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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  [2467 journals]
  • Residual analysis and parameter estimation of uncertain differential
           equations

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      Abstract: Abstract All existing methods to estimate unknown parameters in uncertain differential equations are based on difference scheme, and do not work when the time intervals between observations are not short enough. In order to overcome this shortage, this paper presents a concept of residual. Afterwards, an algorithm is designed for calculating residuals of uncertain differential equation corresponding to observed data. In addition, this paper presents a method of moments based on residuals to estimate the unknown parameters in uncertain differential equations. Finally, some examples (including Alibaba stock price) are provided to illustrate the parameter estimation method.
      PubDate: 2022-12-01
       
  • Finding minimal solutions to the system of addition-min fuzzy relational
           inequalities

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      Abstract: Abstract In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not unique and are often infinite in number. In this paper, we study the properties of the minimal solutions of such a system and propose an iterative algorithm to find the minimal solutions for any given solution (included the maximum solution). The proposed algorithm not only finds the minimal solutions efficiently, but also finds many minimal solutions in different iterative sequences of variables.
      PubDate: 2022-12-01
       
  • Cost-allocation problems for fuzzy agents in a fixed-tree network

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      Abstract: Abstract Cost-allocation problems in a fixed network are concerned with distributing the costs for use by a group of clients who cooperate in order to reduce such costs. We work only with tree networks and we assume that a minimum cost spanning tree network has already been constructed and now we are interested in the maintenance costs. The classic problem supposes that each agent stays for the entire time in the same node of the network. This paper introduces cost-allocation problems in a fixed-tree network with a set of agents whose activity over the nodes is fuzzy. Agent’s needs to pay for each period of time may differ. Moreover, the agents do not always remain in the same node for each period. We propose the extension of a very well-known solution for these problems: Bird’s rule.
      PubDate: 2022-12-01
       
  • Multilinear target-based decision analysis with hybrid-information targets
           and performance levels

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      Abstract: Abstract For several classes of decisions, the use of target-based decision analysis (TBDA) is more appropriate than utility analysis. Recent literature on TBDA mainly focuses on different expression forms of targets and performance levels, and on different types of aggregation operators in terms of multi-attribute preference functions. However, different expression forms are usually introduced separately in literature, which cannot fully support the inherent complexity of problems along with different perception and knowledge levels of decision makers during assessing targets and performance levels. Furthermore, although there are attractive features of multilinear target-based preference functions (MTPFs), its applications are seldom considered because of the complexity of identifying their coefficients. In order to solve these two issues, an integrated approach is proposed for multilinear hybrid-information target-based decision analysis, which can deal with diverse forms of targets and performance levels, and identify the coefficients of MTPFs. First, given targets and performance levels for each attribute being expressed in multiple forms simultaneously, a generalized procedure is proposed to transform different forms into probability distributions, and to measure probability of target achievement for each attribute. Second, a novel procedure to identify the coefficients of MTPFs is proposed. This procedure is based on the multilinear model and 2-additive fuzzy measures, which is based on the equivalence between multilinear model based on fuzzy measures and MTPFs. The approach is applied to a case study involving customer competitive evaluation of smart thermometer patches to demonstrate its feasibility and advantages.
      PubDate: 2022-12-01
       
  • Structure, trend and prospect of operational research: a scientific
           analysis for publications from 1952 to 2020 included in Web of Science
           database

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      Abstract: Abstract As an important research direction, operational research (OR) has always attracted scholars worldwide. We study the structure, trend and prospect in the OR field by conducting a bibliometric analysis of publications in the period of 1952–2020, which are included in the Web of Science (WoS) database. Using three effective bibliometric tools, namely, VOS viewer, CiteSpace, and Bibliometrix, a total of 5,353 publications were retrieved to show clear visual results using a series of scientific analyses. First, a performance analysis revealed the basic characteristics of publications considering the type distribution, annual trend, quantity and quality. Then, a cooperation analysis presented the influential countries/regions and showed the relationships among countries/regions, institutions and authors during different periods based on bibliometric indicators and co-authorship networks. Moreover, a keyword analysis was conducted to investigate the hot topics and development of the OR field, using co-occurrence analysis, timeline view analysis and evolution analysis. Finally, we discussed the implications and limitations, and summarized the main findings. This study hopes to provide important and valuable references for future research on the OR field.
      PubDate: 2022-12-01
       
