Incomplete Preference Information Research Articles

Group decision making with incomplete triangular fuzzy multiplicative preference relations for evaluating third-party reverse logistics providers

The strategic management of reverse logistics (RL) is essential for enterprises to enhance their operational efficiency, customer satisfaction, and sustainability performance in today's competitive marketplace. Many manufacturing firms have to cooperate with professional RL providers to overcome resource constraints and technological limitations, ultimately driving business success. Thus, it is critical for every enterprise to select the most suitable third-party RL provider (3PRLP). This paper provides a novel group decision making (GDM) method with incomplete triangular fuzzy multiplicative preference relations (TFMPRs) to cope with the selection of the most optimal 3PRLP. Firstly, a definition of acceptable incomplete TFMPRs is given. Then, the sufficient and necessary condition of an acceptable incomplete TFMPR is proposed. By analyzing the properties of consistent TFMPRs, a graph-based algorithm is designed to estimate the unknown elements in incomplete TFMPRs. Based on the proposed acceptable consistency definition of TFMPRs, an optimization model is set up to improve the consistency degree of inconsistent TFMPRs. The optimal normalized triangular fuzzy multiplicative weight vector (Tri-MWV) is obtained by computing two analytic expressions and solving a linear programming model. To measure the closeness degree of two TFMPRs, the concept of logarithmic correlation coefficient (LCC) between two TFMPRs is proposed. Combining the incomplete preference information in incomplete TFMPRs with the LCCs of any two TFMPRs, an algorithm of computing experts’ weights is displayed. Subsequently, a novel method of GDM with incomplete TFMPRs is presented. Lastly, a practical example of evaluating 3PRLPs is conducted to illustrate the effectiveness of the proposed GDM method with incomplete TFMPRs.

A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information

Uncertainties are often present in typical portfolio decision analysis (PDA), and it is prudent to conduct a robust PDA to identify project portfolios that perform reasonably well across the entire range of uncertain parameter values. Previous research on robust PDA and applications has almost entirely relied on additive portfolio preference functions, with little research on robustness under multilinear portfolio utility functions (PUFs). A ranking approach for robust PDA is proposed based on multilinear PUFs, incomplete preference information, and the algorithm for accelerating stochastic multicriteria acceptability analysis (SMAA). First, the initial set of portfolios is screened through various constraints to produce a smaller set of desirable portfolios. Second, several types of incomplete preference information are thought to be elicited with regard to multilinear PUFs, including preference information on coefficients, portfolios, and uncertainties on preference elicitation techniques. Third, the SMAA decomposition algorithm is implemented as a ranking approach to perform robust PDA on the basis of multilinear PUFs, incomplete preference information, and potentially numerous portfolios in the set of desirable portfolios. Finally, the approach is applied to a case to validate its effectiveness, and comparisons among additive, multiplicative, and multilinear PUFs in terms of decision recommendations are performed.

A CVaR optimization method for priority of hesitant fuzzy preference relation with chance constraint

In this paper, we establish a chance constrained model for the priority of hesitant fuzzy preference relation based on the idea of statistical distribution for preference information as stochastic variables with unknown distribution. Inspired by the idea of conditional value-at-risk (CVaR) robust optimization, a deterministic convex reformulation is proposed for tackling the chance constrained problem. The existing state-of-the-art methods usually assume that the probability density function of preference information is known a priori, such as Gaussian distribution. However, it is generally over-conservatism. On the contrary, our proposed method provides a tractable second-order cone (SOC) reformulation for the chance constrained problem with the first and second moments, which is easy to handle and calculate. We also analyze the weight acquisition problem of hesitant fuzzy preference relation with unknown distribution preference using the SOC programming method, and obtain the priority weight with its approximately equivalent computationally tractable conic optimization model. A case study is conducted which shows that the proposed method achieves a good general conclusion by comparing it with the optimization method under Gaussian distribution. In addition, this method can also get better decision support for incomplete preference information.

A novel Group-FlowSort method for sorting large-scale problems with application to market segmentation

In the big data era, promising telecom companies need to develop their user strategies when facing large-scale data. For this purpose, we considered a typical strategy decision problem like market segmentation using a novel group sorting method based on FlowSort and applied it to a real case in the telecom market. A novel Group-FlowSort procedure based on stochastic multi-criteria acceptability analysis (SMAA) was developed for sorting large-scale problems. This method could process and integrate multiple expert opinions to reach a consensus by using the Clustering In QUEst (CLIQUE) algorithm and an improved Jaya algorithm. Furthermore, Group-FlowSort based on SMAA-2 is proposed to eliminate the impact of incomplete preference information and several main characteristics and properties are discussed. In addition, a real case study including 8000 customers and 25 experts is used to illustrate the feasibility of the proposed method for telecom market segmentation. Finally, a comparative analysis with FlowSort-GDSS and sensitivity analysis using SMAA-2 are demonstrated to verify the effectiveness and robustness of the method.

