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This paper presents a new ranking method to deal with asymmetric uncertainty information for multi-attribute decision making problem. The uncertainty information of the multi-attribute decision making can be expressed by possibility distribution, and it can be measured to the profit and investment on an organization. In the new ranking method, three coefficients of possibilistic distribution are introduced in order to incorporate a measurement of the uncertainty information firstly. Then the possibilistic mean matrix, possibilistic standard variance matrix and possibilistic skewness matrix are constructed, and the positive ideal solution and the negative ideal solution of decision matrix are determined. Finally, a composite closeness coefficient of each alternative is calculated by separation measure between each alternative in order to rank the preference order of all alternatives and select the most suitable one. Two case studies of tailings dam have been shown to demonstrate the feasibility and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

Abstract: The theory of interval-valued intuitionistic fuzzy sets is useful and beneficial for handling uncertainty and imprecision in multiple criteria decision analysis. In addition, the theory allows for convenient quantification of the equivocal nature of human subjective assessments. In this paper, by extending the traditional linear assignment method, we propose a useful method for solving multiple criteria evaluation problems in the interval-valued intuitionistic fuzzy context. A ranking procedure consisting of score functions, accuracy functions, membership uncertainty indices, and hesitation uncertainty indices is presented to determine a criterion-wise preference of the alternatives. An extended linear assignment model is then constructed using a modified weighted-rank frequency matrix to determine the priority order of various alternatives. The feasibility and applicability of the proposed method are illustrated with a multiple criteria decision-making problem involving the selection of a bridge construction method. Additionally, a comparative analysis with other methods, including the approach with weighted aggregation operators, the closeness coefficient-based method, and the auxiliary nonlinear programming models, has been conducted for solving the investment company selection problem to validate the effectiveness of the extended linear assignment method. [Copyright &y& Elsevier]

Abstract: Soft set theory was originally proposed by Molodtsov as a general mathematical tool for dealing with uncertainty in 1999. Recently, researches of decision making based on soft sets have got some progress, but few people consider multi-experts situation. As such, this paper discusses multi-experts group decision making problems. Firstly, we give a concept of intuitionistic fuzzy soft matrix (IFSM) and prove some relevant properties of IFSM. Then, an adjustable approach is presented by means of median level soft set and p-quantile level soft set for dealing with decision making problems based on IFSM. Thirdly, we study aggregation methods of IFSM, give two kinds of aggregation operators and methods that how to determine experts’ weights under different situation with programming models, four corresponding algorithms have been proposed, too. Finally, a practical example has been demonstrated the reasonability and efficiency of these new algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the multiple attribute decision making (MADM) problems with uncertain linguistic information. Motivated by the ideal of Bonferroni mean and geometric Bonferroni mean, we develop two aggregation techniques called the uncertain linguistic Bonferroni mean (ULBM) operator and the uncertain linguistic geometric Bonferroni mean (ULGBM) operator for aggregating the uncertain linguistic information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the uncertain linguistic weighted Bonferroni mean (ULWBM) operator and the uncertain linguistic weighted geometric Bonferroni mean (ULWGBM) operator, based on which we develop two procedures for multiple attribute decision making under the uncertain linguistic environments. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [Copyright &y& Elsevier]

Abstract: Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. By combining the multi-fuzzy set and soft set models, the purpose of this paper is to introduce the concept of multi-fuzzy soft sets. Some operations on a multi-fuzzy soft set are defined, such as complement operation, “AND” and “OR” operations, Union and Intersection operations. Then, the DeMorgan’s laws are proved. Finally, by means of level soft set, an algorithm is presented, and a decision problem is analyzed using multi-fuzzy soft set. [Copyright &y& Elsevier]

Abstract: Success of a contracted project requires collaborative effort from many parties, such as the project owner, the winning tender or contractor, and various suppliers in between. Many studies have been conducted in tender evaluation occurring early in the project life cycle from project owner’s viewpoint. However, responsible tenders are also necessary to evaluate the quality of a potential project owner to ensure that a bid/no-bid decision is correctly made. Such a decision-making problem is likely based on some uncertain factors and imprecise information about a particular owner. Fuzzy theory and probability have been commonly used in general evaluation problems. Since either works within its specified domain, integration of these two approaches within a unique domain becomes a difficult task. In this paper, we explore the usefulness of a novel evaluation model that combines both cloud theory and utility theory together for supporting decision making of multi-attribute evaluation problems under uncertainty. An application of this novel approach to owner evaluation demonstrates that this proposed novel approach is not only useful in dealing with owner evaluation in tendering, but also generic for solving multi-attribute evaluation problems in many disciplines. [Copyright &y& Elsevier]

Abstract: Game theory provides a useful framework for studying Multi-Criteria Decision Making problems. This paper suggests modeling Multi-Criteria Decision Making problems as strategic games and solving them using non-cooperative game theory concepts. The suggested method can be used to prescribe non-dominated solutions and also can be used as a method to predict the outcome of a decision making problem. Non-cooperative stability definitions for solving the games allow consideration of non-cooperative behaviors, often neglected by other methods which assume perfect cooperation among decision makers. To deal with the uncertainty in input variables a Monte-Carlo Game Theory (MCGT) approach is suggested which maps the stochastic problem into many deterministic strategic games. The games are solved using non-cooperative stability definitions and the results include possible effects of uncertainty in input variables on outcomes. The method can handle multi-criteria multi-decision-maker problems with uncertainty. The suggested method does not require criteria weighting, developing a compound decision objective, and accurate quantitative (cardinal) information as it simplifies the decision analysis by solving problems based on qualitative (ordinal) information, reducing the computational burden substantially. The MCGT method is applied to analyze California’s Sacramento-San Joaquin Delta problem. The suggested method provides insights, identifies non-dominated alternatives, and predicts likely decision outcomes. [Copyright &y& Elsevier]

