Ambiguity aversion and ambiguity content in decision making under uncertainty

The Subjectively Weighted Linear Utility (SWLU) model for decision making under uncertainty can accommodate non-neutral attitudes toward ambiguity. We first characterize ambiguity aversion in terms of the SWLU model parameters. In addition, we show that ambiguity content may reasonably be regarded as residing in the decision maker's subjective probability distribution of induced utility. In particular, (a) a special kind of mean preserving spread of the induced utility distribution will always increase ambiguity content, and (b) utility distributions which are more shiftable by new information have higher ambiguity content.     

Expert knowledge and computer-aided group decision making: Some pragmatic reflections

Based on a simple outranking method of multi-attribute decision making (MADM), called Dichotomy-Cut, developed in recent years and published elsewhere, this paper describes how to reliably elicit the necessary decision knowledge for implementing various decision modes via this method and its computerized support - UNIDAS 2. The most important features of this method are outlined, namely, how to compose the preference ordered matrices and which are the basic decision rules. Special attention should be paid to specific interactive group decision behaviour of experts. Two examples plainly explain the contents discussed.     

Influence of model management systems on decision making: empirical evidence and implications

Model management (MM) regards decision models as an important organisational resource deserving prudent management. Despite the remarkable volume of model management literature compiled over the past twenty-odd years, very little is known about how decision makers actually benefit from employing model management systems (MMS). In this paper, we report findings from an experiment designed to verify the idea that the adequacy of modeling support provided by a MMS influences the decision maker's problem solving performance and behaviour. We show that the decision makers who receive adequate modelling support from MMS outperform those without such support. Also, we provide empirical evidence that the MMS help turn the decision makers' perception of problem solving from a number crunching task into development of solution strategies, consequently changing their decision making behaviour.     

Effects of fuzzy data on decision making in a competitive supply chain

The essence of data plays a critical role in decision making in supply chain management (SCM). When data embedded in supply chains (SCs) are fuzzy, the associated equilibrium and performance measures also become fuzzy. This paper investigates the effects of fuzzy data on decision making in a two-echelon SC with a supplier and duopolistic retailers playing a Stackelberg strategic game in both intra- and inter-echelons. In contrast to existing approaches, this paper devises an analysis method to provide a likely interval of the fuzzy maximal profit with a known possibility level (degree of certainty) rather than a singleton (crisp value). The idea is based on the extension principle to reformulate the two-level optimization problem as a pair of parametric quadratic programs in order to calculate the lower and upper bounds of the leader’s fuzzy maximal profit at each possibility level of the obtained information. The analytic results indicate that the higher the degree of uncertainty, the smaller (larger) the lower (upper) bound of the maximum profit of each SC member. Moreover, the main results obtained from eight scenarios show that when the degree of demand diversity between the two retailers is significantly high, the Stackelberg leader is most likely to obtain lower profit and the marginal contribution of the primary demand to the total profit of the duopolistic retailers will exceed that of the powerful supplier’s maximum profit.     

Developments in time preference and their implications for medical decision making

The field of time preference is developing rapidly. It concerns important concepts for many economic issues. One important domain of application is health economics. This paper reviews several empirical and theoretical developments for time preference with special attention to the health economics field. In addition, the implications for medical decision making, long-term health-care planning and health economic evaluation are discussed. Recognition of this empirical evidence in health-care policy making is recommended, as well as a more transparent process of the framing and analysis of, and deliberation on, public policy.     

DEA-based hypothesis tests for comparing two groups of decision making units

In this paper, we develop five statistical tests to compare the efficiencies of different groups of DMUs. We consider a data generating process (DGP) that models the deviation of the output from the best practice frontier as the sum of two components, a one-sided inefficiency term and a two-sided random noise term. We use simulation to evaluate the performance of the five tests against the Banker tests (Banker, 1993) that were designed for DGPs containing a single one-sided error term. It is found that while the Banker tests are very effective when efficiency dominates noise, the tests developed in this paper perform better than the Banker tests when noise levels are significant.     

Some applications of polynomial optimization in operations research and real-time decision making

We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (1) wireless coverage of targeted geographical regions with guaranteed signal quality and minimum transmission power, (2) computing real-time certificates of collision avoidance for a simple model of an unmanned vehicle (UV) navigating through a cluttered environment, and (3) designing a nonlinear hovering controller for a quadrotor UV, which has recently been used for load transportation. On our smaller-scale applications, we apply the sum of squares (SOS) relaxation and solve the underlying problems with semidefinite programming. On the larger-scale or real-time applications, we use our recently introduced “SDSOS Optimization” techniques which result in second order cone programs. To the best of our knowledge, this is the first study of real-time applications of sum of squares techniques in optimization and control. No knowledge in dynamics and control is assumed from the reader.     

