scholarly journals Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 764
Author(s):  
Pingping Gu ◽  
Jiubing Liu ◽  
Xianzhong Zhou
Keyword(s):  
Loss Function ◽  
Rough Sets ◽  
Optimal Solution ◽  
Equivalent Model ◽  
Linguistic Terms ◽  
Function Matrix

The method of determining probability thresholds of three-way decisions (3WDs) has always been the key of research, especially in the current environment with a large number of data and uncertainties. Among these problems, there will be correlation and similarity between them. In the light of these problems, the loss function with Probabilistic Linguistic Terms Sets (PLTSs) is introduced in the paper, and then we propose a PLTS evaluation-based approach to determine the thresholds and derive 3WDs. According to the definition and characters of PLTSs, the PLTSs loss function matrix is constructed firstly. Then using the equivalent model of Decision-theoretic rough sets (DTRSs), we construct the equivalent model (i.e., the αopt-model and the βopt-model, which are symmtrical) and try to find the optimal solution to determine the thresholds. Based on that, we propose a novel three-way decision approach under PLTSs evaluations. Finally, the validity of the method is verified by an example.

Three-way decisions with decision-theoretic rough sets based on covering-based q-rung orthopair fuzzy rough set model

2021 ◽  
pp. 1-21
Author(s):  
Fang Liu ◽  
Yi Liu ◽  
Saleem Abdullah
Keyword(s):  
Rough Set ◽  
Loss Function ◽  
Rough Sets ◽  
Fuzzy Numbers ◽  
Fuzzy Rough Set ◽  
Decision Method ◽  
Fuzzy Environment ◽  
Multi Attribute Decision Making ◽  
The Stability ◽  
Function Matrix

Based on decision theory rough sets (DTRSs), three-way decisions (TWDs) provide a risk decision method for solving multi-attribute decision making (MADM) problems. The loss function matrix of DTRS is the basis of this method. In order to better solve the uncertainty and ambiguity of the decision problem, we introduce the q-rung orthopair fuzzy numbers (q-ROFNs) into the loss function. Firstly, we introduce concepts of q-rung orthopair fuzzy β-covering (q-ROF β-covering) and q-rung orthopair fuzzy β-neighborhood (q-ROF β-neighborhood). We combine covering-based q-rung orthopair fuzzy rough set (Cq-ROFRS) with the loss function matrix of DTRS in the q-rung orthopair fuzzy environment. Secondly, we propose a new model of q-ROF β-covering DTRSs (q-ROFCDTRSs) and elaborate its relevant properties. Then, by using membership and non-membership degrees of q-ROFNs, five methods for solving expected losses based on q-ROFNs are given and corresponding TWDs are also derived. On this basis, we present an algorithm based on q-ROFCDTRSs for MADM. Then, the feasibility of these five methods in solving the MADM problems is verified by an example. Finally, the sensitivity of each parameter and the stability and effectiveness of these five methods are compared and analyzed.

scholarly journals The inventory replenishment policy in an uncertain production-inventory-routing system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chenyin Wang ◽  
Yaodong Ni ◽  
Xiangfeng Yang
Keyword(s):  
Programming Model ◽  
Optimal Solution ◽  
Maximum Level ◽  
Equivalent Model ◽  
Uncertain Programming ◽  
Inventory Routing ◽  
Routing Problem ◽  
Uncertain Variables ◽  
Confidence Levels ◽  
Production Inventory

<p style='text-indent:20px;'>This study introduces an uncertain programming model for the integrated production routing problem (PRP) in an uncertain production-inventory-routing system. Based on uncertainty theory, an uncertain programming model is proposed firstly and then transformed into a deterministic and equivalent model. The study further probes into different types of replenishment policies under the condition of uncertain demands, mainly the uncertain maximum level (UML) policy and the uncertain order-up to level (UOU) policy. Some inequalities are put forward to define the UML policy and the UOU policy under the uncertain environments, and the influences brought by uncertain demands are highlighted. The overall costs with optimal solution of the uncertain decision model grow with the increase of the confidence levels. And they are simultaneously affected by the variances of uncertain variables but rely on the value of confidence levels. Results show that when the confidence levels are not less than 0.5, the cost difference between the two policies begins to narrow along with the increase of the confidence levels and the variances of uncertain variables, eventually being trending to zero. When there are higher confidence levels and relatively large uncertainty in realistic applications, in which the solution scale is escalated, being conducive to its efficiency advantage, the comprehensive advantages of the UOU policy is obvious.</p>

