Solution Of Decision Problem Research Articles

English

In recent years, artificial intelligence applications for understanding the human thinking process and transferring it to virtual environments come into prominence. The fuzzy logic which paves the way for modeling human behaviors and expressing even vague concepts mathematically, and is also regarded as an artificial intelligence technique has become one of the most preferred methods in the solution of decision problems. Numerous decision-making situations are faced in education as well. Particularly, it is rather challenging and requires experience to decide in a fair way and assessing students' performances without making any error in the process of assessment and evaluation. The purpose of the current study is to assess students' performance with the fuzzy analytic hierarchy process (FAHP), one of the multi-criteria decision making methods based on the fuzzy logic approach. The formation of the proposed system on the basis of fuzzy set theory determines that it can provide benefits in modeling these ambiguities in human mental processes and also it can reach fairer, more sensitive and objective results. Being used especially in making important decisions in companies and in developing smart vehicles in engineering, FAHP methods have brought into question whether this method can be used in education or not. This study reveals that FAHP method can be used in the evaluation of students' projects in education. Key words: Performance evaluation, fuzzy multi criteria decision making methods.

Optimality conditions for vector optimization problems with variable ordering structures

Our main concern in this article are concepts of nondominatedness w.r.t. a variable ordering structure introduced by Yu [P.L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. Optim. Theory Appl. 14 (1974), pp. 319–377]. Our studies are motivated by some recent applications e.g. in medical image registration. Restricting ourselves to the case when the values of a cone-valued map defining the ordering structure are Bishop–Phelps cones, we obtain for the first time scalarizing functionals for nondominated elements, Fermat rule, Lagrange multiplier rule and duality results for a single- or set-valued vector optimization problem with a variable ordering structure.

Black Swans, New Nostradamuses, Voodoo decision theories, and the science of decision making in the face of severe uncertainty

AbstractThe recent global financial crisis, natural disasters, and ongoing debate on global warming and climate change are a stark reminder of the huge challenges that severe uncertainty presents in decision and policy making. My objective in this paper is to look at some of the issues that need to be taken into account in the modeling and analysis of decision problems that are subject to severe uncertainty, paying special attention to some of the misconceptions that are being promulgated in this area. I also examine two diametrically opposed approaches to uncertainty. One, that emphasizes that the difficulties encountered in the modeling, analysis, and solution of decision problems in the face of severe uncertainty are in fact insurmountable, and another that claims to provide, against all odds, a reliable strategy for a successful handling of situations subject to severe uncertainty.

An integration of the fuzzy reasoning technique and the fuzzy optimization method in construction project management decision-making

Most real world decision-making combines quantitative and qualitative (linguistic) variables. Conventional mathematics that combines qualitative and quantitative concepts exhibits difficulty in modelling actual problems. The research presented in this paper illustrates a mathematical approach to the solution of decision-making problems that combine qualitative and quantitative objectives. A methodical system for construction project management decision-making was developed using a combination of fuzzy multiple-objective decision-making theory and the fuzzy reasoning technique. The mathematical model can be applied to construction project management problems by suggesting an optimal path of corporate cash flow that results in the minimum use of resources. The information provided by the mathematical model allows the planner to eliminate excess use, or idleness, of resources during the construction of a project. Such information is indispensable for decision-makers in analysing the best time to invest in a new project. A case study is demonstrated to illustrate the application to a management decision problem.

Representation and Solution of Decision Problems Using Sequential Decision Diagrams

In this paper we introduce a new graph, the sequential decision diagram, to aid in modeling formulation, and solution of sequential decision problems under uncertainty. While as compact as an influence diagram, the sequential diagram captures the asymmetric and sequential aspects of decision problems as effectively as decision trees. We show that a unified framework consisting of a sequential diagram, an influence diagram, and a common formulation table for the problem’s data, suffices for compact and consistent representation, economical formulation, and efficient solution of (asymmetric) decision problems. In addition to asymmetry, the framework exploits other sources of computational efficiency, such as conditional independence and value function decomposition, making it also useful in evaluating dynamic-programming problems. The formulation table and recursive algorithm can be readily implemented in computers for solving large-scale problems. Examples are provided to illustrate the methodology in both asymmetric and symmetric cases.

Ein numerisches Verfahren zur Bestimmung maxeminoptimaler Aktionen

For decision problems with only incomplete informations about the distribution of the states the numerical computing of all maxEmin-optimal solutions often is difficult or impossible. In this paper we present a numerical solution method for the computing of all maxEmin-optimal solutions for decision problems with a finite number of actions and states. Having a linear partial information essentially only linear programs must be solved for finding all optimal solutions.

Necessary and sufficient conditions for local and global nondominated solutions in decision problems with multi-objectives

In this paper, the decision problem with multi-objectives is considered, and the nondominated solutions associated with a polyhedral domination cone are discussed. The necessary and sufficient conditions for the solutions are given in the decision space rather than the objective space. The similarity of the solution conditions obtained in this article to the Kuhn-Tucker condition of a convex programming problem is examined. As an application of the solution condition, an algorithm to locate the set of all nondominated solutions is shown for the linear multi-objective decision problem.

Mathematical programming models as tools for centralized planning in decentralized decision situations:

Summary We consider the solution of decision problems of political agencies that are interested in the agricultural production activity, its spatial or temporal distribution etc. on a regional, national or international level. These agencies are faced with decision problems concerning the realization of economic activities that are basically determined by the decisions of individual farms that are free to make their own decisions within the limits of economic and technological constraints. This raises the question of to what extent an agency's computations of possible future economic activities will conform to reality if its information about the farms' future decision situation is not complete. Examples show that the computed results might be so unreliable that their relevance for the solution of an agency's decision problem might be very limited. In an economy of a non-command decision structure this applies to the use of ‘positive’ and ‘normative’ models. The paper discusses the relevance of reliability examinations for the evaluation of computed agricultural production activity. Furthermore, approaches for the identification and improvement of the reliability of computed results are discussed. Although the article concentrates on the use of programming models for the simulation of possible activities of the farms, it refers also to other types of models that might be used for this purpose.

Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives

Although there is no universally accepted solution concept for decision problems with multiple noncommensurable objectives, one would agree that agood solution must not be dominated by the other feasible alternatives. Here, we propose a structure of domination over the objective space and explore the geometry of the set of all nondominated solutions. Two methods for locating the set of all nondominated solutions through ordinary mathematical programming are introduced. In order to achieve our main results, we have introduced the new concepts of cone convexity and cone extreme point, and we have explored their main properties. Some relevant results on polar cones and polyhedral cones are also derived. Throughout the paper, we also pay attention to an important special case of nondominated solutions, that is, Pareto-optimal solutions. The geometry of the set of all Pareto solutions and methods for locating it are also studied. At the end, we provide an example to show how we can locate the set of all nondominated solutions through a derived decomposition theorem.

Decision-theoretic aspects of risk-taking behaviour

A crucial problem in economic decision (game) theory is to specify by an algorithm the standards of behaviour which determine the process of decision-making. Recent research has indicated that the attitude to risk is an important argument for finding unique solutions for decision problems. In this study different behaviour-constants of decision-making are reported which clarify that a logical equivalency exists between decision-making, conflict, achievement motive and risk-taking. By using information theoretic arguments as a transform rule, it is suggested to measure risk-preference and risk-aversion in terms of redundancy and related measures.