Interactive fuzzy decision making method for solving bilevel programming problem

In this paper, an interactive fuzzy decision making method is proposed for solving bilevel programming problem. Introducing a new balance function, we consider the overall satisfactory balance between the leader and the follower. Then, a satisfactory solution can be obtained by the proposed method. Finally, numerical examples are reported to illustrate the feasibility of the proposed method.     

Hierarchical multi-objective decision making

This paper proposes a hierarchical procedure for solving decision problems with multiple objectives. The procedure consists of two levels, a top- and a base-level. The main idea is that the top-level only provides general preference information. Taking this information into account the base-level then determines a compromise solution. For a multi-objective linear program it will be shown how such a hierarchical procedure can be structured by deriving weight restrictions from the general preference information of the top-level and by using the interactive MODM procedure of Zionts and Wallenius on the base-level.     

Interactive decision making: Equivalence of modified formulations

We discuss the use of a quadratic norm for departures from the bliss value of a decision problem under conflicting objectives. The use of a quadratic norm is, for example, of interest within the dynamic framework of optimal control. The symmetric nature of the quadratic norm is relaxed to allow for nonsymmetric preferences. The possibility of tailoring the quadratic objective function to generate optimal policies which are acceptable to the policy maker is explored with two alternative interactive algorithms. One of these is for objective functions with diagonal weighting matrices and uses updates of the bliss values. The second algorithm proceeds by updating non-diagonal weights, while keeping the bliss values fixed. The equivalence of both algorithms is established.     

Interactive weight assessment in multiple attribute decision making

A weight assessing method is given for solving a multiple attribute decision problem involving one decision maker. The method provides significant freedom to the decision maker who is asked only to specify certain groups of attributes and the corresponding joint weights. The method then provides a sophisticated interaction between various levels of the attributes involved. Furthermore, if the decision maker wishes to give additional information of the above-mentioned kind, he establishes an interaction on the level of the solution process. This can compensate for the inherent limitations of any method based on scalar utility functions by allowing a certain intransitivity and incomparability of preferences, which are natural in multiple attribute situations.     

Model and extended Kuhn–Tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation

When multiple followers are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. One of the popular situations within this bilevel multi-follower issue is where these followers are uncooperatively making their decisions while having cross reference to decision information of the other followers. This situation is called a referential-uncooperative situation in this paper. The well-known Kuhn–Tucker approach has been previously successfully applied to a one-leader-and-one-follower linear bilevel decision problem. This paper extends this approach to deal with the above-mentioned linear referential-uncooperative bilevel multi-follower decision problem. The paper first presents a decision model for this problem. It then proposes an extended Kuhn–Tucker approach to solve this problem. Finally, a numerical example illustrates the application of the extended Kuhn–Tucker approach.     

Interactive multiobjective decision making by the sequential proxy optimization technique: SPOT

In this paper, we propose a new interactive multiobjective decision making technique, which we call the Sequential Proxy Optimization Technique (SPOT), in order to overcome the drawbacks of the conventional multiobjective decision making methods. Our method combines the desirable features of both the Surrogate Worth Trade-off (SWT) method and the Multiattribute Utility Function (MUF) method. We can interactively derive the preferred solution of the decision maker efficiently by assessing his marginal rate of substitution and maximizing sequentially the local proxy preference function. A numerical example illustrates the feasibility and efficiency of the proposed method.     

Interactive fuzzy goal programming approach for bilevel programming problem

This paper presents an interactive fuzzy goal programming (FGP) approach for bilevel programming problems with the characteristics of dynamic programming (DP).     

Microcomputer programs for multi-objective decision analysis

Two menu-driven microcomputer programs written in Turbo Pascal are available to assist with multi-objective decision analysis. Multiplicative and additive multi-attribute utility functions are supported along with exponential or linear single-attribute utility functions. Decision trees are not supported. The Pearson-Turkey approximation is used for expected utility calculations.     