A TWO-STAGE MATHEMATICAL PROGRAMMING MODEL FOR DISTRIBUTED PHOTOVOLTAIC PROJECT PORTFOLIO SELECTION WITH INCOMPLETE PREFERENCE INFORMATION

With the rapid growth of the solar photovoltaic (PV) market, many distributed PV power projects are introduced to the market. Selecting a rational project investment portfolio is a complex and challenging task for energy enterprises as both financial and non-financial factors of projects are needed to be considered under limited information and resources. This study presents a two-stage hybrid multi-attribute decision-making and integer programming model for distributed PV project portfolio selection. In Stage I, a multiple attribute group decision-making method based on mathematical programming is used to evaluate the non-financial value of projects under incomplete preference information. Compensative weighted averaging operators with an adjustable parameter are utilized to capture the subjective attitudinal character of an expert in the aggregation process. Then, a rank acceptability index is developed to measure each project’s group support degree in non-financial dimension. In Stage II, a bi-objective integer programming model is constructed to optimize project portfolios, which considers both financial and non-financial values of projects under resource, carbon emission and other strategic constraints. The applicability and effectivity of the proposed approach are demonstrated by a case study of a distributed PV project portfolio selection.

Managing minority opinions in large-scale group decision making based on community detection and group polarization

As the decision environment becomes increasingly complicated, the demand for large-scale group decision making (LSGDM) is increasing. Because of the differences in decision-makers’ (DMs’) personalities, knowledge, and experience, and incomplete information, irrational decision making behaviors, and minority opinion situation frequently appears. This study considers this phenomenon and proposes an LSGDM method by developing a similarity network of DMs on the basis of incomplete preference information. Moreover, the large number of DMs is divided into several clusters using a community detection model, and minority opinions are identified. To show the attitudes of DMs in different decision scenarios, the group polarization effects of individuals within communities are analyzed, and minority opinions using the family aggregation operators of the ordered weighted averaging operator are managed. Given the massive user involvement in online restaurant ratings, the recommendation list of Dianping.com is determined using the proposed LSGDM method. The results of the sensitivity and comparative analyses show that the LSGDM method is flexible and applicable because the attitude of DMs is considered.

Granular computing and optimization model-based method for large-scale group decision-making and its application

In large-scale group decision-making process, some decision makers hesitate among several linguistic terms and cannot compare some alternatives, so they often express evaluation information with incomplete hesitant fuzzy linguistic preference relations. How to obtain suitable large-scale group decision-making results from incomplete preference information is an important and interesting issue to concern about. After analyzing the existing researches, we find that: i) the premise that complete preference relation is perfectly consistent is too strict, ii) deleting all incomplete linguistic preference relations that cannot be fully completed will lose valid assessment information, iii) semantics given by decision makers are greatly possible to be changed during the consistency improving process. In order to solve these issues, this work proposes a novel method based on Granular computing and optimization model for large-scale group decision-making, considering the original consistency of incomplete hesitant fuzzy linguistic preference relation and improving its consistency without changing semantics during the completion process. An illustrative example and simulation experiments demonstrate the rationality and advantages of the proposed method: i) semantics are not changed during the consistency improving process, ii) completion process does not significantly alter the inherent quality of information, iii) complete preference relations are globally consistent, iv) final large-scale group decision-making result is acquired by fusing complete preference relations with different weights.

A benefit-to-cost ratio based approach for portfolio selection under multiple criteria with incomplete preference information

Benefit-to-cost ratio (BCR) measuring is a useful approach for selecting portfolios of projects when they are evaluated applying multiple and conflicting criteria. A multiattribute value function can be used to measure the benefit of each project, which allows one to evaluate the BCRs, rank projects, and select them according to the available budget. However, here, there is a significant difficulty associated with the inaccuracy in the values of criteria scaling constants, which may not be exactly known by decision makers (DMs). Considering this, the present work is directed at overcoming this difficulty by developing a BCR-based model for selecting portfolios under incomplete information about criteria scaling constants. During the elicitation process, DMs answer questions on preferences by considering tradeoffs amongst criteria. The provided information is converted into inequalities forming a space of criteria weights. These inequalities serve as constraints for linear programming models, which are processed to find dominance relations between projects, considering their BCRs. The process is supported by developed computing tools. The formation of a portfolio of research and development projects, which are to be executed by a Brazilian electric energy utility, is presented to illustrate the paper results and their practical applicability.

