Application of Uncertain Variables to Knowledge-Based Resource Distribution

Application of Uncertain Variables to Knowledge-Based Resource Distribution

Donat Orski
Copyright: © 2012 |Pages: 23
DOI: 10.4018/978-1-60960-818-7.ch412
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Abstract

The chapter concerns a class of systems composed of operations performed with the use of resources allocated to them. In such operation systems, each operation is characterized by its execution time depending on the amount of a resource allocated to the operation. The decision problem consists in distributing a limited amount of a resource among operations in an optimal way, that is, in finding an optimal resource allocation. Classical mathematical models of operation systems are widely used in computer supported projects or production management, allowing optimal decision making in deterministic, well-investigated environments. In the knowledge-based approach considered in this chapter, the execution time of each operation is described in a nondeterministic way, by an inequality containing an unknown parameter, and all the unknown parameters are assumed to be values of uncertain variables characterized by experts. Mathematical models comprising such two-level uncertainty are useful in designing knowledge-based decision support systems for uncertain environments. The purpose of this chapter is to present a review of problems and algorithms developed in recent years, and to show new results, possible extensions and challenges, thus providing a description of a state-of-the-art in the field of resource distribution based on the uncertain variables.
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Introduction

Among many theories of uncertainty (Klir, 2006) developed for different applications the uncertain variables introduced by Bubnicki (2001a, 2001b) may be considered as a useful tool for modeling expert’s knowledge in knowledge-based decision systems. In the definition of the uncertain variable 978-1-60960-818-7.ch412.m01 we consider two soft properties: “978-1-60960-818-7.ch412.m02” which means “978-1-60960-818-7.ch412.m03 is approximately equal to x” or “x is the approximate value of 978-1-60960-818-7.ch412.m04,” and “978-1-60960-818-7.ch412.m05” which means “978-1-60960-818-7.ch412.m06 approximately belongs to the set Dx” or “the approximate value of 978-1-60960-818-7.ch412.m07 belongs to Dx.” The uncertain variable978-1-60960-818-7.ch412.m08 is defined by a set of values X (real number vector space), the function 978-1-60960-818-7.ch412.m09 (i.e., the certainty index that 978-1-60960-818-7.ch412.m10, given by an expert) and the following definitions for Dx, D1, D2 ⊆X:

978-1-60960-818-7.ch412.m12,

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