Class Of Decision Problems Research Articles

Review of "The classical decision problem" by Egon Börger,Erich Grädel and Yuri Gurevich. Springer-Verlag 1997.

Review of "The classical decision problem" by Egon Börger,Erich Grädel and Yuri Gurevich. Springer-Verlag 1997.

An empirical study on using decision support systems to solve very large choice decision problems

Choice problems as a class of decision problems have attracted great attention for the last couple of decades. As problem size increases, a decision process may be detoured and the decision outcome may be different. The impact of problem size on three important aspects of the computer-aided decision process – strategy selection, decision time/effort, and decision quality – has been investigated by Wang and Chu. This paper investigates the way a decision support system (DSS) is used to solve very large choice problems (VLCP) as well as its implications for small to medium-sized enterprises (SMEs).

Generic-case complexity, decision problems in group theory, and random walks

We give a precise definition of “generic-case complexity” and show that for a very large class of finitely generated groups the classical decision problems of group theory—the word, conjugacy, and membership problems—all have linear-time generic-case complexity. We prove such theorems by using the theory of random walks on regular graphs.

Using Evolutionary Algorithms to Generate Alternatives for Multiobjective Site-Search Problems

Multiobjective site-search problems are a class of decision problems that have geographical components and multiple, often conflicting, objectives; this kind of problem is often encountered and is technically difficult to solve. In this paper we describe an evolutionary algorithm (EA) based approach that can be used to address such problems. We first describe the general design of EAs that can be used to generate alternatives that are optimal or close to optimal with respect to multiple criteria. Then we define the problem addressed in this research and discuss how the EA was designed to solve it. In this procedure, called MOEA/Site, a solution (that is, a site) is encoded by using a graph representation that is operated on by a set of specifically designed evolutionary operations. This approach is applied to five different types of cost surfaces and the results are compared with 10 000 randomly generated solutions. The results demonstrate the robustness and effectiveness of this EA-based approach to geographical analysis and multiobjective decisionmaking. Critical issues regarding the representation of spatial solutions and associated evolutionary operations are also discussed.

The complexity of acyclic conjunctive queries

This paper deals with the evaluation of acyclic Boolean conjunctive queries in relational databases. By well-known results of Yannakakis[1981], this problem is solvable in polynomial time; its precise complexity, however, has not been pinpointed so far. We show that the problem of evaluating acyclic Boolean conjunctive queries is complete for LOGCFL, the class of decision problems that are logspace-reducible to a context-free language. Since LOGCFL is contained in AC1 and NC2, the evaluation problem of acyclic Boolean conjunctive queries is highly parallelizable. We present a parallel database algorithm solving this problem with alogarithmic number of parallel join operations. The algorithm is generalized to computing the output of relevant classes of non-Boolean queries. We also show that the acyclic versions of the following well-known database and AI problems are all LOGCFL-complete: The Query Output Tuple problem for conjunctive queries, Conjunctive Query Containment, Clause Subsumption, and Constraint Satisfaction. The LOGCFL-completeness result is extended to the class of queries of bounded tree width and to other relevant query classes which are more general than the acyclic queries.

The fundamental class of a rational space, the graph coloring problem and other classical decision problems

The fundamental class of a rational space, the graph coloring problem and other classical decision problems

Multicriterion Decision Merging: Competitive Development of an Aboriginal Whaling Management Procedure

International Whaling Commission management of aboriginal subsistence whaling will eventually use an aboriginal whaling management procedure (AWMP) chosen from a collection of candidate procedures after grueling simulation testing. An AWMP is a fully automatic algorithm designed to operate on the results of an assessment (i.e., a statistical estimation problem relying on sparse series of whale abundance data) to produce a catch limit in each year of real or simulated management. An AWMP should, as much as possible, meet the conflicting objectives of low population risk, high satisfaction of needed catch, and high rate of population recovery. The choice of the best procedure falls naturally in the multicriterion decision making framework, because one of several candidates must be chosen on the basis of high-dimensional simulated performance summaries over a wide range of assumptions about whales and whaling. However, standard multicriterion decision making methods are impractical and unsatisfying for this problem. A method is developed to merge competing procedures into a new procedure that is an admissible Bayes rule. The approach is constructive rather than selective, meaning that it is not intended to produce an automatic winner, but rather a promising new candidate. This merging approach allows the best performance aspects of competing procedures to be combined. Ideally, and in examples shown, the newly constructed procedure outperforms all previous candidates. The approach also permits tuning of a single procedure to enhance performance or to more closely reflect design goals, without a simulation-intensive search over the tuning parameter space. These methods are generalizable to a larger class of decision problems.