Abstract: How to select suitable partners is critical to virtual enterprise (VE) success and has attracted much attention for both researchers and practitioners. In many practical situations, there usually exists incomplete and uncertain information, and the decision makers cannot easily express their judgments on the candidates with exact and crisp values. Therefore, an extended technique for order preference by similarity to ideal solution (TOPSIS) method for group decision making with interval-valued intuitionistic fuzzy numbers is proposed to solve the partner selection problem under incomplete and uncertain information environment in this paper. And the feasibility and practicability of the extended TOPSIS method are further manifested through an illustrative example. Results show that this extended TOPSIS method for group decision making with interval-valued intuitionistic fuzzy numbers is more suitable to cope with the partner selection problem under incomplete and uncertain information environment. [Copyright &y& Elsevier]

Abstract: Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy–Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated. [Copyright &y& Elsevier]

Abstract: This paper explores the usefulness of cumulative prospect theory (CPT), an inductive–descriptive model for how people make choices with a priori unknown consequences, in the context of travelers’ coping with unreliable transport networks through the estimation of coefficients characterizing CPT’s value and weighting functions. Attention is directed toward employed parents’ trips to collect their child(ren) from the nursery at the end of workday because of parents’ strong sensitivity to the possibility of late arrivals there. Analysis of a stated response experiment about parents’ coping with unreliable transport networks en route to the nursery provides further evidence for a series of violations of the axioms underlying expected utility theory (EUT) – a deductive–normative model of decision-making under uncertainty that is widely used in transportation studies. The results also show that linkages exist between respondents’ everyday life and their responses in the stated response experiment and, by implication, the shape of CPT’s value function. It is therefore concluded that analytical frameworks for describing activity-travel behavior in situations of unreliability, variability and uncertainty should be both psychologically and socially realistic. [Copyright &y& Elsevier]

Abstract: The interpretation phase of Life Cycle Assessment (LCA) studies is often hampered by the number and the heterogeneity of impact assessment results as well as by the uncertainties arising from data, models and practitioner’s choices. While decision-aiding methods have proven to support this key LCA phase, the inclusion of uncertainty evaluations in these methods is still a new topic in the LCA community. The fuzzy multicriteria method NAIADE [Munda G., 1995. Multicriteria Evaluation in a Fuzzy Environment. Heidelberg: Springer-Verlag.] has already been used in several LCA case studies and its framework is well suited for the consideration of uncertainty evaluations as well. This paper proposes a modified version of NAIADE, which conforms to the LCA requirements and to the type of uncertainties to be addressed, with an application example. The discussion of the rankings obtained showed how the integration of uncertainty results could help focusing on critical LCA issues and could be coupled with dominance, contribution and gravity analysis for the interpretation of LCA results, especially when the rankings are not fully consistent. This could support engineers and scientists working in LCA discipline as well as managers and decision-makers faced with decision-making problems based on LCA. [Copyright &y& Elsevier]

Abstract: In this paper, some behavioral (or descriptive) models of individual decision making under risk and/or uncertainty are discussed. Firstly, a model to explain the violations of expected utility hypothesis is described. In this model outcome-dependent, non-additive probabilities are introduced in a measurable value function under risk where probability of each event occurring is known. The effective application of this approach to the public sector is shown in modeling risks of extreme events with low probability and high outcome. Next, a measurable value function under uncertainty is also described where basic probability of a set of event is known but occurrence probability of each event is not known. Potential applicability to evaluating a global warming problem is mentioned. As a special case of the measurable value function under uncertainty an extended Kahneman–Tversky model of prospect theory under uncertainty (PTU) is described. An application of PTU in evaluating the sense of security provided by nursing care robots is described. [Copyright &y& Elsevier]

The challenge problems for the Epistemic Uncertainty Workshop at Sandia National Laboratories provide common ground for comparing different mathematical theories of uncertainty, referred to as General Information Theories (GITs). These problems also present the opportunity to discuss the use of expert knowledge as an important constituent of uncertainty quantification. More specifically, how do the principles and methods of eliciting and analyzing expert knowledge apply to these problems and similar ones encountered in complex technical problem solving and decision making? We will address this question, demonstrating how the elicitation issues and the knowledge that experts provide can be used to assess the uncertainty in outputs that emerge from a black box model or computational code represented by the challenge problems. In our experience, the rich collection of GITs provides an opportunity to capture the experts'' knowledge and associated uncertainties consistent with their thinking, problem solving, and problem representation. The elicitation process is rightly treated as part of an overall analytical approach, and the information elicited is not simply a source of data. In this paper, we detail how the elicitation process itself impacts the analyst''s ability to represent, aggregate, and propagate uncertainty, as well as how to interpret uncertainties in outputs. While this approach does not advocate a specific GIT, answers under uncertainty do result from the elicitation. [Copyright &y& Elsevier]

This paper discusses two main ideas. First, we focus on info-gap uncertainty, as distinct from probability. Info-gap theory is especially suited for modelling and managing uncertainty in system models: we invest all our knowledge in formulating the best possible model; this leaves the modeller with very faulty and fragmentary information about the variation of reality around that optimal model.Second, we examine the interdependence between uncertainty modelling and decision-making. Good uncertainty modelling requires contact with the end-use, namely, with the decision-making application of the uncertainty model. The most important avenue of uncertainty-propagation is from initial data- and model-uncertainties into uncertainty in the decision-domain. Two questions arise. Is the decision robust to the initial uncertainties? Is the decision prone to opportune windfall success?We apply info-gap robustness and opportunity functions to the analysis of representation and propagation of uncertainty in several of the Sandia Challenge Problems. [Copyright &y& Elsevier]