Valuation and Hedging of Limited Price Indexed Liabilities

2004 ◽  
Vol 10 (3) ◽  
pp. 627-663 ◽  
Author(s):  
H.-C. Huang ◽  
A. J. G. Cairns
Keyword(s):  
Loss Function ◽  
Economic Valuation ◽  
Economic Value ◽  
Optimal Solution ◽  
Investment Portfolio ◽  
Hedging Strategy ◽  
Vector Autoregressive ◽  
Hedging Strategies ◽  
Mean Variance

ABSTRACTThis paper considers the market or economic valuation and the hedging of Limited Price Indexed (LPI) liabilities. This involves finding optimal static and dynamic hedging strategies which minimise the riskiness of the investment portfolio relative to the liability.In this paper we do not aim to find the perfect hedge in a perfect world. Instead, it is assumed that optimisation is restricted to three commonly used asset classes in pension funds: cash; long-term (or irredeemable) fixed-interest bonds; and long-dated index-linked bonds. The economic value of the liability is then defined as the value of the best matching portfolio using a mean/variance type of loss function. Specifically, we adopt the risk minimising approach of Föllmer & Sondermann (1986) and Schweizer & Föllmer (1988). Even with such a simple loss function, establishing the theoretically optimal solution can be difficult. We propose that a practical solution close to the theoretical optimum can be found using two approximations. First, we approximate the ‘true’ stochastic economic model by a vector autoregressive model of order one. Second, we use a sequence of linearisations to approximate non-linear by straightforward quadratic minimisation problems.The proposed approach is illustrated with various numerical examples, and we compare the results of the approximately optimal hedging strategy with static strategies.

scholarly journals Electrical Capacitance Tomography Measurement of the Migration of Ice Frontal Surface in Freezing Soil

2016 ◽  
Vol 16 (6) ◽  
pp. 280-286 ◽  
Author(s):  
J. Liu ◽  
X.M. Suo ◽  
S.S. Zhou ◽  
S.Q. Meng ◽  
S.S. Chen ◽  
...  
Keyword(s):  
Loss Function ◽  
Optimal Solution ◽  
Frozen Soil ◽  
Freezing Process ◽  
Electrical Capacitance Tomography ◽  
Electrical Capacitance ◽  
Split Bregman ◽  
Frontal Surface ◽  
Freezing Soil ◽  
Capacitance Tomography

AbstractThe tracking of the migration of ice frontal surface is crucial for the understanding of the underlying physical mechanisms in freezing soil. Owing to the distinct advantages, including non-invasive sensing, high safety, low cost and high data acquisition speed, the electrical capacitance tomography (ECT) is considered to be a promising visualization measurement method. In this paper, the ECT method is used to visualize the migration of ice frontal surface in freezing soil. With the main motivation of the improvement of imaging quality, a loss function with multiple regularizers that incorporate the prior formation related to the imaging objects is proposed to cast the ECT image reconstruction task into an optimization problem. An iteration scheme that integrates the superiority of the split Bregman iteration (SBI) method is developed for searching for the optimal solution of the proposed loss function. An unclosed electrodes sensor is designed for satisfying the requirements of practical measurements. An experimental system of one dimensional freezing in frozen soil is constructed, and the ice frontal surface migration in the freezing process of the wet soil sample containing five percent of moisture is measured. The visualization measurement results validate the feasibility and effectiveness of the ECT visualization method

scholarly journals A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks

Electronics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 26 ◽  
Author(s):  
Oscar Danilo Montoya ◽  
Alexander Molina-Cabrera ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios ◽  
Edwin Rivas-Trujillo
Keyword(s):  
Optimal Power Flow ◽  
Hybrid Approach ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Equivalent Model ◽  
Mixed Integer ◽  
Discrete Version ◽  
Distributed Generators

