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Abstract: Abstract The return rates of risky assets in financial markets are usually assumed as random variables or fuzzy variables. For the ever-changing real asset market, this assumption may not always be satisfactory. Thus, it is sometimes more realistic to take the return rates as uncertain variables. However, for the existing works on multi-period uncertain portfolio selection problems, they do not find analytic optimal solutions. In this paper, we propose a method for deriving an analytic optimal solution to a multi-period uncertain portfolio selection problem. First, a new uncertain risk measure is defined to model the investment risk. Then, we formulate a bi-criteria optimization model, where the investment return is maximized, while the investment risk is minimized. On this basis, an equivalent transformation is presented to convert the uncertain bi-criteria optimization problem into an equivalent bi-criteria optimization problem. Then, by applying dynamic programming method, an analytic optimal solution is obtained. Finally, a numerical simulation is carried out to show that the proposed model is realistic and the method being developed is applicable and effective. PubDate: 2022-06-01
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Abstract: Abstract This paper first establishes uncertain hypothesis test as a mathematical tool that uses uncertainty theory to help people rationally judge whether some hypotheses are correct or not, according to observed data. As an application, uncertain hypothesis test is employed in uncertain regression analysis to test whether the estimated disturbance term and the fitted regression model are appropriate. In order to illustrate the test process, some numerical examples are documented. PubDate: 2022-06-01
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Abstract: Abstract For the decision-making problems based on decision makers’ judgments in terms of linguistic terms, we propose type-2 fuzzy numbers (T2FNs) that allow decision makers better formalize their judgments. A T2FN has two components: a primary membership and a secondary membership. Compared with T1FSs and interval type-2 fuzzy sets, T2FNs consider an additional dimension by introducing the secondary membership. The primary membership indicates the truth degree of judgment, and the secondary membership further indicates the reliability degree of the truth. We define simple operation rules on T2FNs such that they can be easily used to deal with decision-making problems, such as multi-criteria decision making and multi-stages decision making. Compared with existing related approaches, we verify our approach with several numerical examples. PubDate: 2022-06-01
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Abstract: Abstract In this paper, we study a new type of fuzzy relation system called fuzzy relational inequalities with addition-min-product composition operations to model a peer-to-peer (P2P) file sharing system. Some properties of this addition-min-product system are investigated. We then characterize the structure of the solution set. Furthermore, to reduce the network congestion and improve the stability of data transmission, a min–max programming problem with constraints of addition-min-product fuzzy relation inequalities is established and investigated. We divide this min–max programming problem into several subproblems with the constraint of a single equation. Based on the optimal solutions to these subproblems, we can solve the original fuzzy relation min–max programming problem. Two algorithms, with polynomial computational complexity, are developed to search for an optimal solution to our studied problem. The validity of the algorithms is examined through a numerical example. PubDate: 2022-06-01
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Abstract: Abstract In the decision-making process, retaining the original data information has become a most crucial step. Dual hesitant fuzzy sets (DHFS), which can reflect the original membership degree and non-membership degree information given by the DMs, is a kind of new tool for the DMs to provide the original information as much as possible. In this paper, we focus on the decision- making problem by a projection model (Algorithm I) whose attribute values are given in the forms of dual hesitant fuzzy elements (DHFEs). In order to reflect the information of the data more accurately, we first divide the dual hesitant fuzzy decision matrix into membership degree matrix and non-membership degree matrix. Then we gain the virtual positive ideal solution from the membership degree matrix and the negative positive ideal solution from the non-membership degree matrix. And then the projection values from every solution to the virtual positive ideal solution and the negative positive ideal solution are calculated. In combination with the two projection values, the relative consistent degree is further calculated to rank all the alternatives. At the same time, in order to guarantee the rationality of the decision-making result, a variation coefficient method is developed to determine the weights of the attributes under dual hesitant fuzzy environment objectively. Finally, the existing algorithms (Algorithm II and Algorithm III, Algorithm IV, Algorithm V) are compared with our algorithm (Algorithm I). The comparison result shows that Algorithm I is a valuable tool for decision making. PubDate: 2022-06-01
