Practical Decision Problems Research Articles

Outranking Decision-Making Method with Z-Number Cognitive Information

The Z-number provides an adequate and reliable description of cognitive information. The nature of Z-numbers is complex, however, and important issues in Z-number computation remain to be addressed. This study focuses on developing a computationally simple method with Z-numbers to address multicriteria decision-making (MCDM) problems. Processing Z-numbers requires the direct computation of fuzzy and probabilistic uncertainties. We used an effective method to analyze the Z-number construct. Next, we proposed some outranking relations of Z-numbers and defined the dominance degree of discrete Z-numbers. Also, after analyzing the characteristics of elimination and choice translating reality III (ELECTRE III) and qualitative flexible multiple criteria method (QUALIFLEX), we developed an improved outranking method. To demonstrate this method, we provided an illustrative example concerning job-satisfaction evaluation. We further verified the validity of the method by a criteria test and comparative analysis. The results demonstrate that the method can be successfully applied to real-world decision-making problems, and it can identify more reasonable outcomes than previous methods. This study overcomes the high computational complexity in existing Z-number computation frameworks by exploring the pairwise comparison of Z-numbers. The method inherits the merits of the classical outranking method and considers the non-compensability of criteria. Therefore, it has remarkable potential to address practical decision-making problems involving Z-information.

Some Interval Neutrosophic Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making

There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear and uncertain information and give their operational rules and comparison methods. In addition, since the Maclaurin symmetric mean (MSM) operator has the special characteristic of capturing the interrelationships among multi-input arguments, we further propose an MSM operator for INLNs (INLMSM). Furthermore, considering the weights of attributes are the important parameters and they can influence the decision results, we also propose a weighted INLMSM (WINLMSM) operator. Based on the WINLMSM operator, we develop a multiple attribute decision making (MADM) method with INLNs and some examples are used to show the procedure and effectiveness of the proposed method. Compared with the existing methods, the proposed method is more convenient to express the complex and unclear information. At the same time, it is more scientific and flexible in solving the MADM problems by considering the interrelationships among multi-attributes.

Multiperiod mean absolute deviation uncertain portfolio selection with real constraints

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. Most of existing mean---absolute deviation models are devoted to stochastic single-period portfolio optimization. However, practical investment decision problems often involve the uncertain dynamic information. Considering transaction costs, borrowing constraints, threshold constraints, cardinality constraints and risk control, we present a novel multiperiod mean absolute deviation uncertain portfolio selection model, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. In proposed model, the return rate of asset and the risk are quantified by uncertain expected value and uncertain absolute deviation, respectively. Cardinality constraints limit the number of risky assets in the optimal portfolio. Threshold constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. Based on uncertainty theories, the model is transformed into a crisp dynamic optimization problem. Because of the transaction costs and cardinality constraints, the multiperiod portfolio selection is a mix integer dynamic optimization problem with path dependence, which is "NP hard" problem that is very difficult to solve. The proposed model is approximated to a mix integer dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

A system approach to decision support on basis of hierarchical and network models

A methodology and a system approach to decision support based on hierarchical and network models are proposed, which include methods for estimating and improving the consistency of pairwise comparison matrices (PCM), calculating fuzzy local weights for model elements based on fuzzy PCM, calculating confidence intervals for local weights, finding aggregated weights and aggregated belief functions for model elements, estimating the sensitivity of the results, tools for analyzing the effectiveness of the methods and an expert evaluation modeling system. A decision support system is built on basis of the proposed methodology. The proposed methodology makes it possible to increase the reliability of solutions of practical weakly structured decision-making problems by using more efficient methods at each of the stages of solving the problem. Reliability of results of application of the methodology while solving a practical decision-making problem can be assessed by means of sensitivity analysis using the stability indices of the computed local and global rankings of the decision alternatives.

