Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization

This paper considers stochastic two-level linear programming problems. Using the concept of chance constraints and probability maximization, original problems are transformed into deterministic ones. An interactive fuzzy programming method is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance

Improved two-phase solution strategy for multiobjective fuzzy stochastic linear programming problems with uncertain probability distribution

Multiobjective Fuzzy Stochastic Linear Programming (MFSLP) problem where the linear inequalities on the probability are fuzzy is called a Multiobjective Fuzzy Stochastic Linear Programming problem with Fuzzy Linear Partial Information on Probability Distribution (MFSLPPFI). The uncertainty presents unique difficulties in constrained optimization problems owing to the presence of conflicting goals and randomness surrounding the data. Most existing solution techniques for MFSLPPFI problems rely heavily on the expectation optimization model, the variance minimization model, the probability maximization model, pessimistic/optimistic values and compromise solution under partial uncertainty of random parameters. Although these approaches recognize the fact that the interval values for probability distribution have important significance, nevertheless they are restricted by the upper and lower limitations of probability distribution and neglected the interior values. This limitation motivated us to search for more efficient strategies for MFSLPPFI which address both the fuzziness of the probability distributions, and the fuzziness and randomness of the parameters. The proposed strategy consists two phases: fuzzy transformation and stochastic transformation. First, ranking function is used to transform the MFSLPPFI to Multiobjective Stochastic Linear Programming Problem with Fuzzy Linear Partial Information on Probability Distribution (MSLPPFI). The problem is then transformed to its corresponding Multiobjective Linear Programming (MLP) problem by using a-cut technique of uncertain probability distribution and linguistic hedges. In addition, Chance Constraint Programming (CCP), and expectation of random coefficients are applied to the constraints and the objectives respectively. Finally, the MLP problem is converted to a single-objective Linear Programming (LP) problem via an Adaptive Arithmetic Average Method (AAAM), and then solved by using simplex method. The algorithm used to obtain the solution requires fewer iterations and faster generation of results compared to existing solutions. Three realistic examples are tested which show that the approach used in this study is efficient in solving the MFSLPPFI

Interactive Fuzzy Random Two-level Linear Programming through Fractile Criterion Optimization

This paper considers two-level linear programming problems involving fuzzy random variables. Having introduced level sets of fuzzy random variables and fuzzy goals of decision makers, following fractile criterion optimization, fuzzy random two-level programming problems are transformed into deterministic ones. Interactive fuzzy programming is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance

Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds

In the interdisciplinary and intercultural systems analysis that constitutes the main theme of research in IIASA, a basic question is how to analyze and support decisions with help of mathematical models and logical procedures. This question -- particularly in its multi-criteria and multi-cultural dimensions -- has been investigated in System and Decision Sciences Program (SDS) since the beginning of IIASA. Researchers working both at IIASA and in a large international network of cooperating institutions contributed to a deeper understanding of this question. Around 1980, the concept of reference point multiobjective optimization was developed in SDS. This concept determined an international trend of research pursued in many countries cooperating with IIASA as well as in many research programs at IIASA -- such as energy, agricultural, environmental research. SDS organized since this time numerous international workshops, summer schools, seminar days and cooperative research agreements in the field of decision analysis and support. By this international and interdisciplinary cooperation, the concept of reference point multiobjective optimization has matured and was generalized into a framework of aspiration based decision analysis and support that can be understood as a synthesis of several known, antithetical approaches to this subject -- such as utility maximization approach, or satisficing approach, or goal -- program -- oriented planning approach. Jointly, the name of quasisatisficing approach can be also used, since the concept of aspirations comes from the satisficing approach. Both authors of the Working Paper contributed actively to this research: Andrzej Wierzbicki originated the concept of reference point multiobjective optimization and quasisatisficing approach, while Andrzej Lewandowski, working from the beginning in the numerous applications and extensions of this concept, has had the main contribution to its generalization into the framework of aspiration based decision analysis and support systems. This paper constitutes a draft of the first part of a book being prepared by these two authors. Part I, devoted to theoretical foundations and methodological background, written mostly by Andrzej Wierzbicki, will be followed by Part II, devoted to computer implementations and applications of decision support systems based on mathematical programming models, written mostly by Andrzej Lewandowski. Part III, devoted to decision support systems for the case of subjective evaluations of discrete decision alternatives, will be written by both authors

