Multigranulation decision-theoretic rough sets

Decision-theoretic rough set model and spatial analysis-based waste-to-energy incineration plant site selection: a case study in first-tier cities of China

Selecting a sustainable waste-to-energy (WTE) incineration plant site is important for handling huge challenges created by on-going municipal solid waste. However, many studies with WTE incineration plant site problems fail to determine alternative evaluation criteria and cities beforehand, which may increase decision costs and evaluation risks. This paper proposes a novel methodology based on decision-theoretic rough set model and suitable analysis for selecting the optimal WTE incineration plant site. Firstly, from the features of cities, alternative evaluation criteria are determined by three-phase method. Considering different geographical features, a geographical index system is established. Secondly, subjective and objective criteria weights are determined by an improved DEMATEL (Decision Making Trial and Evaluation Laboratory) method and TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method-based linear programming model under the hesitant fuzzy linguistic context, respectively. Subjective and objective criteria weights are combined to form the final criteria weights by building an optimization model. Thirdly, the decision-theoretic rough set model is utilized to select alternative WTE incineration plant sites. We utilize spatial analysis adopting Geographic Information System technology to rank all alternative cities to build facilities. Finally, a numerical case is performed to illustrate the feasibility of the proposed methodology. The sensitivity analysis with the parameter [Formula: see text] ranking from 0 to 1 is performed, the result confirms that the proposed methodology has better robustness. Compared with the multi-criteria decision-making methods, the effectiveness and superiority of the proposed methodology are demonstrated.

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models for uncertainty quantification are firstly reviewed, and theories and advances on probabilistic, non-probabilistic and hybrid ones are discussed. Subsequently, numerical methods for uncertainty propagation are broadly reviewed under different computational strategies. Thirdly, several popular single surrogate models and novel hybrid techniques are reviewed, together with some general criteria for accuracy evaluation. In addition, sample generation techniques to improve the accuracy of surrogate models are discussed for both static sampling and its adaptive version. Finally, closing remarks are provided and future prospects are suggested.

Advantage matrix: two novel multi-attribute decision-making methods and their applications

By comparing attributes of objects in an information system, the advantage matrix on the object set is established in this paper. The contributions can be identified as follows: (1) The advantage degree is proposed by the accumulation of the advantage matrix. (2) Based on the advantage matrix, the advantage (disadvantage) neighborhood approximation operator and the advantage (disadvantage) correlation approximation operator are defined and studied. Based on these two new operators, the neighborhood degree and the correlation degree are presented. The relationships between them are also investigated to demonstrate the value of the proposed method. (3) Finally, based on the above three degrees, new algorithms are designed, in which the effectiveness and robustness of the algorithms are analyzed by practical examples.

(α, β)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making

Pawlak’s rough set theory based on single granulation has been extended to multi-granulation rough set structure in recent years. Multi-granulation rough set theory has become a flouring research direction in rough set theory. In this paper, we propose the notion of (α, β)-multi-granulation bipolar fuzzified rough set ((α, β)-MGBFRSs). For this purpose, a collection of bipolar fuzzy tolerance relations has been used. In the framework of multi-granulation, we proposed two types of (α, β)-multi-granulation bipolar fuzzified rough sets model. One is called the optimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) o-MGBFRSs) and the other is called the pessimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) p-MGBFRSs). Subsequently, a number of important structural properties and results of proposed models are investigated in detail. The relationships among the (α, β)-MGBFRSs, (α, β) o-MGBFRSs and (α, β) p-MGBFRSs are also established. In order to illustrate our proposed models, some examples are considered, which are helpful for applying this theory in practical issues. Moreover, several important measures associated with (α, β)-multi-granulation bipolar fuzzified rough set like the measure of accuracy, the measure of precision, and accuracy of approximation are presented. Finally, we construct a new approach to multi-criteria group decision-making method based on (α, β)-MGBFRSs, and the validity of this technique is illustrated by a practical application. Compared with the existing results, we also expound its advantages.

A comprehensive study of upward fuzzy preference relation based fuzzy rough set models: Properties and applications in treatment of coronavirus disease

In this paper, we first introduce a new type of rough sets called α -upward fuzzified preference rodownward fuzzy preferenceugh sets using upward fuzy preference relation. Thereafter on the basis of α -upward fuzzified preference rough sets, we propose approximate precision, rough degree, approximate quality and their mutual relationships. Furthermore, we presented the idea of new types of fuzzy upward β -coverings, fuzzy upward β -neighborhoods and fuzzy upward complement β -neighborhoods and some relavent properties are discussed. Hereby, we formulate a new type of upward lower and upward upper approximations by applying an upward β -neighborhoods. After employing the upward β -neighborhoods based upward rough set approach to it any times, we can only get the six different sets at most. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Subsequently, we presented the idea to combine the fuzzy implicator and t -norm to introduce multigranulation ( ℐ , T ) -fuzzy upward rough set applying fuzzy upward β -covering and some relative properties are discussed. Finally we presented a new technique for the selection of medicine for treatment of coronavirus disease (COVID-19) using multigranulation ( ℐ , T ) -fuzzy upward rough sets.

On local multigranulation covering decision-theoretic rough sets

Multi-granulation decision-theoretic rough sets uses the granular structures induced by multiple binary relations to approximate the target concept, which can get a more accurate description of the approximate space. However, Multi-granulation decision-theoretic rough sets is very time-consuming to calculate the approximate value of the target set. Local rough sets not only inherits the advantages of classical rough set in dealing with imprecise, fuzzy and uncertain data, but also breaks through the limitation that classical rough set needs a lot of labeled data. In this paper, in order to make full use of the advantage of computational efficiency of local rough sets and the ability of more accurate approximation space description of multi-granulation decision-theoretic rough sets, we propose to combine the local rough sets and the multigranulation decision-theoretic rough sets in the covering approximation space to obtain the local multigranulation covering decision-theoretic rough sets model. This provides an effective tool for discovering knowledge and making decisions in relation to large data sets. We first propose four types of local multigranulation covering decision-theoretic rough sets models in covering approximation space, where a target concept is approximated by employing the maximal or minimal descriptors of objects. Moreover, some important properties and decision rules are studied. Meanwhile, we explore the reduction among the four types of models. Furthermore, we discuss the relationships of the proposed models and other representative models. Finally, illustrative case of medical diagnosis is given to explain and evaluate the advantage of local multigranulation covering decision-theoretic rough sets model.

A three-way decision method based on hybrid data1

An information system as a database that represents relationships between objects and attributes is an important mathematical model in the field of artificial intelligence. Hybrid data means boolean, categorical, real-valued, set-valued data and missing data in this paper. A hybrid information system is an information system where its attribute is hybrid data. This paper proposes a three-way decision method based on hybrid data. First, the distance between two objects based on the conditional attribute set in a given hybrid information system is developed and Gaussian kernel based on this distance is acquired. Then, the fuzzy Tcos-equivalence relation, induced by this information system, is obtained by using Gaussian kernel. Next, the decision-theoretic rough set model in this hybrid information system is presented. Moreover, a three-way decision method is given by means of this decision-theoretic rough set model and inclusion degree between two fuzzy sets. Finally, an example is employed to illustrate the feasibility of the proposed method, which may provide an effective method for hybrid data analysis in real applications.