A programming-based algorithm for interval-valued intuitionistic fuzzy group decision making

Interval-valued intuitionistic fuzzy preference relations (IVIFPRs) are powerful to express the uncertain preferred and non-preferred judgments of decision makers simultaneously. After reviewing previous researches about IVIFPRs, we find that several limitations exist. Especially, previous methods are insufficient to address inconsistent and incomplete cases. Considering these issues, this paper first analyzes the limitations of the previous consistency concepts for IVIFPRs and then introduces a new one that avoids the disadvantages of previous ones. 0–1 mixed programming models are built for judging the multiplicative consistency of IVIFPRs. Subsequently, several multiplicative consistency-based 0–1 mixed programming models are constructed for determining missing values that can address the situation where ignored objects exist. For group decision making, a distance measure on IVIFPRs is defined, by which the weights of the decision makers are derived. Meanwhile, a consensus index is offered. A multiplicative consistency and consensus based algorithm to group decision making with IVIFPRs is proposed. Finally, two practical decision-making problems are offered to show the application of the new algorithm, and theoretical and numerical analysis of several related methods is made.

A consensus-based method for group decision making with incomplete uncertain linguistic preference relations

In practical group decision-making (GDM) problems, it is nature for experts to express their preference relations in uncertain linguistic pattern, due to the ambiguity of the external environments and the internal nature of human judgments. In this paper, a consensus process is introduced to deal with GDM problems with incomplete uncertain linguistic preference relations (ULPRs). Firstly, a consistency level for ULPRs is defined. Secondly, a linear goal programming model is furnished to estimate the missing uncertain linguistic preference values with respect to consistency property. Thirdly, an additively consistent ULPR is constructed. What’s more, one can obtain the collective ULPR by aggregating individual additively consistent ULPRs, where the order-inducing variable is consistency level (CL), based on the thought of more importance will be given to the larger CL. Furthermore, a consensus reaching process is presented to make experts’ opinions achieve to a predefined level. In the end, a new algorithm is proposed to solve the GDM problem with incomplete ULPR, which is further applied to the selection of best cooperator in a water conservancy project.

On transformations from semi-three-way decision spaces to three-way decision spaces based on triangular norms and triangular conorms

Recently, three-way decisions on three-way decision spaces based on partially ordered sets have been proposed by the axiomatic definitions. And, in the theory of three-way decision spaces, the decision evaluation function (which is defined by the so-called minimum element axiom, monotonicity axiom and complement axiom) is a vital notion and plays pretty important role in practical decision-making problems. However, there are many meaningful handy functions which can not become decision evaluation functions because they only satisfy minimum element axiom and monotonicity axiom in general. Therefore, there arises one discussion in which the author introduced the concept of semi-decision evaluation function without complement axiom lately. And three-way decisions based on semi-three-way decision spaces are proposed. This paper continues this research topic and gives several transformation methods from semi-three-way decision spaces to three-way decision spaces based on triangular norms and triangular conorms. Based on them, decision-makers can obtain more useful decision evaluation functions thereby having more choices in realistic decision-making problems. In addition, as an application, we analyse a reality example of an evaluation problem of credit card applicants by using the results obtained in this paper.

Grey Relational Analysis Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Geometric Bonferroni Mean

In practical decision-making problems, probabilistic linguistic term sets (PLTSs) are a very useful and flexible way to represent the qualitative judgments of experts. The PLTSs also have strong ability to express the information vagueness and uncertainty in the real-world applications. Considering the interrelationship among the input arguments of PLTSs, we extend the geometric Bonferroni mean to the probabilistic linguistic environment and design an approach for the application of multi-criteria group decision-making with PLTSs. First, we develop the probabilistic linguistic geometric Bonferroni mean and the weighted probabilistic linguistic geometric Bonferroni mean (WPLGBM) operators. The properties of these aggregation operators are investigated. Second, we utilize the WPLGBM operators to fuse the information in the probabilistic linguistic multi-criteria group decision-making (PLMCGDM) problem, which can obtain much more information in the process of group decision-making. By introducing the grey relational analysis method, we present its extension and further design a new approach for the PLMCGDM. Finally, an example is given to elaborate our proposed algorithm and successfully validate its performance.

