By N. Apostolatos (auth.), Dr. Herbert Fischer, Dr. Bruno Riedmüller, Priv.-Doz. Dr. Stefan Schäffler (eds.)

The authors of this Festschrift ready those papers to honour and convey their friendship to Klaus Ritter at the get together of his 60th birthday. Be reason for Ritter's many pals and his overseas attractiveness between math ematicians, discovering individuals was once effortless. in truth, constraints at the measurement of the publication required us to restrict the variety of papers. Klaus Ritter has performed very important paintings in various components, particularly in var ious purposes of linear and nonlinear optimization and likewise in reference to facts and parallel computing. For the latter we need to point out Rit ter's improvement of transputer computing device undefined. The large scope of his learn is mirrored by means of the breadth of the contributions during this Festschrift. After a number of years of clinical learn within the united states, Klaus Ritter used to be ap pointed as complete professor on the collage of Stuttgart. seeing that then, his identify has turn into inextricably attached with the usually scheduled meetings on optimization in Oberwolfach. In 1981 he grew to become complete professor of utilized arithmetic and Mathematical statistics on the Technical collage of Mu nich. as well as his college educating tasks, he has made the task of using mathematical tips on how to difficulties of to be centrally important.

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7] Behringer, FA, "A Simplex Based Algorithm for the Lexicographically Extended Linear Maxmin Problem". European Joumal of Operational Research 7 (1981),274-283. [8] Behringer, FA, "Uniformly quasiconvexlike functions". Optimization 17 (1986), 19-29. , "A Local Version of Karamardian's Theorem on Lower Semicontinuous Strictly Quasiconvex Functions". European Joumal of Operational Research 43 (1989),245-262. [10] Behringer, FA, "Lexmaxmin in Fuzzy Multiobjective Decision-Making". Optimization21 (1990),23-49.

Soc. 68 (1962), 405-410. , "Convex Functions'. New York, 1973. , and Ziemba w'T. ), "Generalized Concavity in Optimization and EconomicS'. New York, 1981. , 'The Nucleolus of a Characteristic Function Game", SIAMJ. Appl. Math. 17 (1969),1163-1170. , "The Theory of Games', Oxford, 1988. , "Interaktive Entscheidungsunterstotzung durch ein flexibles mathematisches Programmierungssysterrl'. MOnchen, 1984. , "Interactive Multiple Objective Programming Subject to Flexible Constraints". European Joumal of Operational Research 31 (1987), 342-349.

Cix < Cj 1 Cj";Cix. e. multiobjective) fuzzy decision problem means taking the intersection of the individual fuzzy sets. ; b, x;;. 0 Here, the minimum comes from fuzzification. Maximizing the minimum has nothing to do with Pareto optimization. \/\lith multiobjective decision problems, however, Pareto optimization is a widely accepted sine-quanon condition. There is a close connection between Pareto optimality of the above fuzzy problem (5) and the underlying crisp problem (1) ([30],[10]). One way of adding the Pareto aspect to problem (5) is by considering a lexicographicaLLy extended version of it instead of only maximizing the minimum.