This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool.

scholarly journals Material Selection in Engineering Design Using Choquet Integral-Based Linguistic Operators under Hybrid Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Anhua Peng ◽  
Xiqin Wen ◽  
Kaibo Wu
Keyword(s):  
Decision Making ◽  
Phase Change ◽  
Phase Change Materials ◽  
Choquet Integral ◽  
Material Selection ◽  
Optimal Solution ◽  
Linguistic Terms ◽  
Fuzzy Measures ◽  
Linguistic Term ◽  
The Individual

The performance of phase change materials directly influences the performance and cost of thermal energy storage, and it is the first important task to select the suitable phase change materials for use in a particular kind of applications. Due to the decision maker’s knowledge field and the nature of evaluated attributes, assessments are always with different formats, which were first unified into the linguistic terms in the basic linguistic term set. Two-additive fuzzy measures were used to model criteria interactions by pairs, and the special expressions of Marichal entropy and Choquet integral were derived, more convenient to use in practice. Fuzzy measures were identified based on the maximum of Marichal entropy, and, based on the Choquet integral, the linguistic hybrid weighted geometric averaging with interaction was developed for integrating the individual attributes’ ratings. The detailed decision making procedure was illustrated, with the material 33.2Cu as the optimal solution, which by comparison is reasonable and trustworthy.

Valence electron spectroscopy of inhomogeneous media

1992 ◽  
Vol 50 (2) ◽  
pp. 1150-1151
Author(s):  
A. Howie ◽  
D.W. McComb
Keyword(s):  
Specific Gravity ◽  
Loss Function ◽  
Electron Spectroscopy ◽  
Valence Electron ◽  
Peak Height ◽  
Loss Functions ◽  
Loss Peak ◽  
High Energies ◽  
Valence Electron Density ◽  
Electron Microscopist

The bulk loss function Im(-l/ε (ω)), a well established tool for the interpretation of valence loss spectra, is being progressively adapted to the wide variety of inhomogeneous samples of interest to the electron microscopist. Proportionality between n, the local valence electron density, and ε-1 (Sellmeyer's equation) has sometimes been assumed but may not be valid even in homogeneous samples. Figs. 1 and 2 show the experimentally measured bulk loss functions for three pure silicates of different specific gravity ρ - quartz (ρ = 2.66), coesite (ρ = 2.93) and a zeolite (ρ = 1.79). Clearly, despite the substantial differences in density, the shift of the prominent loss peak is very small and far less than that predicted by scaling e for quartz with Sellmeyer's equation or even the somewhat smaller shift given by the Clausius-Mossotti (CM) relation which assumes proportionality between n (or ρ in this case) and (ε - 1)/(ε + 2). Both theories overestimate the rise in the peak height for coesite and underestimate the increase at high energies.

Identifying Measurement Invariant Item Sets in Cross-Cultural Settings Using an Automated Item Selection Procedure

Methodology ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 177-188 ◽  
Author(s):  
Martin Schultze ◽  
Michael Eid
Keyword(s):  
Measurement Invariance ◽  
Optimal Solution ◽  
Selection Procedure ◽  
Cross Cultural ◽  
Item Selection ◽  
Ant System ◽  
Item Quality ◽  
Ant System Algorithm ◽  
Selection For ◽  
Selection Of

Abstract. In the construction of scales intended for the use in cross-cultural studies, the selection of items needs to be guided not only by traditional criteria of item quality, but has to take information about the measurement invariance of the scale into account. We present an approach to automated item selection which depicts the process as a combinatorial optimization problem and aims at finding a scale which fulfils predefined target criteria – such as measurement invariance across cultures. The search for an optimal solution is performed using an adaptation of the [Formula: see text] Ant System algorithm. The approach is illustrated using an application to item selection for a personality scale assuming measurement invariance across multiple countries.

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