Graph-based multi-agent decision making

In lots of practical multi-criteria decision making (MCDM) problems, there exist various and changeable relations among the criteria which cannot be handled well by means of the existing methods. Considering that graphic or netlike structures can be used to describe the relationships among several individuals, we first introduce the graphic structure into MCDM and formalize the relations among criteria. Then, we develop a new tool, called graph-based multi-agent decision making (GMADM) model, to deal with a kind of MCDM problems with the interrelated criteria. In the model, the graphic structure is paid sufficient attention to in two main aspects: (1) how the graphic structure has influence on the benefits of agents (or the criteria values); and (2) the relation between the graphic structure and the importance weights of agents (criteria). In this case, we can select the best plan(s) (or alternative(s)) according to the overall benefits (the overall criteria values) resulting from the model. Moreover, a fuzzy graph-based multi-agent decision making (FGMADM) method is developed to solve a common kind of situations where the graphic structure of agents is uncertain (confidential or false). Three examples are used to illustrate the feasibility of these two developed methods.     

Possibilistic sequential decision making

When the information about uncertainty cannot be quantified in a simple, probabilistic way, the topic of possibilistic decision theory is often a natural one to consider. The development of possibilistic decision theory has lead to the proposition a series of possibilistic criteria, namely: optimistic and pessimistic possibilistic qualitative criteria [7], possibilistic likely dominance [2], [9], binary possibilistic utility [11] and possibilistic Choquet integrals [24]. This paper focuses on sequential decision making in possibilistic decision trees. It proposes a theoretical study on the complexity of the problem of finding an optimal strategy depending on the monotonicity property of the optimization criteria – when the criterion is transitive, this property indeed allows a polytime solving of the problem by Dynamic Programming. We show that most possibilistic decision criteria, but possibilistic Choquet integrals, satisfy monotonicity and that the corresponding optimization problems can be solved in polynomial time by Dynamic Programming. Concerning the possibilistic likely dominance criteria which is quasi-transitive but not fully transitive, we propose an extended version of Dynamic Programming which remains polynomial in the size of the decision tree. We also show that for the particular case of possibilistic Choquet integrals, the problem of finding an optimal strategy is NP-hard. It can be solved by a Branch and Bound algorithm. Experiments show that even not necessarily optimal, the strategies built by Dynamic Programming are generally very good.     

Search during decision making

Nearly four hundred non-routine organizational decisions were investigated to discover search approaches––determining the frequency of use and success of each search approach uncovered. A “search approach” is made up of a direction and a means to uncover solution ideas. Direction indicates desired results and it can be either implicit or explicit, with an explicit direction offering either a problem or a goal-like target. Solutions can be uncovered by opportunity, bargaining, and chance as well as by rational approaches. Defining a search approach as a direction coupled with a means of search, search approaches were linked with indicators of success, measured by the decision's adoption, value and timeliness, noting frequency. A rational, goal-directed, search approach was more apt to produce successful outcomes. Bargaining with stakeholders to uncover solutions was always combined some of the search approaches in this study, and this merger improved the prospects of success. Searches with an opportunistic or chance (emergent opportunity) features and rational searches with a problem target were more apt to produce unsuccessful outcomes. The means used to come up with a solution had less bearing on success than did the type of direction, with goal-directed searches leading to the best outcomes. Each search approach is discussed to reveal best practices and to offer suggestions to improve practice.     

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.     

Self-consistency of decision rules for group decision making

The author treats, in this paper, a group of decision makers, where each of them already has preference on a given set of alternatives but the group as a whole does not have a decision rule to make their group decision, yet. Then, the author examines which decision rules are appropriate. As a criterion of “appropriateness” the author proposes the concepts of self-consistency and universal self-consistency of decision rules. Examining the existence of universally self-consistent decision rules in two cases: (1) decision situations with three decision makers and two alternatives, and (2) those with three decision makers and three alternatives, the author has found that all decision rules are universally self-consistent in the case (1), whereas all universally self-consistent decision rules have one and just one vetoer in the essential cases in (2). The result in the case (2) implies incompatibility of universal self-consistency with symmetry. An example of applications of the concept of self-consistency to a bankruptcy problem is also provided in this paper, where compatibility of self-consistency with symmetry in a particular decision situation is shown.     

