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Fuzzy Optimization and Decision Making
Journal Prestige (SJR): 0.878
Citation Impact (citeScore): 3
Number of Followers: 8  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-2908 - ISSN (Online) 1568-4539
Published by Springer-Verlag Homepage  [2469 journals]
  • A systematic review of uncertainty theory with the use of scientometrical
           method

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      Abstract: Abstract Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems.
      PubDate: 2022-09-13
       
  • Bayesian rule in the framework of uncertainty theory

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      Abstract: Abstract In Bayesian rule an unknown parameter is thought to be a quantity whose variation can be characterized by a prior distribution. Then some data are observed from a population whose distribution function is indexed by the unknown parameter and then the prior distribution is updated according to the observed data. The updated prior distribution is named as the posterior distribution. Based on uncertainty theory, this paper first makes a connection between posterior uncertainty distribution and likelihood function, and proposes a new method to obtain the posterior uncertainty distribution from the prior uncertainty distribution with given observed data. Some examples with special uncertainty distributions are employed to explain the calculation. Furthermore, an uncertain urn problem is provided to illustrate the application of the new method.
      PubDate: 2022-09-05
       
  • Capacity reliability under uncertainty in transportation networks: an
           optimization framework and stability assessment methodology

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      Abstract: Abstract Destruction of the roads and disruption in transportation networks are the aftermath of natural disasters, particularly if they are of great magnitude. As a version of the network capacity reliability problem, this work researches a post-disaster transportation network, where the reliability and operational capacity of links are uncertain. Uncertainty theory is utilized to develop a model of and solve the uncertain maximum capacity path (UMCP) problem to ensure that the maximum amount of relief materials and rescue vehicles arrive at areas impacted by the disaster. We originally present two new problems of \(\alpha\) -maximum capacity path ( \(\alpha\) -MCP), which aims to determine paths of highest capacity under a given confidence level \( \alpha\) , and most maximum capacity path (MMCP), where the objective is to maximize the confidence level under a given threshold of capacity value. We utilize these auxiliary programming models to explicate the method to, in an uncertain network, achieve the uncertainty distribution of the MCP value. A novel approach is additionally suggested to confront, in the framework of uncertainty programming, the stability analysis problem. We explicitly enunciate the method of computing the links’ tolerances in \({\mathcal{O}}\left( m \right)\) time or \({\mathcal{O}}\left( {\left {P^{*} } \right m} \right)\) time (where \(m\) indicates the number of links in the network and \(\left {{\text{P}}^{*} } \right \) the number of links on the given MCP \({\text{P}}^{*}\) ). After all, the practical performance of the method and optimization model is illustrated by adopting two network samples from a real case study to show how our approach works in realistic contexts.
      PubDate: 2022-09-01
      DOI: 10.1007/s10700-021-09374-9
       
  • Stability analysis for uncertain nonlinear switched systems with
           infinite-time domain

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      Abstract: Abstract In this paper, an uncertain nonlinear switched system is a nonlinear switched system disturbed by subjective uncertainties, which can be illustrated by uncertain differential equations. Stability issues have been deeply studied on switched systems while few results about stability analysis for uncertain switched systems were published before. In order to fill this gap, three different types of stabilities called stability in measure, almost sure stability and stability in mean concerning uncertain nonlinear switched systems with infinite-time domain and countable switches are investigated in order. The internal property of the uncertain switched systems will be described and captured from diverse perspectives on the basis of the above stability analysis. The corresponding criteria to judge these stabilities are obtained according to uncertainty theory and stability theory. A numerical example concerning stability in measure is provided to show the effectiveness of the results derived.
      PubDate: 2022-09-01
      DOI: 10.1007/s10700-021-09372-x
       
