### A Solution To Rational Decision Making Via Compositional Data Analysis: A Case Study Using Students Cellular Phone Tendencies

#### Abstract

Decisions can be simple or complex depending on the alternatives available to the decision maker, and also, to the different state of the worlds. In classical decision theory, a pay-off table is analysed in order to make an optimal decision. Here, the decision process involves the definition of different alternatives and state of the worlds, cost or profit calculations of the pay-off table, and probability values, if any, related to state of the worlds. In decision problems, sometimes, it may be necessary to involve emotional attachments in order to create pay-off table. In this setting, rather than using the usual cost or profit values, some satisfaction values can be assigned to the criteria and the rationality of different alternatives can be investigated. In this study, the rationality approach to decision pay-off matrix is demonstrated using a real life example regarding a cellular phone purchase. Furthermore, a compositional data analysis approach is also suggested, and the contributions of the compositional data analysis to decision theory are given.

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PDFDOI: http://dx.doi.org/10.17093/aj.2015.3.1.5000107125

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