  • Convexity and level sets for interval-valued fuzzy sets

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      Abstract: Abstract Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity is required as well and some important applications can be found fuzzy optimization, in particular convexity of fuzzy sets. In this paper we have extended the notion of convexity for interval-valued fuzzy sets in order to be able to cover some wider area of imprecision. We show some of its interesting properties, and study the preservation under the intersection and the cutworthy property. Finally, we applied convexity to decision-making problems.
      PubDate: 2022-12-01
       
  • Fermat-curve based fuzzy inference system for the fuzzy logic controller
           performance optimization in load frequency control application

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      Abstract: Abstract One of the main challenges in the security of energy supply in modern power systems is the frequency deviation. Appearance of an imbalance between the demand and supply of electrical energy is the main reason for any change in the frequency level of the grid. Thus, the Load Frequency Control (LFC) operation is usually performed automatically to restore the stability in the frequency level of the system. LFC has been studied with different controllers previously. However, this study concentrates on proposing a new configuration for the Fuzzy Logic Controller (FLC) to be implemented in the modeling of a test two-area power system under two different operational conditions and challenges to analyze its performance. A Third-Order Fermat Curve-based Fuzzy Inference System (TOFC-FIS) is designed for the FLC with the aim of optimizing the performance of type-I FLCs in the LFC application. The motive for this study was to mathematize the FIS of FLC to prepare a basis for further performance enhancement using optimization algorithms. Thus, the proposed FIS is optimized using a Neural Network (NN) to create an Adaptive Neuro-Fuzzy Inference System for the FLC in the studied scenarios. The results of typical and NN-trained TOFC-FIS-based FLC illustrate the considerable improvement in performance indexes of LFC in two-area power systems compared to both conventional and intelligent control methods.
      PubDate: 2022-11-16
       
  • A sustainable medical waste management system design in the face of
           uncertainty and risk during COVID-19

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      Abstract: Abstract COVID-19's developing trend has put the waste management systems of governments all over the world in jeopardy. The increasing rise of infectious medical waste has now become a serious problem. This paper presents a multi-period multi-objective model for designing a medical waste management system during the COVID-19 pandemic. The model aims to reduce total costs of infectious medical waste management while also reducing the environmental impact of treatment centers, disposal centers, and transportation. It also aims to maximize the suitability of treatment technology based on social considerations and reduce the risk associated with processing and transporting COVID-19 waste. Different strategic and operational decisions are taken into account that include the selection of treatment technologies, the location of treatment and disposal centers, the flow of generated medical waste between facilities, and the number of vehicles required for the medical waste transport. The model tackles the uncertainty associated with model parameters, and it uses a credibility-based possibilistic programming method to deal with uncertainties. The suggested model is solved using an interactive fuzzy programming method and the importance of social indicators for selecting treatment technology is determined using the fuzzy best–worst approach. The effectiveness of the model is demonstrated by a practical case study in Shiraz, Iran. The numerical results can help system designers to achieve the most suitable trade-off between the sustainability goals and the safety viewpoint.
      PubDate: 2022-11-01
       
  • 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
      DOI: 10.1007/s10700-022-09400-4
       
  • 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
      DOI: 10.1007/s10700-022-09395-y
       
  • 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
      DOI: 10.1007/s10700-022-09399-8
       
  • 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
      DOI: 10.1007/s10700-022-09397-w
       
  • 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
      DOI: 10.1007/s10700-022-09398-9
       
  • 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
      DOI: 10.1007/s10700-022-09393-0
       
 
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