function removal. The proven theorems allow us to create methods based on the analysis of a simplex tableau.     

An external penalty-type method for multicriteria

We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued method uses an auxiliary function, which can be chosen among large classes of “monotonic” real-valued mappings. We analyze the properties of the auxiliary functions in those classes and exhibit some examples. The convergence results are similar to those of the scalar-valued method, and depending on the kind of auxiliary function used in the implementation, under standard assumptions, the generated infeasible sequences converge to weak Pareto or Pareto optimal points. We also propose an implementable local version of the external penalization method and study its convergence results.