An Approach for Group Decision Making With Interval Fuzzy Preference Relations Based on Additive Consistency and Consensus Analysis

Interval fuzzy preference relations (IFPRs) that can simply denote the lower and upper bounds of decision makers’ uncertain judgments are keenly studied by researchers and are widely used in practical decision-making problems. Consistency analysis is vitally important to avoid illogical ranking orders. First, this paper analyzes issues in previous additive consistency concepts for IFPRs. Then, it presents a new additive consistency definition that overcomes issues in previous ones. A linear programming model to judge the additive consistency of IFPRs is constructed, and a method to derive additive consistent IFPRs is proposed. Furthermore, a goal programming model to determine missing values in an incomplete IFPR is built, which have the highest consistent level with respect to known values. Regarding group decision making, a group consensus index is defined to measure the consensus of individual IFPRs, and an approach to improve the consensus level is introduced. Finally, a method for group decision making with IFPRs is developed, which can address incomplete and inconsistent cases. Associated examples are given to show the efficiency and feasibility of the developed theoretical results and comparative analysis is made.

Multi-criteria Outranking Methods with Hesitant Probabilistic Fuzzy Sets

Due to the defects of hesitant fuzzy sets (HFSs) in the actual decision-making process, it is necessary to add the probabilities corresponding to decision maker’s preferences to the values in HFSs. Hesitant probabilistic fuzzy sets (HPFSs) are suitable for presenting this kind of information and contribute positively to the efficiency of depicting decision maker’s preferences in practice. However, some important issues in HPFSs utilization remain to be addressed. In this paper, the qualitative flexible multiple criteria method (QUALIFLEX) and the preference ranking organization method for enrichment evaluations II (PROMETHEE II) are extended to HPFSs. First, we provide a comparison method for hesitant probabilistic fuzzy elements (HPFEs). Second, we propose a novel possibility degree depicting the relations between two HPFEs, and then, employ the possibility degree to extend the QUALIFLEX and PROMETHEE II methods to hesitant probabilistic fuzzy environments based on the proposed possibility degree. Third, an information integration method is introduced to simplify the processing of HPFE evaluation information. Finally, we provide an example to demonstrate the usefulness of the proposed methods. An illustrative example in conjunction with comparative analyses is employed to demonstrate that our proposed methods are feasible for practical multi-criteria decision-making (MCDM) problems, and the final ranking results show that the proposed methods are more accurate than the compared methods in an actual decision-making processes. HPFSs are more practical than HFSs due to their efficiency in comprehensively representing uncertain, vague, and probabilistic information. The proposed methods are effective for solving hesitant probabilistic MCDM problems and are expected to contribute to the solution of MCDM problems involving uncertain or vague information.

An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis

This paper proposes an approach to interval-valued intuitionistic stochastic multi-criteria decision-making (MCDM) problems using set pair analysis. This approach is applicable to MCDM problems in which the criterion weights are incomplete or the weights are certain, and evaluation values of alternatives take the form of interval-valued intuitionistic stochastic variables. To begin with, we briefly introduce the concepts of interval-valued intuitionistic fuzzy set, interval-valued intuitionistic stochastic variable, and set pair analysis. Then, we define a new similarity measure between interval-valued intuitionistic fuzzy numbers, after which we establish a mathematical programming model based on the technique for order preference by similarity to an ideal solution method and the maximizing deviation method in order to determine criterion weights. We then use connection degree to represent interval-valued intuitionistic fuzzy information and transform the interval-valued intuitionistic stochastic decision-making matrixes into corresponding connection degree matrixes. Finally, we rank the alternatives according to the value of set pair potential after calculating the connection degree of each alternative. After defining the method, we apply it to a practical decision-making problem and provide a comparison analysis with existing methods to illustrate the feasibility and validity of the proposed approach.

Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. The existing mean-absolute deviation models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical investment decision problems often involve the mixture of randomness and fuzziness such as stochastic returns with fuzzy information. Thus it is necessary to model portfolio selection problem in such a hybrid uncertain environment. In this paper, we employ random fuzzy variable to describe the stochastic return on individual security with ambiguous information. We first define the absolute deviation of random fuzzy variable and then employ it as risk measure to formulate mean-absolute deviation portfolio optimization models. To find the optimal portfolio, we design random fuzzy simulation and simulation-based genetic algorithm to solve the proposed models. Finally, a numerical example for synthetic data is presented to illustrate the validity of the method.

