Интервальное оценивание альтернатив в задачах принятия решений

Побудовано інтервальні математичні моделі задач прийняття рішень в умовах інтервальної невизначеності. Для розв’язання задач, вихідні дані яких задані в інтервальному вигляді, запропоновано модифіковані методи на базі детермінованих методів прийняття рішень та інтервального аналізу.The article considers interval models of decision-making problems under interval uncertainty. The solution approach for realization of the models is provided based on deterministic methods of decision-making and interval analysis

A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information

This article proposes an approach to handle multi-attribute decision making (MADM) problems under the interval-valued intuitionistic fuzzy environment, in which both assessments of alternatives on attributes (hereafter, referred to as attribute values) and attribute weights are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). The notion of relative closeness is extended to interval values to accommodate IVIFN decision data, and fractional programming models are developed based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to determine a relative closeness interval where attribute weights are independently determined for each alternative. By employing a series of optimization models, a quadratic program is established for obtaining a unified attribute weight vector, whereby the individual IVIFN attribute values are aggregated into relative closeness intervals to the ideal solution for final ranking. An illustrative supplier selection problem is employed to demonstrate how to apply the proposed procedure

Unified Bayesian Frameworks for Multi-criteria Decision-making Problems

This paper presents Bayesian frameworks for different tasks within multi-criteria decision-making (MCDM) based on a probabilistic interpretation of the MCDM methods and problems. Owing to the flexibility of Bayesian models, the proposed frameworks can address several long-standing and fundamental challenges in MCDM, including group decision-making problems and criteria correlation, in a statistically elegant manner. Also, the models can accommodate different forms of uncertainty in the preferences of the decision makers (DMs), such as normal and triangular distributions as well as interval preferences. Further, a probabilistic mixture model is developed that can group the DMs into several exhaustive classes. A probabilistic ranking scheme is also designed for both criteria and alternatives, where it identifies the extent to which one criterion/alternative is more important than another based on the DM(s) preferences. The experiments validate the outcome of the proposed frameworks on several numerical examples and highlight its salient features compared to other methods

Consistency test and weight generation for additive interval fuzzy preference relations

Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino (Fuzzy Sets Syst 12:117–131, 1984), a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in Xu and Chen (Eur J Oper Res 184:266–280, 2008b)

TOPSIS-RTCID for range target-based criteria and interval data

[EN] The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is receiving considerable attention as an essential decision analysis technique and becoming a leading method. This paper describes a new version of TOPSIS with interval data and capability to deal with all types of criteria. An improved structure of the TOPSIS is presented to deal with high uncertainty in engineering and engineering decision-making. The proposed Range Target-based Criteria and Interval Data model of TOPSIS (TOPSIS-RTCID) achieves the core contribution in decision making theories through a distinct normalization formula for cost and benefits criteria in scale of point and range target-based values. It is important to notice a very interesting property of the proposed normalization formula being opposite to the usual one. This property can explain why the rank reversal problem is limited. The applicability of the proposed TOPSIS-RTCID method is examined with several empirical litreture’s examples with comparisons, sensitivity analysis, and simulation. The authors have developed a new tool with more efficient, reliable and robust outcomes compared to that from other available tools. The complexity of an engineering design decision problem can be resolved through the development of a well-structured decision making method with multiple attributes. Various decision approches developed for engineering design have neglected elements that should have been taken into account. Through this study, engineering design problems can be resolved with greater reliability and confidence.Jahan, A.; Yazdani, M.; Edwards, K. (2021). TOPSIS-RTCID for range target-based criteria and interval data. International Journal of Production Management and Engineering. 9(1):1-14. https://doi.org/10.4995/ijpme.2021.13323OJS11491Ahn, B.S. (2017). 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An ACO-based Hyper-heuristic for Sequencing Many-objective Evolutionary Algorithms that Consider Different Ways to Incorporate the DM's Preferences

Many-objective optimization is an area of interest common to researchers, professionals, and practitioners because of its real-world implications. Preference incorporation into Multi-Objective Evolutionary Algorithms (MOEAs) is one of the current approaches to treat Many-Objective Optimization Problems (MaOPs). Some recent studies have focused on the advantages of embedding preference models based on interval outranking into MOEAs; several models have been proposed to achieve it. Since there are many factors influencing the choice of the best outranking model, there is no clear notion of which is the best model to incorporate the preferences of the decision maker into a particular problem. This paper proposes a hyper-heuristic algorithm—named HyperACO—that searches for the best combination of several interval outranking models embedded into MOEAs to solve MaOPs. HyperACO is able not only to select the most appropriate model but also to combine the already existing models to solve a specific MaOP correctly. The results obtained on the DTLZ and WFG test suites corroborate that HyperACO can hybridize MOEAs with a combined preference model that is suitable to the problem being solved. Performance comparisons with other state-of-the-art MOEAs and tests for statistical significance validate this conclusion

Parameter reduction analysis under interval-valued m-polar fuzzy soft information

[EN] This paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.J. C. R. Alcantud is grateful to the Junta de Castilla y León and the European Regional Development Fund (Grant CLU-2019-03) for the financial support to the research unit of excellence “Economics Management for Sustainability” (GECOS).Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

Day-ahead energy and reserve dispatch problem under non-probabilistic uncertainty