  • Uncertain seepage equation in fissured porous media

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      Abstract: Abstract Seepage equation in fissured porous media is a partial differential equation describing the variation of pressure of a given area over time. In traditional seepage equation, the strength of mass source is supposed to be deterministic. However, the mass source in practice is often affected by noise such as transformation of underground environment and geological activities. To depict the noise, some scholars attempted to employ a technique called Winner process. Unfortunately, it is unreasonable to model the noise in seepage equation with Winner process, since change rate of pressure will be infinite. As a alternative tool in uncertainty theory, Liu process is introduced to model the noise, which can refrain from the problem of infinity. Then this paper deduces the uncertain seepage equation in fissured porous media driven by Liu process. Furthermore, the analytic solution and its inverse uncertainty distribution are derived. Finally, a paradox of stochastic seepage equation in fissured porous media is presented.
      PubDate: 2022-09-01
      DOI: 10.1007/s10700-021-09370-z
       
  • A graph model for conflict resolution with inconsistent preferences among
           large-scale participants

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      Abstract: Abstract As a flexible and powerful method to resolve strategy conflicts, the graph model for conflict resolution has drawn much attention. In the graph model for conflict resolution, decision-makers need to provide their preference information for all possible scenarios. Most existing studies assumed that decision-makers adopt quantitative representation formats. However, in some real-life situations, decision-makers may tend to use qualitative assessments due to their cognitive expression habits. In addition, stakeholders involved in a graph model can be a group that is composed of a large number of participants. How to manage these participants’ inconsistent preference assessments is also a debatable issue. To fit these gaps, in this study, we propose a graph model for conflict resolution with linguistic preferences, and this model allows participants to use inconsistent assessments. To do this, we first construct a linguistic preference structure, with the necessary concepts being defined. Then, four stability definitions for both a two-decision-maker scenario and an n-decision-maker scenario are introduced. To illustrate the usefulness of the proposed model, an illustrative example regarding the Huawei conflict is provided.
      PubDate: 2022-09-01
      DOI: 10.1007/s10700-021-09373-w
       
  • An innovative unification process for probabilistic hesitant fuzzy
           elements and its application to decision making

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      Abstract: Abstract The probabilistic hesitant fuzzy element (PHFE) is a worthwhile extension of hesitant fuzzy element (HFE) which is a means of allowing the decision makers more flexibility in expressing their preferences by the use of hesitant information in practical decision making process. To derive a more realistic expression of decision information, it is necessary to unify the arrangement of elements in PHFEs without imposing artificial elements. Up to now, several processes concerning the unification and arrangement of elements in PHFEs have been proposed, and while, most suffer from different drawbacks being critically discussed in the present study. The main aim of this study is to propose a PHFE unification process which does not have the shortcomings of existing processes, and does not change the inherent characteristic of PHFE probabilities. Based on the proposed unification process, the current study seeks to extend the theory of arithmetic operations on PHFEs by proposing and developing novel types of PHFS division and subtraction. Finally, the proposed PHFE unification process is applied to a number of multiple criteria decision-making (MCDM) problems for illustrating its vast range of applicability.
      PubDate: 2022-09-01
      DOI: 10.1007/s10700-021-09369-6
       
  • Some results for the minimal optimal solution of min-max programming
           problem with addition-min fuzzy relational inequalities

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      Abstract: Abstract In this study, a BitTorrent-like peer-to-peer (BT-P2P) file-sharing system is reduced into a system of fuzzy relational inequalities (FRI) with addition-min composition. To study the stability of data transmission and network congestion, a min-max programming problem subject to addition-min FRI is proposed. From a cost-saving perspective, the optimal solution to the min-max programming problem may not be the minimal optimal solution. Furthermore, while the “optimal” solution provides better cost performance, the “minimal” solution provides for the least congestion of the file-sharing system. In this paper, we propose adopting a binding variable approach based on certain new theoretical properties to find a minimal optimal solution for the min-max programming problem. It is for these new properties that the minimal optimal solution obtained via the binding variable approach would minimize the maximum transmission level; further, the amounts of data download in the optimal solution would be as balanced as possible. Some numerical examples are provided after each of the new properties to illustrate the advantages of our approach.
      PubDate: 2022-09-01
      DOI: 10.1007/s10700-021-09371-y
       
  • Uncertain interest rate model for Shanghai interbank offered rate and
           pricing of American swaption