Generalization of a lemma of kiefer and weiss for the case of sequentially planned decision problems with more than two hypotheses

In Lemma 4.1 of Kiefer and Weiss (1957) the duality between Bayesian tests and optimal sequential tests with prescribed upper bounds for the risks of first and second kind is shown. We provide a generalization of this lemma for more than two hypotheses and a more general class of decision problems. The result could be used for instance, if the optimal sequential tests are to be constructed by means of iteratively applied backward induction.

Rough set approach to multi-attribute decision analysis

We review the methodology of the rough set analysis of multi-attribute decision problems. Rough set theory proved to be a useful tool for analysis of a vague description of decision situations. It answers two basic questions related to multi-attribute decision problems: one about explanation of a decision situation and, another, about prescription of some decisions basing on analysis of a decision situation. We define four classes of multi-attribute decision problems, depending on the structure of their representation, its interpretation and the kind of questions related. Then, we characterize the rough set methodology for each particular class of decision problems. We use simple practical examples to illustrate this presentation. A review of related literature is made throughout the paper.

The effectiveness of finite improvement algorithms for finding global optima

This paper investigates the effectiveness of using finite improvement algorithms for solving decision, search, and optimization problems. Finite improvement algorithms operate in a finite number of iterations, each taking a polynomial amount of work, where strict improvement is required from iteration to iteration. The hardware, software, and way of measuring complexity found in the polynomial setting are modified to identify the concept of repetition and define the new classes of decision problems,FI andNFI. A firstNFI-complete problem is given using the idea ofFI-transformations. Results relating these new classes toP, NP, andNP-complete are given. It is shown that if an optimization problem in a new classPGS isNP-hard, thenNP=co-NP. TwoPGS problems are given for which no polynomial algorithms are known to exist.

Normal and sinkless petri nets

We examine both the modeling power of normal and sinkless Petri nets and the computational complexities of various classical decision problems with respect to these two classes. We argue that although neither normal nor sinkless Petri nets are strictly more powerful than persistent Petri nets, they nonetheless are both capable of modeling a more interesting class of problems. On the other hand, we give strong evidence that normal and sinkless Petri nets are easier to analyze than persistent Petri nets. In so doing, we apply techniques originally developed for conflict-free Petri nets—a class defined solely in terms of the structure of the net—to sinkless Petri nets—a class defined in terms of the behavior of the net. As a result, we give the first comprehensive complexity analysis of a class of potentially unbounded Petri nets defined in terms of their behavior.

Hamlet and the Psychology of Rational Choice Under Uncertainty

Shakespeare's Hamlet is the classic case of an individual who cannot make a decision, and classic explanations are in terms of “deep psychology”—a paradigm that searches for causes of behavior deep within the individual's psyche. This article shows, however, that the play can be coherently and simply understood in terms of “shallow psychology”—a paradigm that turns attention to the difficulties attendant on rational decision making, emphasizing, most importantly, constraints on information that is necessary for good decision making. Hamlet is shown to be a case of decision making under uncertainty, where the consequences of error are unthinkable and where a decision cannot be avoided. Far from showing us a personality constitutionally unable (for whatever deep reason) to decide, the play shows us the difficulties attendant on this class of decision problems—a demonstration highlighted by the fact that those difficulties must be faced by an individual better equipped than most for decisive action. The play also shows us the only satisfactory way for resolving such a problem. A de-emphasis on personality and a turning of critical attention to the structure of situations that normal people confront might contribute not only to an understanding of this particular play and of dramatic tragedy but also to our understanding of decision making in general.

Inadmissibility of the Empirical Distribution Function in Continuous Invariant Problems

Consider the classical invariant decision problem of estimating an unknown continuous distribution function $F,$ with the loss function $L(F, a) = \int(F(t) - a(t))^2\lbrack F(t) \rbrack^\alpha \lbrack 1 - F(t) \rbrack^\beta dF(t),$ and a random sample of size $n$ from $F.$ It is proved that the best invariant estimator is inadmissible when: 1. $ n > 0, - 1 < \alpha, \beta \leq 0 \text{and} -1 \leq \alpha + \beta.$ 2. $ n > 0, -1 < \alpha = \beta \leq - \frac{1}{2}.$ 3. $ n > 1, (\mathrm{i}) \alpha = -1 \text{and} \beta = 0, \text{or} (\mathrm{ii}) \alpha = 0 \text{and} \beta = -1.$ 4. $ n > 2, \alpha = \beta = -1.$ Thus the empirical distribution function, which is the best invariant estimator when $\alpha = \beta = -1,$ is inadmissible when $n \geq 3.$ This extends some results of Brown.

