Fuzzy set based models and methods of multicriteria group decision making

In the paper, the term consensus scheme is utilized to denote a dynamic and iterative process where the experts involved discuss a multicriteria decision problem. This discussion process is conducted by a human or artificial moderator, with the purpose of minimizing the discrepancy between the individual opinions.During the process of decision making, each expert involved must provide preference information. The information format and the circumstances where it must be given play a critical role in the decision process. This paper analyses a generic consensus scheme, which considers many different preference input formats, several possible interventions of the moderator, as well as admitting several stop conditions for interrupting the discussion process. In addition, a new consensus scheme is proposed with the intention of eliminating some difficulties met when the traditional consensus schemes are utilized in real applications. It preserves the experts’ integrity through the intervention of an external person, to supervise and mediate the conflicting situations. The human moderator is supposed to interfere in the discussion process by adjusting some parameters of the mathematical model or by inviting an expert to update his opinion. The usefulness of this consensus scheme is demonstrated by its use to solve a multicriteria group decision problem, generated applying the Balanced Scorecard methodology for enterprise strategy planning. In the illustrating problem, the experts are allowed to give their preferences in different input formats. But the information provided is made uniform on the basis of fuzzy preference relations through the use of adequate transformation functions, before being analyzed. The advantage of using fuzzy set theory for solving multiperson multicriteria decision problems lies in the fact that it can provide the flexibility needed to adequately deal with the uncertain factors intrinsic to such problems.     

Some pathological configurations of noninferior set appearing in multicriteria optimization problems of chemical processes

The noninferior set of multicriteria optimization problems may sometimes include some inactive subset in which a scalar-valued objective function of weighted-mean type cannot be minimal. It is shown that there exists such an inactive noninferior subset within the noninferior set of two multicriteria optimization problems concerning a cross-current multistage extraction process and a fluidized reactor-heater system.     

A fast method of ranking alternatives using fuzzy numbers

We show a very fast method of ranking alternatives using fuzzy numbers discussed in [1] and [2].     

A cone separation theorem

The notion of separation is extended here to include separation by a cone. It is shown that two closed cones, one of them acute and convex, can be strictly separated by a convex cone, if they have no point in common. As a matter of fact, an infinite number of convex closed acute cones can be constructed so that each of them is a separating cone.The research was done while the author was a visiting professor at the University of British Columbia, Vancouver, British Columbia, Canada.     

Proper inequality constraints and maximization of index vectors

For obtaining the set of all quasi-supremal index vectors (or all maximal index vectors, or all Pareto-optimal solutions) of a multiple-objective optimization problem, we present, in this paper, the method of proper inequality constraints, which does not rely on any convexity condition at all, but by which one can obtain the entire desired set. This method is based on the observation that optimizing the index of one of the objectives, with some arbitrary bounds assigned to all other objectives, may still result in inferior solutions, unless these bounds areproper. Various necessary and/or sufficient conditions are presented for the properness test.This work was supported by the National Science Foundation under Grant No. GK-32701.     

Multicriteria Modelling of Repair Contract Based on Utility and ELECTRE I Method with Dependability and Service Quality Criteria

A DM faces a choice among several alternatives of repair contract for a system. Each alternative of a repair contract implies specific results regarding the following characteristics or criteria: response time, quality service, dependability and related cost. This problem has been analysed through a multicriteria decision model. The model is based on the ELECTRE method combined with utility functions. Main theoretical aspects and practical implications are presented, including a numerical application.     

A multicriteria ranking of organotin(IV) compounds with fungicidal properties

The application of multicriteria decision‐making methods to the results of in vitro antifungal properties of organotin compounds of the type Ph_xSnX_z (x = 2 or 3; X = O₂CC₆H₄OH, O₂CC₆H₄OCOCH₃, Cl or O₂CCH₃; z = 1 or 2) and of free 2‐hydroxybenzoic and 2‐acetoxybenzoic acids against Aspergillus niger, Aspergillus flavus, Candida albicans, Penicillium citrinum, Trichophyton rubrum and Trichophyton violaceum have been described. Ranking information necessary to select one toxicant in preference to others and to assess the properties influencing the preference has been obtained. Patterns in the multivariate analyses suggest that cationic and anionic moieties of the toxicant play some roles in their fungicidal activities. The triphenyltin compounds were generally more active than their diphenyltin analogues, but the acetoxybenzoates were more active than the corresponding hydroxybenzoates, acetates or chlorides. Thus, triphenyltin acetoxybenzoate is up to 7.5 times as active as the corresponding acetate, which is commercially marketed as a fungicide. The results of the analyses have been discussed in the light of the mechanism of antifungal activity of organotin compounds and the potential of multivariate data analysis techniques to facilitate the screening and ranking of antifungal agents. Copyright © 2003 John Wiley & Sons, Ltd.     

Sufficient conditions in vector-valued maximin problems

Constructive sufficient conditions for the existence of a Slater maximin in strictly convex (in the uncertainty) multicriteria problems without restrictions are introduced.     

PARETO EQUILIBRIA OF MULTICRITERIA GAMES WITHOUT COMPACTNESS，CONTINUITY AND CONCAVITY

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