Clustering and group selection of multiple criteria alternatives with application to space-based networks

In many real-world problems, the range of consequences of different alternatives are considerably different. In addition, sometimes, selection of a group of alternatives (instead of only one best alternative) is necessary. Traditional decision making approaches treat the set of alternatives with the same method of analysis and selection. In this paper, we propose clustering alternatives into different groups so that different methods of analysis, selection, and implementation for each group can be applied. As an example, consider the selection of a group of functions (or tasks) to be processed by a group of processors. The set of tasks can be grouped according to their similar criteria, and hence, each cluster of tasks to be processed by a processor. The selection of the best alternative for each clustered group can be performed using existing methods; however, the process of selecting groups is different than the process of selecting alternatives within a group. We develop theories and procedures for clustering discrete multiple criteria alternatives. We also demonstrate how the set of alternatives is clustered into mutually exclusive groups based on 1) similar features among alternatives; 2) ideal (or most representative) alternatives given by the decision maker; and 3) other preferential information of the decision maker. The clustering of multiple criteria alternatives also has the following advantages. 1) It decreases the set of alternatives to be considered by the decision maker (for example, different decision makers are assigned to different groups of alternatives). 2) It decreases the number of criteria. 3) It may provide a different approach for analyzing multiple decision makers problems. Each decision maker may cluster alternatives differently, and hence, clustering of alternatives may provide a basis for negotiation. The developed approach is applicable for solving a class of telecommunication networks problems where a set of objects (such as routers, processors, or intelligent autonomous vehicles) are to be clustered into similar groups. Objects are clustered based on several criteria and the decision maker's preferences.

[1]  João Paulo Costa,et al.  A parallel approach to the analytic hierarchy process decision support tool , 1995 .

[2]  M. Zeleny.  Linear Multiobjective Programming , 1974 .

[3]  Rakesh K. Sarin,et al.  Ranking with Partial Information: A Method and an Application , 1985, Oper. Res..

[4]  R. Michalski,et al.  Learning from Observation: Conceptual Clustering , 1983 .

[5]  Sowmyanarayanan Sadagopan,et al.  Interactive algorithms for multiple criteria nonlinear programming problems , 1986 .

[6]  I. B. Muchnik,et al.  Linguistic Analysis of 0-1 Matrices using Monotone Systems * , 1986 .

[7]  H. Spath.  Cluster Dissection and Analysis , 1985 .

[8]  Kaisa Miettinen,et al.  Decision-aid for discrete multiple criteria decision making problems with imprecise data , 1999, Eur. J. Oper. Res..

[9]  D. Hand.  Cluster dissection and analysis: Helmuth SPATH Wiley, Chichester, 1985, 226 pages, £25.00 , 1986 .

[10]  Robert F. Ling,et al.  Classification and Clustering. , 1979 .

[11]  Theodor J. Stewart,et al.  Use of piecewise linear value functions in interactive multicriteria decision support: a Monte Carlo study , 1993 .

[12]  Jacques-François Thisse,et al.  On Efficient Solutions To Multiple Objective Mathematical Programs , 1984 .

[13]  Behnam Malakooti,et al.  Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[14]  E. Choo,et al.  Connectedness in Multiple Linear Fractional Programming , 1983 .

[15]  W. Edwards,et al.  Decision Analysis and Behavioral Research , 1986 .

[16]  Ralph E. Steuer,et al.  An interactive weighted Tchebycheff procedure for multiple objective programming , 1983, Math. Program..

[17]  Behnam Malakooti,et al.  An adaptive feedforward artificial neural network with the applications to multiple criteria decision making , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[18]  Ilya Muchnik,et al.  Fixed points approach to clustering , 1993 .

[19]  Sriram Subramanian,et al.  Generalized polynomial decomposable multiple attribute utility functions for ranking and rating multiple criteria discrete alternatives , 1999, Appl. Math. Comput..

[20]  Behnam Malakooti,et al.  Clustering and selection of multiple criteria alternatives using unsupervised and supervised neural networks , 2000, J. Intell. Manuf..

[21]  I. B. Muchnik,et al.  Incomplete classifications of a finite set of objects using Monotone Systems , 1989 .

[22]  Behnam Malakooti,et al.  A decision support system and a heuristic interactive approach for solving discrete multiple criteria problems , 1988, IEEE Trans. Syst. Man Cybern..

[23]  Behnam Malakooti,et al.  A variable-parameter unsupervised learning clustering neural network approach with application to machine-part group formation , 1995 .

[24]  H. Raiffa,et al.  Decisions with Multiple Objectives , 1993 .

[25]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

[26]  B. Malakooti,et al.  Feedforward artificial neural networks for solving discrete multiple criteria decision making problems , 1994 .

[27]  Behnam Malakooti.  A generalized decomposable multiattribute utility function , 1991 .

[28]  Andrew P. Sage,et al.  Decision Support with Partially Identified Parameters. , 1981 .

[29]  Manjaree Pandit,et al.  Contingency ranking for voltage collapse using parallel self-organizing hierarchical neural network , 2001 .

[30]  D. A. Milner,et al.  Direct clustering algorithm for group formation in cellular manufacture , 1982 .

[31]  D. Matula.  Graph Theoretic Techniques for Cluster Analysis Algorithms , 1977 .