An overview of interval-valued intuitionistic fuzzy information aggregations and applications

Interval-valued intuitionistic fuzzy set, generalized by Atanassov and Gargov, can be used to characterize the uncertain information more sufficiently and accurately when we face the fact that the values of the membership function and the non-membership function in an intuitionistic fuzzy set are difficult to be expressed as exact real numbers in many real-world decision-making problems. In this paper, we provide an overview of interval-valued intuitionistic fuzzy information aggregation techniques, and their applications in various fields such as decision-making, entropy measure, supplier selection and some practical decision-making problems. Meanwhile, we also review some important methods for decision-making with interval-valued intuitionistic fuzzy information, including the QUALIFLEX-based method, the TOPSIS method, the extended VIKOR method, the module partition schemes evaluation (MPSE) approach, the outranking choice method, the inclusion-based LINMAP method and the risk attitudinal ranking method, the evidential reasoning methodology, etc. Finally, we point out some possible directions for future research.

Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study

To examine the multiplicative consistency of interval fuzzy preference relations (IFPRs), this paper first analyzes the limitations associated with the previous consistency concepts. Accordingly, a new consistency concept is defined that is an extension of the crisp case and overcomes limitations in the previous concepts. Next, a linear programming model to judge the consistency of IFPRs is constructed, and an approach to derive multiplicative consistent IFPRs is introduced. Furthermore, goal-programming models to determine missing values in an incomplete IFPR are constructed that have the highest consistent level with respect to known values. Moreover, a multiplicative consistency and consensus based method for group decision making with IFPRs is developed that can address incomplete and inconsistent cases. Finally, two practical decision-making problems are offered to demonstrate the feasibility and efficiency of the new method, and an analysis of a numerical and theoretical comparison with several related methods is performed.

Coil Batching to Improve Productivity and Energy Utilization in Steel Production

This paper investigates a practical batching decision problem that arises in the batch annealing operations in the cold rolling stage of steel production faced by most large iron and steel companies in the world. The problem is to select steel coils from a set of waiting coils to form batches to be annealed in available batch annealing furnaces and choose a median coil for each furnace. The objective is to maximize the total reward of the selected coils less the total coil–coil and coil–furnace mismatching cost. For a special case of the problem that arises frequently in practical settings where the coils are all similar and there is only one type of furnace available, we develop a polynomial-time dynamic programming algorithm to obtain an optimal solution. For the general case of the problem, which is strongly NP-hard, an exact branch-and-price-and-cut solution algorithm is developed using a column and row generation framework. A variable reduction strategy is also proposed to accelerate the algorithm. The algorithm is capable of solving medium-size instances to optimality within a reasonable computation time. In addition, a tabu search heuristic is proposed for solving larger instances. Three simple search neighborhoods, as well as a sophisticated variable-depth neighborhood, are developed. This heuristic can generate near-optimal solutions for large instances within a short computation time. Using both randomly generated and real-world production data sets, we show that our algorithms are superior to the typical rule-based planning approach used by many steel plants. A decision support system that embeds our algorithms was developed and implemented at Baosteel to replace their rule-based planning method. The use of the system brings significant benefits to Baosteel, including an annual net profit increase of at least 1.76 million U.S. dollars and a large reduction of standard coal consumption and carbon dioxide emissions.

A Hybrid Evolutionary Hyper-Heuristic Approach for Intercell Scheduling Considering Transportation Capacity

The problem of intercell scheduling considering transportation capacity with the objective of minimizing total weighted tardiness is addressed in this paper, which in nature is the coordination of production and transportation. Since it is a practical decision-making problem with high complexity and large problem instances, a hybrid evolutionary hyper-heuristic (HEH) approach, which combines heuristic generation and heuristic selection, is developed in this paper. In order to increase the diversity and effectiveness of heuristic rules, genetic programming is used to automatically generate new rules based on the attributes of parts, machines, and vehicles. The new rules are added to the candidate rule set, and a rule selection genetic algorithm is developed to choose appropriate rules for machines and vehicles. Finally, scheduling solutions are obtained using the selected rules. A comparative evaluation is conducted, with some state-of-the-art hyper-heuristic approaches which lack some of the strategies proposed in HEH, with a meta-heuristic approach that is suitable for large scale scheduling problems, and with adaptations of some well-known heuristic rules. Computational results show that the new rules generated in HEH have similarities to the best-performing human-made rules, but are more effective due to the evolutionary processes in HEH. Moreover, the HEH approach has advantages over other approaches in both computational efficiency and solution quality, and is especially suitable for problems with large instance sizes.