Some decision and counting problems of the Duquenne-Guigues basis of implications

Implications of a formal context obey Armstrong rules, which allows one to define a minimal (in the number of implications) implication basis, called Duquenne-Guigues basis or stem base in the literature. In this paper we show how implications are reduced to functional dependencies and prove that the problem of determining the size of the stem base is a #P-complete problem.     

Orderings based on the banks set: Some new scoring methods for multicriteria decision making

This article introduces new methods for ranking alternatives in multicriteria decision making situations. Each is based on the normative position that the strength of an alternative is inversely related to the number of alternatives that could prevent it from being chosen. The scores discriminate among elements of the Banks set (Banks, Soc Choice Welfare, 1985, 1, 295–306). The new scoring methods are compared to traditional scoring methods and related to the amount of intransitivity (specifically, the size of the top‐cycle) of aggregated preference. The new scores are shown to measure important aspects of alternatives not captured by extant scoring methods and are illustrated in collective choice settings. © 2014 Wiley Periodicals, Inc. Complexity 20: 63–76, 2015     

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.     

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.     

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.     

Wisdom,decision support and paradigms of decision making

Many decision support tools have been developed over the last 20 years and, in general, they support what Simon termed substantive rationality. However, such tools are rarely suited to helping people tackle wicked problems, for which a form of procedural rationality is better suited. Procedurally rational approaches have appeared in both management science and computer science, examples being the soft OR approach of cognitive mapping and the design rationale based on IBIS. These approaches are reviewed and the development of Wisdom, a procedurally rational decision support process and accompanying tool, is discussed and evaluated.     

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.     

Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making

This paper deals with multiattribute group decision making (MAGDM) problems with interval-valued 2-tuple linguistic information. First, we introduce some new aggregation operators, such as the interval-valued 2-tuple weighted geometric (IVTWG) operator, the interval-valued 2-tuple ordered weighted geometric (IVTOWG) operator, the generalized interval-valued 2-tuple weighted average (GIVTWA) operator and the generalized interval-valued 2-tuple ordered weighted average (GIVTOWA). Then, we discuss their desired properties and relationships among them. Furthermore, we put forward a new method to determine the weight vector of interval-valued 2-tuple aggregation operator based on the concept of degree of precision. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in dealing with interval-valued 2-tuple linguistic information under multi-granular linguistic contexts.     

Some implications of the union-intersection principle for tests of sphericity

The sphericity hypothesis may be expressed as an intersection of simpler hypotheses on the invariant subspaces of the variance matrix. Applying the union-intersection principle to dissections of this type establishes a link between tests of independence and tests of sphericity. We use some recent results of Bloomfield and Watson [2] and Knott [4] to derive a class of union-intersection tests for sphericity from likelihood ratio tests of independence of two sets of variates. As well, we show that the ordinary likelihood ratio test for sphericity has a natural union-intersection interpretation.     

Q-analysis for modeling and decision making

This paper provides an overview of existing and potential applications of a system-theoretic approach called Q-analysis, using the examples of design and analysis of expert systems in medical image processing and analysis: namely the organization of a histopathologic knowledge base. Q-analysis is also applied to a multicriterion decision-making (MCDM) problem using a method called multicriterion Q-analysis (MCQA). A brief discussion of the advantages and limitations of Q-analysis is given, with suggestions for further applications.     

Artificial intelligence and human decision making

Decision is obviously related to reasoning. One of the possible definitions of artificial intelligence (AI) refers to cognitive processes and especially to reasoning. Before making any decision, people also reason, it is therefore natural to explore the links between AI and decision making. This paper distinguishes between two aspects of decision making: diagnosis and look-ahead. It is shown that, on the one hand, AI has many relationships with diagnosis (expert systems, case-based reasoning, fuzzy set and rough set theories). On the other hand, AI has not paid enough attention to look-ahead reasoning, whose main components are uncertainty and preferences. These aspects of AI and decision making are reviewed in the paper.     

Stochastic multicriteria decision making and uncertainty

We define the notion of stochastic multicriteria decision problem to take into account uncertainty in the data. A general approach is proposed to analyse these problems. As a special case, project evaluation by experts is considered. Stochastic independence problems are discussed and the notion of expected preference function is defined to introduce a stochastic extension of the Promethee outranking method.