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1

Metryki Minkowskiego w tworzeniu uniwersalnych algorytmów rankingowych

Ameljańczyk A.

Biuletyn Wojskowej Akademii Technicznej

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2014

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Vol. 63, nr 2

29-44

PL

W pracy przedstawiono ogólną procedurę tworzenia rankingów zbioru obiektów przy relacji preferencji bazującej na dowolnej funkcji rankingowej. Analizę możliwych do wykorzystania funkcji rankingowych rozpoczęto od pokazania fundamentalnych wad powszechnie stosowanych funkcji w postaci sumy ważonej. Jako szczególny przypadek procedury rankingowej w przestrzeni z relacją zaproponowano procedurę bazującą na pojęciu elementu idealnego i uogólnionej odległości Minkowskiego od tego elementu. Procedura ta przedstawiona w postaci uniwersalnego algorytmu rankingowego eliminuje większość wad funkcji rankingowej w postaci sumy ważonej.

EN

The paper presents a general procedure for creating the rankings of a set of objects, while the relation of preference based on any ranking function. The analysis was possible to use the ranking functions began by showing the fundamental drawbacks of commonly used functions in the form of a weighted sum. As a special case of the ranking procedure in the space of a relation, the procedure based on the notion of an ideal element and generalized Minkowski distance from the element was proposed. This procedure, presented as universal ranking algorithm, eliminates most of the disadvantages of ranking functions in the form of a weighted sum.

2

A modified ranking approach for solving fuzzy critical path problems with LR flat fuzzy numbers

Kaur P., Kumar A.

Control and Cybernetics

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2012

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Vol. 41, no. 1

171-190

EN

There are several fuzzy critical path methods for solving fuzzy critical path problems in which ranking approaches are used for comparing fuzzy numbers. In this paper, it is shown that if the existing ranking approaches are used for solving such fuzzy critical path problems in which duration times of activities are represented by LR flat fuzzy numbers, then more than one fuzzy numbers, representing the fuzzy project completion time, are ob- tained and a new ranking approach for comparing LR flat fuzzy numbers is proposed. Also, it is proved that if the proposed rank- ing approach is used for solving fuzzy critical path problems then a unique fuzzy number, representing the fuzzy project completion time, is obtained.

3

Ranking of generalized fuzzy numbers with generalized fuzzy simplex algorithm

Kumar A., Singh P.

Journal of Mathematics and Applications

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2011

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Vol. 34

53--73

EN

Ranking of fuzzy numbers play an important role in decision making problems. Fuzzy numbers must be ranked before an action is taken by a decision maker. Jain (Decision-making in the presence of fuzzy variables, IEEE Transactions on Systems, Man and Cybernetics 6 (1976) 698-703) proposed the concept of ranking function for comparing normal fuzzy numbers. Chen (Operations on fuzzy numbers with function principal, Tamkang Journal of Management Science 6 (1985) 13-25) pointed out that in many cases it is not to possible to restrict the membership function to the normal form and proposed the concept of generalized fuzzy numbers. Chen and Chen (Fuzzy risk analysis based on the ranking generalized fuzzy numbers with different heights and different spreads, Expert Systems with Applications 36 (2009) 6833-6842) pointed out the shortcomings of the existing methods for the ranking of generalized fuzzy numbers and proposed a new method. In this paper the shortcomings of the Chen and Chen method are pointed out and a new method is proposed for the ranking of generalized fuzzy numbers. Also using the proposed ranking method, a generalized simplex algorithm is proposed for solving a special type of fuzzy linear programming (FLP) problems. To illustrate the proposed algorithm a numerical example is solved and the advantages of the proposed algorithm are discussed. Since the proposed algorithm is a direct extension of classical algorithm so it is very easy to understand and apply the proposed algorithm to find the optimal solution of FLP problems occurring in the real life situations.