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      Abstract: Abstract In the framework of uncertainty theory, this paper investigates the pricing problem of American swaption. By assuming that the floating interest rate obeys an uncertain differential equation, the pricing formula of American swaption is derived. Furthermore, parameter estimation of the uncertain interest rate model is given, and the uncertain hypothesis test shows that the uncertain interest rate model fits the Shanghai interbank offered rate well. Finally, as a byproduct, this paper also indicates that stochastic differential equations cannot model real-world interest rates.
      PubDate: 2022-08-31
       
  • The potential and consistency of the Owen value for fuzzy cooperative
           games with a coalition structure

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      Abstract: Abstract This paper extends the potential function and consistency to the Owen value for fuzzy cooperative games with a coalition structure. First, we prove that the unique payoff index satisfying the potential function is the Owen value. Then, we characterize the Owen value for fuzzy cooperative games with a coalition structure by fuzzy balanced contributions and fuzzy consistency, respectively. Finally, an example in supply chain is given to illustrate the relationship between the Owen value and potential function for fuzzy cooperative games with a coalition structure and solve the problem of payoff distribution in supply chain under fuzzy environment.
      PubDate: 2022-08-31
       
  • Probabilistic linguistic decision-making based on the hybrid entropy and
           cross-entropy measures

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      Abstract: Abstract In fuzzy decision-making, the probabilistic linguistic term sets (PLTSs) are flexible in depicting people’s linguistic evaluations. As the uncertainty measures of PLTSs, entropy and cross-entropy are the important decision-making tools. Generally speaking, the uncertainty of PLTSs can be studied from two facets, which are known as hesitancy and fuzziness. To better reflect these uncertainties, some hybrid entropy and cross-entropy measures of PLTSs are developed in this work. It is shown that the hybrid entropy measures are simple in structure, clear in physical meaning and strong in discriminating ability, while the hybrid cross-entropy measures can avoid the design flaws of existing measures and possess natural symmetry. It is also shown that the hybrid entropy and cross-entropy measures can be designed in pairs, mutually supportive and inherently unified as the uncertainty measures. In the ends, a multi-attribute decision-making (MADM) model, based on these uncertainty measures of PLTSs, is developed within the famous TOPSIS framework to select the best cloud computing platform.
      PubDate: 2022-08-30
       
  • Variable structure T–S fuzzy model and its application in
           maneuvering target tracking

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      Abstract: Abstract To realize the adaptive identification of T–S fuzzy model structure, we propose a variable structure T–S fuzzy model algorithm. Compare to traditional multi-input single-output in the T–S fuzzy model, we extend single-output fuzzy rules to multi-dimensional output fuzzy rules, which has the advantage that all multi-dimensional outputs share the same premise parameter; Then the joint block structure sparse ridge regression model is used to realize the identification of the consequent parameter, which provides a regression model. In this model, some regression coefficient blocks with small contribution will be reduced to zero accurately, while maintaining high prediction accuracy. Otherwise, the Fuzzy Expectation Maximization (FEM) is proposed to coarse fine the premise parameter. Finally, the variable structure T–S fuzzy model is applied to the maneuvering target tracking without filter. The simulation results show that the proposed algorithm is more accurate and stable than the Interacting Multiple Model (IMM), Interacting Multiple Model Unscented Kalman Filtering (IMMUKF), Interacting Multiple Model Rao-Blackwellized Particle Filtering (IMMRBPF) and T–S Fuzzy semantic Model (TS-FM) algorithms in dealing with uncertain problems in nonlinear maneuvering target tracking systems.
      PubDate: 2022-07-25
       
  • Dynamic pricing and production control for perishable products under
           uncertain environment