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Abstract: Abstract Fuzzy data envelopment analysis (FDEA) is one of the most applicable approaches for performance assessment of peer decision making units under ambiguity which is evolving rapidly and gaining popularity under uncertain data envelopment analysis field. The goal of this paper is to review some FDEA models based on applied possibility, necessity, credibility, general fuzzy measures and chance-constrained programming to deal with data ambiguity. The study presents a comprehensive and structured literature review of fuzzy chance-constrained data envelopment analysis (FCCDEA) studies including 87 studies from 2000 to 2020. The main contributions of this research include the following details: (1) Review of fuzzy chance-constrained programming, (2) Survey of FCCDEA models based on different fuzzy measures, (3) Analysis of FCCDEA applications and features, (4) Classification of FCCDEA studies from modeling and uncertainty type viewpoints, (5) Bibliometric analysis of FCCDEA literature, and (6) Extraction of main research gaps and guidelines for future research directions. PubDate: 2022-06-01
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Abstract: Abstract The outbreak of epidemic has had a big impact on the investment market of China. Facing the turbulence in the investment market, many enterprises find it difficult to judge the development prospects of investment projects and make the right investment decisions. The three-way decisions offer a novel study perspective to solve this problem. Then the developed model is applied to select the investment projects. Firstly, some relevant attributes of the project are described with the double hierarchy hesitant fuzzy linguistic term sets. And a double hierarchy hesitant fuzzy linguistic information system is constructed for each project. Secondly, the weights of attributes are determined with the Choquet integral method. And the closeness degree calculated by Choquet-based bi-projection method is taken as the conditional probability that the project will be profitable. Next, considering the influence of the bounded rationality of decision makers, the threshold parameters are calculated based on prospect theory. Finally, the decision results about investment projects during four stages are deduced based on the principle of maximum-utility, which demonstrates the practicability and effectiveness of the proposed model. PubDate: 2022-05-07
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Abstract: Abstract In this paper, we propose an uncertain energy model with a time-varying volatility factor to describe the electricity and gas futures price dynamics. The corresponding spark-spread option pricing problem is also discussed. Numerical experiments show the effectiveness of proposed pricing method. Compared with the existing stochastic models, our uncertain energy model has a better performance to catch the price evolution of both gas and electricity futures. PubDate: 2022-04-29
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Abstract: Abstract This work implements the BFGS (Broyden-Fletcher-Goldfarb-Shanno) optimization method for training the type-1 and singleton fuzzy logic system applied to solve binary classification problems. The BFGS is a quasi-Newton method that approximates the second-order information using the gradient of the cost function. Additionally, the Golden Section method is used to obtain the step size for each line search in a descent direction. The effectiveness of the proposed method is demonstrated by using well-established classification metrics evaluated in popular datasets from the literature. Comparisons between the proposed approach and well-known gradient-based methods available are also provided, showing that the BFGS achieves improved performance in terms of accuracy, mean squared error, and the number of epoch demanded during the training phase. PubDate: 2022-04-22
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Abstract: Abstract Since the concept of uncertain fractional differential equations was proposed, its wide range of applications have urged us to consider parameter estimation for uncertain fractional differential equations. In this paper, based on the definition of Liu process, we construct a function of unknown parameters which follows a standard normal uncertainty distribution. Then the method of moments is used to build a system of equations whose solutions are the estimated values of unknown parameters. After that, an algorithm of parameter estimation for a special uncertain fractional differential equation is proposed. Finally, the algorithm is applied to two numerical examples and the acceptability of the estimated parameters is proved by using uncertain hypothesis test. PubDate: 2022-04-08
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Abstract: Abstract Explainability is considered essential in enabling artificial intelligence (AI) in some crucial industries, e.g., healthcare and banking. However, conventional algorithms suffer a trade-off between readability and performance, encouraging the emergence of explainable AI. In this paper, we propose a novel method to form the hierarchical Choquet integral (HCI) as an explainable AI to retain the model's accuracy and explainability. To achieve this purpose, we first adopted neuroevolution, which combines a genetic algorithm (GA) and a neural network (NN), and pruned weights to obtain information about the hierarchical decomposition of the Choquet integral. We then fine-tuned the weights of the HCI model for the classification problem. In addition, we use four datasets to illustrate the proposed algorithm and compare the results with the conventional classifiers: decision tree, deep learning, and support vector machine (SVM). The empirical results indicate that the proposed algorithm outperforms others in terms of accuracy, and keeps the Choquet integral's explainable property, justifying this paper's contribution. PubDate: 2022-03-02 DOI: 10.1007/s10700-022-09384-1