Multiperiod Mean Absolute Deviation Uncertain Portfolio Selection

Multiperiod portfolio selection problem attracts more and more attentions because it is in accordance with the practical investment decision-making problem. However, the existing literature on this field is almost undertaken by regarding security returns as random variables in the framework of probability theory. Different from these works, we assume that security returns are uncertain variables which may be given by the experts, and take absolute deviation as a risk measure in the framework of uncertainty theory. In this paper, a new multiperiod mean absolute deviation uncertain portfolio selection models is presented by taking transaction costs, borrowing constraints and threshold constraints into account, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on uncertain theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. To solve the new model in general cases, the forward dynamic programming method is presented. In addition, a numerical example is also presented to illustrate the modeling idea and the effectiveness of the designed algorithm.

A New Method for Triangular Fuzzy Compare Wise Judgment Matrix Process Based on Consistency Analysis

To cope with the uncertainty in the process of decision making, fuzzy preference relations are proposed and commonly applied in many fields. In practical decision-making problems, the decision maker may use triangular fuzzy preference relations to express his/her uncertainty. Based on the row weighted arithmetic mean method, this paper develops an approach for deriving the fuzzy priority vector from triangular fuzzy compare wise judgment matrices. To do this, this paper first analyzes the upper and lower bounds of the triangular fuzzy priority weight of each alternative, which indicates the decision maker’s optimistic and pessimistic attitudes. Based on (acceptably) consistent multiplicative preference relations, the triangular fuzzy priority vector is obtained. Meanwhile, a consistency concept of triangular fuzzy compare wise judgment matrices is defined, and the consistent relationship between triangular fuzzy and crisp preference relations is studied. Different to the existing methods, the new approach calculates the triangular fuzzy priority weights separately. Furthermore, the fuzzy priority vector from trapezoidal fuzzy reciprocal preference relations is considered. Finally, the application of the new method to new product development (NDP) project screening is tested, and comparative analyses are also offered.

Three-way group decisions with decision-theoretic rough sets

On consideration of the effectiveness of group decision making (GDM) in practical complex decision problems, we introduce GDM into three-way decisions with decision-theoretic rough sets (DTRSs) and propose GDM-based three-way decisions. GDM-based three-way decisions extend the range of applications of three-way decisions with DTRSs and provide a novel interpretation of the determination of loss functions. Based on DTRSs, we firstly focus on analyzing the determination for the loss functions under the GDM environment. With the aid of the principle of justifiable granularity, we adopt the important and majority suggestions of experts to measure each loss function, which supports a coherent way of designing information granules in presence of numerics. In this case, the loss functions are determined in the form of interval-valued information granule. By using the interval comparison method, we further deduce the three-way decisions and design a corresponding decision procedure of GDM-based three-way decisions. Then, an example of strategy supply selection is given to elaborate the GDM-based three-way decisions. Finally, we validate the performance of our proposed method by experimental analysis.

Pythagorean Fuzzy Multigranulation Rough Set over Two Universes and Its Applications in Merger and Acquisition

Pythagorean fuzzy set, an extension form of intuitionistic fuzzy set, which owns many advantages for dealing with uncertainties, and it has been developed to deal with various complex decision-making problems. Furthermore, based on lower and upper approximations induced by multiple binary relations, the multigranulation rough set has become one of the most promising directions in rough set theory. To combine the two ideas and explore the practical decision-making problems, we develop a new multigranulation rough set model, called Pythagorean fuzzy multigranulation rough set over two universes. In the framework of our study, we introduce the models of Pythagorean fuzzy rough set over two universes and Pythagorean fuzzy multigranulation rough set over two universes, respectively. Both the definition and basic properties are explored. Finally, we give a general algorithm, which is applied to a decision-making problem in merger and acquisition, and the effectiveness of the algorithm is demonstrated by a numerical example.