The current energy transition and the underlying growth in variable and uncertain renewable-based energy generation challenge the proper operation of power systems. Classical probabilistic uncertainty models, e.g., stochastic programming or robust optimisation, have been used widely to solve problems such as the day-ahead energy and reserve dispatch problem to enhance the day-ahead decisions with a probabilistic insight of renewable energy generation in real-time. By doing so, the scheduling of the power system becomes, production and consumption of electric power, more reliable (i.e., more robust because of potential deviations) while minimising the social costs given potential balancing actions. Nevertheless, these classical models are not valid when the uncertainty is imprecise, meaning that the system operator may not rely on a unique distribution function to describe the uncertainty. Given the Distributionally Robust Optimisation method, our approach can be implemented for any non-probabilistic, e.g., interval models rather than only sets of distribution functions (ambiguity set of probability distributions). In this paper, the aim is to apply two advanced non-probabilistic uncertainty models: Interval and ϵ-contamination, where the imprecision and in-determinism in the uncertainty (uncertain parameters) are considered. We propose two kinds of theoretical solutions under two decision criteria—Maximinity and Maximality. For an illustration of our solutions, we apply our proposed approach to a case study inspired by the 24-node IEEE reliability test system

Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics

Automated synthesis of provably correct controllers for cyber-physical systems is crucial for deployment in safety-critical scenarios. However, hybrid features and stochastic or unknown behaviours make this problem challenging. We propose a method for synthesising controllers for Markov jump linear systems (MJLSs), a class of discrete-time models for cyber-physical systems, so that they certifiably satisfy probabilistic computation tree logic (PCTL) formulae. An MJLS consists of a finite set of stochastic linear dynamics and discrete jumps between these dynamics that are governed by a Markov decision process (MDP). We consider the cases where the transition probabilities of this MDP are either known up to an interval or completely unknown. Our approach is based on a finite-state abstraction that captures both the discrete (mode-jumping) and continuous (stochastic linear) behaviour of the MJLS. We formalise this abstraction as an interval MDP (iMDP) for which we compute intervals of transition probabilities using sampling techniques from the so-called 'scenario approach', resulting in a probabilistically sound approximation. We apply our method to multiple realistic benchmark problems, in particular, a temperature control and an aerial vehicle delivery problem.Comment: 14 pages, 6 figures, under review at QES

WIND POWER PROBABILISTIC PREDICTION AND UNCERTAINTY MODELING FOR OPERATION OF LARGE-SCALE POWER SYSTEMS

Over the last decade, large scale renewable energy generation has been integrated into power systems. Wind power generation is known as a widely-used and interesting kind of renewable energy generation around the world. However, the high uncertainty of wind power generation leads to some unavoidable error in wind power prediction process; consequently, it makes the optimal operation and control of power systems very challenging. Since wind power prediction error cannot be entirely removed, providing accurate models for wind power uncertainty can assist power system operators in mitigating its negative effects on decision making conditions. There are efficient ways to show the wind power uncertainty, (i) accurate wind power prediction error probability distribution modeling in the form of probability density functions and (ii) construction of reliable and sharp prediction intervals. Construction of accurate probability density functions and high-quality prediction intervals are difficult because wind power time series is non-stationary. In addition, incorporation of probability density functions and prediction intervals in power systems’ decision-making problems are challenging. In this thesis, the goal is to propose comprehensive frameworks for wind power uncertainty modeling in the form of both probability density functions and prediction intervals and incorporation of each model in power systems’ decision-making problems such as look-ahead economic dispatch. To accurately quantify the uncertainty of wind power generation, different approaches are studied, and a comprehensive framework is then proposed to construct the probability density functions using a mixture of beta kernels. The framework outperforms benchmarks because it can validly capture the actual features of wind power probability density function such as main mass, boundaries, high skewness, and fat tails from the wind power sample moments. Also, using the proposed framework, a generic convex model is proposed for chance-constrained look-ahead economic dispatch problems. It allows power system operators to use piecewise linearization techniques to convert the problem to a mixed-integer linear programming problem. Numerical simulations using IEEE 118-bus test system show that compared with widely used sequential linear programming approaches, the proposed mixed-integer linear programming model leads to less system’s total cost. A framework based on the concept of bandwidth selection for a new and flexible kernel density estimator is proposed for construction of prediction intervals. Unlike previous related works, the proposed framework uses neither a cost function-based optimization problem nor point prediction results; rather, a diffusion-based kernel density estimator is utilized to achieve high-quality prediction intervals for non-stationary wind power time series. The proposed prediction interval construction framework is also founded based on a parallel computing procedure to promote the computational efficiency for practical applications in power systems. Simulation results demonstrate the high performance of the proposed framework compared to well-known conventional benchmarks such as bootstrap extreme learning machine, lower upper bound estimation, quantile regression, auto-regressive integrated moving average, and linear programming-based quantile regression. Finally, a new adjustable robust optimization approach is used to incorporate the constructed prediction intervals with the proposed fuzzy and adaptive diffusion estimator-based prediction interval construction framework. However, to accurately model the correlation and dependence structure of wind farms, especially in high dimensional cases, C-Vine copula models are used for prediction interval construction. The simulation results show that uncertainty modeling using C-Vine copula can lead the system operators to get more realistic sense about the level of overall uncertainty in the system, and consequently more conservative results for energy and reserve scheduling are obtained