Flexible assembly systems: The scheduling problem for multiple products

Abstract Flexible assembly systems (FAS) promise to be an efficient processing approach for producing small and medium-sized batches of products. One vitally important element which affects the achievement of high performance by the FAS is its scheduling/dispatching component operating within the production planning and control system (PPCS). A detailed definition of the FAS scheduling process is given and key differences between this process and the classical simple job shop scheduling process are discussed. A mathematical model is developed for the minimize makespan problem, and it is shown that the problem is NP-complete, that it is one the most difficult problems in the class of decision problems that can be solved by polynomial time nondeterministic algorithm (NP). The design of heuristic solution procedures is also discussed.

Boundary Crossing Problems for Sample Means

Motivated by several classical sequential decision problems, we study herein the following type of boundary crossing problems for certain nonlinear functions of sample means. Let $X_1, X_2,\ldots$ be i.i.d. random vectors whose common density belongs to the $k$-dimensional exponential family $h_\theta(x) = \exp\{\theta'x - \psi(\theta)\}$ with respect to some nondegenerate measure $\nu$. Let $\bar{X}_n = (X_1 + \cdots + X_n)/n, \hat\theta_n = (\nabla\psi)^{-1}(\bar{X}_n)$, and let $I(\theta, \lambda) = E_\theta\log\{h_\theta(X_1)/h_\lambda(X_1)\}$ ( = Kullback-Leibler information number). Consider stopping times of the form $T_c(\lambda) = \inf\{n: I(\hat\theta_n, \lambda) \geq n^{-1}g(cn)\}, c > 0$, where $g$ is a positive function such that $g(t) \sim \alpha \log t^{-1}$ as $t \rightarrow 0$. We obtain asymptotic approximations to the moments $E_\theta T^r_c(\lambda)$ as $c \rightarrow 0$ that are uniform in $\theta$ and $\lambda$ with $|\lambda - \theta|^2/c \rightarrow \infty$. We also study the probability that $\bar{X}_{Tc(\lambda)}$ lies in certain cones with vertex $\nabla\psi (\lambda)$. In particular, in the one-dimensional case with $\lambda > \theta$, we consider boundary crossing probabilities of the form $P_\theta\{\hat\theta_n \geq \lambda \text{and} I(\hat\theta_n, \lambda) \geq n^{-1} g(cn) \text{for some} n\}$. Asymptotic approximations (as $c \rightarrow 0$) to these boundary crossing probabilities are obtained that are uniform in $\theta$ and $\lambda$ with $|\lambda - \theta|^2/c \rightarrow \infty$.

Informativeness as an ordinal utility function for information retrieval

Information retrieval has all the elements of a classical decision problem: a set of possible actions, a set of potential states, and a reward or utility attached to each combination of action and state. How the actions, states, and utilities are described, however, is variable, and depends very much on the describer's point of view.

Assessment of approximate algorithms: The error measure's crucial role

Initially, the distinction between exact and approximate algorithms is accounted for. We then consider a broad class of decision problems including the so-called account location ork-plant location problem (kPLP), and show that the choice of an appropriate reference value is critical; even an apparent plausible choice may lead to disputable conclusions.

Compatibility of multiple goal programming and the maximize expected utility criterion

Assuming a decision maker accepts the basic axioms of von Neumann-Morgenstern utility theory and is therefore an expected utility maximizer, this paper argues that the domain of the decision variables in a multiobjective program should be altered in order to guarantee that it will be compatible with the maximize expected utility critierion. Stochastic dominance is employed to approximate this new domain, and for a certain class of decision problems it is shown that this approximation is very good.

Decision Making Under Risk: A Comparison of Bayesian and Fuzzy Set Methods

A classical decision problem is considered where a decision maker is to choose one of a number of actions each offering different consequences. The outcome from a choice of action is uncertain because it depends on the existing state of Nature. Also, the outcome, once an action and state of Nature are specified, may be a vector or a random vector. The decision maker employs both Bayesian methods and fuzzy set techniques to handle the uncertainties. The decision maker is also allowed to use multiple, possibly conflicting, goals in order to determine his best strategy. The Bayesian method produces a set of undominated strategies to choose from, whereas the fuzzy set technique usually produces a unique optimal strategy.

A STRUCTURE OF RATIONAL DECISION PRINCIPLES

A problem of decision making under uncertainty or decision making with multiple objectives is not a simple optimization problem and so we have to assume some decision principles on making a decision. So far many decision principles have been proposed as rational ones. This paper tries to reveal an underlying structure of rational decision principles. We first formulate decision problems and principles from the viewpoint of the mathematical general systems theory and then, based on them, specify the class of decision problems as a category and a decision principle as a functor. As a conclusion, we claim that three conditions, i.e., the Pareto consistency, the similarity condition and the invariance condition, compose a fundamental structure of rational decision principles and are naturally represented in the category theoretic framework. In order to support the claim we demonstrated that the linear weighted sum decision principle can be characterized by using these conditions.