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      Abstract: Abstract In actual dynamic system, uncertainty is absolute and certainty is relative. This paper presents the optimal dynamic pricing and production control strategy for perishable products in finite horizon. The influence of external environmental disturbance on the system is considered by means of a special uncertain process (Liu process). Then based on uncertainty theory and Hurwicz criterion, the optimization model is built, where control variables are restricted to an admissible control set. In addition, uncertain differential equation is used to describe the changes of inventory. By applying the optimality equation, we determine the optimal price and production strategy to maximize profit. Besides, both the optimal price and production rate are linearly decreasing with inventory. Afterwards, two numerical examples are given, the results reveal that reducing the uncertain disturbance of inventory and expanding the potential market size are beneficial to improving the optimal profit. Moreover, risk-loving decision makers can gain more profits while facing large risks.
      PubDate: 2022-07-22
      DOI: 10.1007/s10700-022-09396-x
       
  • Multiple stage optimization driven group decision making method with
           interval linguistic fuzzy preference relations based on ordinal
           consistency and DEA cross-efficiency

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      Abstract: Abstract Interval linguistic term (ILT) is highly useful to express decision-makers’ (DMs’) uncertain preferences in the decision-making process. This paper proposes a new group decision-making (GDM) method with interval linguistic fuzzy preference relations (ILFPRs) by integrating ordinal consistency improvement algorithm, cooperative game, Data Envelopment Analysis (DEA) cross-efficiency model, and stochastic simulation. Firstly, the ordinal consistency of ILFPR is developed. For improving the ordinal consistency of an ILFPR, a two-stage integer optimization model is presented to derive an ILFPR with ordinal consistency. Then, a weight-determination method for obtaining DMs’ weights is presented based on cooperative games. Moreover, a DEA cross-efficiency model is presented to obtain the priorities of linguistic preference relation derived from ILFPR. Meanwhile, the expected ranking vector of ILFPR is obtained based on the DEA cross-efficiency model by integrating stochastic preference analysis and Monte Carlo stochastic simulation. Finally, a numerical example of emergency logistics selection illustrates the applicability and credibility of the proposed method.
      PubDate: 2022-07-04
      DOI: 10.1007/s10700-022-09394-z
       
  • Green supplier selection and order allocation using linguistic Z-numbers
           MULTIMOORA method and bi-objective non-linear programming

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      Abstract: Abstract Supplier selection and order allocation are major tasks to companies in green supply chain management. Most literatures consider these two tasks as independent sub-problems. In this paper, we propose an integrated two-stage multiple criteria programming approach to solve them systematically. The approach includes both quantitative and qualitative analyses. In the first stage, an MULTIMOORA method based on linguistic Z-Numbers is employed to rank the green suppliers under multiple qualitative criteria (but that is not the final decision). In the second stage, the ranking result is input to a bi-objective non-linear integer programming model. The model then determines the suppliers selected and the quantity of order allocated to them. Furthermore, the model should determine the configuration of the productions because different configuration implies different resource needed. We present the comparative result with other quantitative methods. An illustrative example proves that our proposed model can achieve the desired consistency among objectives.
      PubDate: 2022-06-17
      DOI: 10.1007/s10700-022-09392-1
       
  • Uncertain hypothesis test for uncertain differential equations

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      Abstract: Abstract Uncertain hypothesis test is a statistical tool that uses uncertainty theory to determine whether some hypotheses are correct or not based on observed data. As an application of uncertain hypothesis test, this paper proposes a method to test whether an uncertain differential equation fits the observed data or not. In order to demonstrate the test method, some numerical examples are provided. Finally, both uncertain currency model and stochastic currency model are used to model US Dollar to Chinese Yuan (USD–CNY) exchange rates. As a result, it is shown that the uncertain currency model fits the exchange rates well, but the stochastic currency model does not.
      PubDate: 2022-06-03
      DOI: 10.1007/s10700-022-09389-w
       
  • An analytic solution for multi-period uncertain portfolio selection
           problem

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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
      DOI: 10.1007/s10700-021-09367-8
       
  • Uncertain hypothesis test with application to uncertain regression
           analysis

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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
      DOI: 10.1007/s10700-021-09365-w
       
  • Type-2 fuzzy numbers made simple in decision making

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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
      DOI: 10.1007/s10700-021-09363-y
       
  • Min–max programming problem with constraints of addition-min-product
           fuzzy relation inequalities

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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
      DOI: 10.1007/s10700-021-09368-7
       
 
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