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Abstract: Abstract Probabilistic linguistic variable is a kind of powerful qualitative fuzzy sets, which permits the decision makers (DMs) to apply several linguistic variables with probabilities to denote a judgment. This paper studies group decision making (GDM) with normalized probability linguistic preference relations (NPLPRs). To achieve this goal, an acceptably multiplicative consistency based interactive algorithm is provided to derive common probability linguistic preference relations (CPLPRs) from PLPRs, by which a new acceptably multiplicative consistency concept for NPLPRs is defined. When the multiplicative consistency of NPLPRs is unacceptable, models for deriving acceptably multiplicatively consistent NPLPRs are constructed. Then, it studies incomplete NPLPRs (InNPLPRs) and offers a common probability and acceptably multiplicative consistency based interactive algorithm to determine missing judgments. Furthermore, a correlation coefficient between CPLPRs is provided, by which the weights of the DMs are ascertained. Meanwhile, a consensus index based on CPLPRs is defined. When the consensus does not reach the requirement, a model to increase the level of consensus is built that can ensure the adjusted LPRs to meet the multiplicative consistency and consensus requirement. Moreover, an interactive algorithm for GDM with NPLPRs is provided, which can address unacceptably multiplicatively consistent InNPLPRs. Finally, an example about the evaluation of green design schemes for new energy vehicles is provided to indicate the application of the new algorithm and comparative analysis is conducted. PubDate: 2022-03-01 DOI: 10.1007/s10700-021-09360-1
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Abstract: Abstract With the emergence of outsourcing logistics and the rapid development of the e-commerce business, Third Party Logistics (TPL) plays an indispensable role in modern business. In the TPL provider selection process, uncertain information brings more challenges to decision makers. This paper uses probabilistic linguistic term sets (PLTSs) to describe uncertain decision making information. Firstly, we propose an improved Decision Making Trial and Evaluation Laboratory method, which allows a certain relationship between decision criteria and calculates criteria weights in multi-criteria decision making (MCDM) problems. Then, in order to make full use of uncertain TPL provider information and maximize the values of data, the probabilistic linguistic complex proportional assessment method is proposed and applied to solve the MCDM problems under probabilistic linguistic environment, which needs much less computation than other MCDM methods. Finally, an application example of TPL provider selection is presented to demonstrate the proposed method. A comparative analysis is further conducted to validate the effectiveness of the proposed method. PubDate: 2022-03-01 DOI: 10.1007/s10700-021-09358-9
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Abstract: Abstract Linguistic information processing exists in multi-criteria decision making, and linguistic truth-valued lattice implication algebra (LTV-LIA) has definite advantages in handling comparable and incomparable linguistic values. To deal with the preference relations with linguistic evaluation information, we establish a novel approach for solving fuzzy multi-criteria decision problem under linguistic information based on LTV-LIA. In this paper, we propose linguistic lattice-valued preference relation (LLVPR). LLVPR positive and negative matrixes are introduced to evaluate the advantages and disadvantages of alternatives respectively. In order to get a reasonable result, we introduce a new algorithm to check and repair the consistency of a LLVPR. A linguistic lattice-valued 2-tuple representation model (LLV2-tuple) and some new aggregation operations are presented to get the comprehensive linguistic information without information loss. Considering different decision makers have different preferences, a multiple preferences implication operation of LLV2-tuple is introduced. Finally, we propose a novel linguistic analytic hierarchy process embedded in aggregation layer and implication layer, introducing algorithm and numerical examples. A comparative analysis is adopted to illustrate the rationality. PubDate: 2022-03-01 DOI: 10.1007/s10700-021-09356-x
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Abstract: Abstract Data envelopment analysis (DEA) is a classical and prevailing tool for estimating relative efficiencies of multiple decision making units (DMUs). However, sometimes DMUs’ inputs and outputs cannot be observed accurately in practical cases, and hence this paper attempts to propose an uncertain random DEA model to evaluate the efficiencies of DMUs with uncertain random inputs and outputs. The sensitivity and stability of this new model are further analyzed with the aim to figure out the stability radius of each DMU. Finally, a numerical example is presented for illustrating the proposed uncertain random DEA model. PubDate: 2022-03-01 DOI: 10.1007/s10700-021-09361-0