Interactive decision making for uncertain minimum spanning tree problems with total importance based on a risk-management approach

This paper deals with a minimum spanning tree problem where each edge cost includes uncertainty and importance measure. In risk management to avoid adverse impacts derived from uncertainty, a d-confidence interval for the total cost derived from robustness is introduced. Then, by maximizing the considerable region as well as minimizing the cost-importance ratio, a biobjective minimum spanning tree problem is proposed. Furthermore, in order to satisfy the objects of the decision maker and to solve the proposed model in mathematical programming, fuzzy goals for the objects are introduced as satisfaction functions, and an exact solution algorithm is developed using interactive decision making and deterministic equivalent transformations. Numerical examples are provided to compare our proposed model with some previous models.     

Energy models for decision making

Since the 1973 oil crisis there has been an explosion in energy modelling activities throughout the world. A bewildering array of models have been or are being developed. The models differ in their geographical scope (local, national, regional or global), their technical scope (a process, an industry, an energy source or all energy industries), their timescale (one to one hundred years) and their systems boundaries (energy, economy, society). In addition there are crucial differences in the level of detail modelled, in the way time is structured and in the way in which decisions are included or perhaps excluded from the model.The natural questions to ask are what sort of models are now available; which models are suitable for which purposes; what has been learnt so far; which are the promising directions for future developments? This paper draws on modelling experience both within the National Coal Board and elsewhere to discuss these questions. The paper contains the following sections: energy models and decision making processes; choosing model boundaries; logic and facts, the basis of the model; choice of energy model; links to the economy; future directions. The subject will be of interest to specialist energy modellers and those interested more generally in strategic modelling for government and industry.     

Improving long-run industrial decision making

The paper describes the present status of new product evaluation and decision making in large and small companies. It discusses the need to draw from a wide range of sources for societal as well as financial and technical information. While deficiencies and the need for improved analytical capabilities are identified, the emphasis is on what can be done, and near term problems using as an example the decision to produce a new type of vehicle engine.     

Confidence structures in decision making

Decision making is defined in terms of four elements: the set of decisions, the set of outcomes for each decision, a set-valued criterion function, and the decision maker's value judgment for each outcome. Various confidence structures are defined, which give the decision maker's confidence of a given decision leading to a particular outcome. The relation of certain confidence structures to Bayesian decision making and to membership functions in fuzzy set theory is established. A number of schemes are discussed for arriving atbest decisions, and some new types of domination structures are introduced.This research was partly supported by Project No. NR-047-021, ONR Contract No. N-00014-75-C-0569 with the Center for Cybernetic Studies, The University of Texas, Austin, Texas, and by ONR Contract No. N-00014-69-A-0200-1012 with the University of California, Berkeley, California.     

Developing models of decision making

Studies that focus on the decision making process can be classified in (at least) two ways: by psychological content and by contextual content. The first describes the degree to which the analysis focuses on the mental processes associated with decision making and the second deals with the degree to which the analysis is dependent upon the study's context. Several studies are examined in terms of where they fall in this two-dimensional taxonomy. Two analyses of maritime command and control conducted by the authors are examined more fully within this taxonomy. Both are context full, but are at opposite ends of the psychological content spectrum. These categorizations are useful in focusing future research aimed at developing models of decision making.     

Multicriteria decision making under uncertainty

Formalization for problems of multicriteria decision making under uncertainty is constructed in terms of guaranteed and weak estimates. A relevant definition of the vector maximinimax value is given. Parameterization and approximation of maximum, minimax, and maximinimax values based on the inverse logical convolution are suggested. An application for multicommodity networks is considered. Received: December 13, 2000 / Accepted: August 21, 2001?Published online May 8, 2002