Interactive Decision Analysis; Proceedings of an International Workshop on Interactive Decision Analysis and Interpretative Computer Intelligence, Laxenburg, Austria, September 20-23, 1983

An International Workshop on Interactive Decision Analysis and Interpretative Computer Intelligence was held at IIASA in September 1983. The Workshop was motivated, firstly, by the realization that the rapid development of computers, especially microcomputers, will greatly increase the scope and capabilities of computerized decision-support systems. It is important to explore the potential of these systems for use in handling the complex technological, environmental, economic and social problems that face the world today. Research in decision-support systems also has another, less tangible but possibly more important, motivation. The development of efficient systems for decision support requires a thorough understanding of the differences between the decision-making processes in different nations and cultures. An understanding of the different rationales underlying decision making is not only necessary for the development of efficient decision-support systems, but it is also an important factor in encouraging international understanding and cooperation. The Proceedings of the Workshop which are contained in this volume are divided in four main sections. The first section consists of an introductory lecture in which a unifying approach to the use of computers and computerized mathematical models for decision analysis and support is described. The second section is concerned with approaches and concepts in interactive decision analysis and section three is devoted to methods and techniques for decision analysis. The final section contains descriptions of a wide range of applications of interactive techniques, covering the fields of economics, public policy planning, energy policy evaluation, hydrology and industrial development

Reference Point Methods in Vector Optimization and Decision Support

This paper presents a summary of reference point methodology in vector optimization and decision support. The methodology was developed at IIASA since 1980 and applied in numerous projects, both in IIASA and elsewhere. The paper presents methodological foundations, basic concepts and notation, reference points and achievement functions, neutral and weighted compromise solutions, issues of modeling for multi-objective analysis, some basic applications of reference point methods and a discussion of a decision process type supported by reference point methodology

Large-Scale Modelling and Interactive Decision Analysis

These Proceedings report the scientific results of an International Workshop attended by more than fifty scientists from thirteen countries. This volume is structured in three parts: (I) Theory and Methodology, (II) Interaction Principles and Computational Aspects and (III) Applications. Part I contains papers dealing with utility and game theory, multicriteria optimizations theory and interactive procedures, dynamic models/systems and concepts of multicriteria analysis. Papers dealing with the user-machine interface, intelligent (user-friendly) decision support and problems of computational aspects are included in Part II. Contributions with applications are mainly concentrated in Part III but can also be found in several papers in other parts. Use of the term "large-scale" in the title of the Proceedings was especially substantiated by contributions dealing with modelling and decision analysis problems of the size of a whole national economy like structuring the carbochemical industry, the energy system or even natural gas trade in Europe

System reliability optimization : a fuzzy genetic algorithm approach

System reliability optimization is often faced with imprecise and conflicting goals such as reducing the cost of the system and improving the reliability of the system. The decision making process becomes fuzzy and multi-objective. In this paper, we formulate the problem as a fuzzy multi-objective nonlinear program (FMOOP). A fuzzy multiobjective genetic algorithm approach (FMGA) is proposed for solving the multi-objective decision problem in order to handle the fuzzy goals and constraints. The approach is able flexible and adaptable, allowing for intermediate solutions, leading to high quality solutions. Thus, the approach incorporates the preferences of the decision maker concerning the cost and reliability goals through the use of fuzzy numbers. The utility of the approach is demonstrated on benchmark problems in the literature. Computational results show that the FMGA approach is promising