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Abstract: Abstract Online reviews have become an increasingly popular information source in consumer’s decision making process. To help consumers make informed decisions, how to select products through online reviews is a valuable research topic. This work deals with a personized product selection problem with review sentiments under probabilistic linguistic circumstances. To this end, we propose a multi-criteria decision making (MCDM) method incorporating personalized heuristic judgments in the prospect theory (PT). We focus on the role of personalized heuristic judgments on review helpfulness in the final decision outcomes. We demonstrate the consistency between the three common heuristic judgments (with respect to review valence, sentiment extremity, and aspiration levels) and the three behavioral principles of the PT. Then, the products are ranked with the probabilistic linguistic term set (PLTS) input, based on the proposed adjustable PT framework, in which the coefficients of negativity bias are derived from the consumer’s heuristic judgments. Finally, a real case on TripAdvisor.com and two simulation experiments are given to illustrate the validity of the proposed method. PubDate: 2022-03-01 DOI: 10.1007/s10700-021-09359-8
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Abstract: Abstract When a decision-maker prefers to compare different alternatives in pairs to handle real situations, there are many different expression styles that can be used. Two representative expression styles are the probabilistic linguistic preference relation (PLPR), which originates from the fuzzy linguistic approach and the distributed preference relation (DPR), which originates from the evidential reasoning approach. Although these two expression styles look quite similar, their meanings, operations, and relevant decision making processes are significantly different. This presents the decision-maker with the challenge of selecting either PLPRs or DPRs in different real cases. To address this issue, this paper provides a detailed analysis of the similarities and differences between PLPRs and DPRs. The analysis is conducted from five perspectives, including modeling of decision making problems, handling of uncertainty, consistency between preference relations, information aggregation, and elicitation process. An engineer selection problem for an automobile manufacturing enterprise is investigated to demonstrate how to appropriately select PLPRs or DPRs to model and analyze decision making problems in real situations with consideration for the preferences of decision-makers. PubDate: 2022-03-01 DOI: 10.1007/s10700-021-09357-w
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Abstract: Abstract In this paper, the definitions of Clarke generalized directional \(\alpha \) -derivative and Clarke generalized gradient are introduced for a locally Lipschitz fuzzy function. Further, a nonconvex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush-Kuhn-Tucker optimality conditions are established for such a nonsmooth extremum problem. For proving these conditions, the approach is used in which, for the considered nonsmooth fuzzy optimization problem, its associated bi-objective optimization problem is constructed. The bi-objective optimization problem is solved by its associated scalarized problem constructed in the weighting method. Then, under invexity hypotheses, (weakly) nondominated solutions in the considered nonsmooth fuzzy minimization problem are characterized through Pareto solutions in its associated bi-objective optimization problem and Karush-Kuhn-Tucker points of the weighting problem. PubDate: 2022-02-22 DOI: 10.1007/s10700-022-09381-4
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Abstract: Abstract The necessarily optimal solution is known as the most reasonable solution to linear programming problems with interval/fuzzy objective function coefficients. As it remains optimal against the certain fluctuations of objective function coefficients, the necessarily optimal solution can be seen as a robust optimal solution. In this paper, we demonstrate that the necessary optimality degree of a non-degenerate basic feasible solution can be obtained easily by utilizing the tolerance approach. The necessary optimality degree evaluates to what extent the solution remains optimal against the fluctuations of objective function coefficients. Several types of fuzzy subsets showing the possible range of the objective function coefficient vector are considered. For each type of fuzzy subset, an efficient calculation method of necessary optimality degree is proposed. Numerical examples are given to illustrate the proposed methods. PubDate: 2022-02-16 DOI: 10.1007/s10700-022-09383-2
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Abstract: Abstract It is very common to use linguistic information to solve decision-making problems in real life, and the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) has been widely used because of its powerful ability of expressing complex linguistic information. There is no doubt that the comparison method of double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) not only occupies an important theoretical and practical position, but also is the basis for further study of DHHFLTSs. However, the existing comparison methods of DHHFLEs still have some limitations. Therefore, this paper proposes a new DHHFLE comparison method, which is an improvement and perfection of the existing DHHFLE comparison methods. In addition, considering that the current research on distance and similarity measures of DHHFLEs is mostly based on the algebraic point of view, this paper proposes a cosine similarity measure of DHHFLEs, which fills the gap in the study of distance and similarity measures from the geometric point of view. Then, the cosine similarity-based DHHFL-ELECTRE II method is proposed to solve the multi-attribute decision-making (MADM) problem in the double hierarchy hesitant fuzzy linguistic environment. Finally, this method is used to solve a MADM problem in the performance evaluation of financial logistics enterprises. The results show that the proposed method has certain applicability and feasibility. PubDate: 2022-02-03 DOI: 10.1007/s10700-022-09382-3
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