Personalized individual semantics-based approach for linguistic failure modes and effects analysis with incomplete preference information

Failure Modes and Effects Analysis (FMEA) is a very useful reliability-management instrument for detecting and mitigating risks in various fields. The linguistic assessment approach has recently been widely used in FMEA. Words mean different things to different people, so FMEA members may present Personalized Individual Semantics (PIS) in their linguistic assessment information. This article presents the design of a PIS-based FMEA approach, in which members express their opinions over failure modes and risk factors using Linguistic Distribution Assessment Matrices (LDAMs) and also provide their opinions over failure modes using incomplete Additive Preference Relations (APRs). A preference information preprocessing method with a two-stage optimization model is presented to generate complete APRs with acceptable consistency levels from incomplete APRs. Then, a deviation minimum-based optimization model is designed to personalize individual semantics by minimizing the deviation between APR and the numerical assessment matrix derived from the corresponding LDAM. This is followed by the development of a ranking process to generate the risk ordering of failure modes. A case study and a detailed comparison analysis are presented to show the effectiveness of the PIS-based linguistic FMEA approach.

Efficient allocation of resources to a portfolio of decision making units

Efficiency analysis is widely employed to evaluate decision making units (DMUs) which convert input resources into outputs. In this paper, we develop models for allocating these resources to DMUs in order to maximize the overall efficiency of the portfolio formed by these DMUs. Our models do not require complete preference information about how valuable the inputs and outputs are relative to each other. Rather, based on incomplete preference information and explicit assumptions about the DMUs’ production possibilities, they determine all efficient DMUs portfolios which are then analyzed to provide robust decision recommendations on how much resources should be allocated to each DMU. We illustrate our models by revisiting earlier case studies and show that the use of conventional efficiency analysis in guiding resource allocation decisions can cause inefficiencies.

An improved iterative stochastic multi-objective acceptability analysis method for robust alternative selection in new product development

Alternative selection in new product development (NPD) is a multi-criteria decision-making (MCDM) problem. It usually starts with incomplete, imprecise or even partially missing information. Currently, most existing methods in dealing with this problem cannot work well if required information is incomplete or missing. It is acknowledged that stochastic multi-objective acceptability analysis (SMAA) can be applied to address MCDM problem with incomplete preference information and uncertain criteria measurements. In SMAA, alternatives are evaluated based on SMAA measurements (acceptability index, central weight vector and confidence factor). The discriminability of SMAA for the optimum alternative heavily depends on differences of SMAA measurements among different alternatives. Usually, a large number of alternatives and high level of uncertainty are involved in alternative selection in NPD. In this situation, the differences among SMAA measurements are not obvious, and therefore SMAA cannot deal with such problem very well. To this end, this paper proposes an improved SMAA method called Iterative-SMAA (I-SMAA) for alternative selection in NPD. In the I-SMAA, an iterative multi-step decision-making process is suggested to improve differences of SMAA measurements among different alternatives, and thus assist decision makers (DMs) to positively discern from the most preferred alternative. To enhance the decision-making efficiency, sensitive criteria are acquired in each iteration by ranking sensitivity analysis. DMs are guided to provide partial preference information and give more accurate criteria measurements for sensitive criteria rather than all criteria. Eventually, to verify the proposed method, a numerical example of the existing literature is solved with the method, and the results are compared. And then, a practical example of a preparation equipment for coal samples is further employed to verify the practicability of the proposed I-SMAA.

Price limits under incomplete preference information based on almost stochastic dominance

We derive price limits as decision aids for identifying favorable and unfavorable contracts from the perspective of a selling firm in face of uncertain outcomes. The analysis is based on the concept of almost stochastic dominance to incorporate incomplete information about the decision-maker’s preferences. The main challenges to use this concept in practice are to define and limit the required preference information and to demonstrate the performance of the resulting price limits. We propose price limits that are suitable for a wide range of applications, in particular services. While their information requirements vary, all price limits refer to the same type of aggregate information about marginal utilities and risk aversion. In the scenario with the lowest requirements, the preference information shrinks to a single number which is easy to approximate and to communicate. A comprehensive numerical study featuring fixed-price contracts shows that the incomplete preference information may lead to substantial improvements of the price limits over the situation of no preference information. We also discuss determinants and caveats of these improvements. For instance, the improvements increase with decreases of the decision-maker’s risk sensitivity and may differ substantially in magnitude between the lower and the upper price limit.

A trust propagation and collaborative filtering based method for incomplete information in social network group decision making with type-2 linguistic trust

Abstract A theoretical framework to deal with incomplete preference information in social network group decision making (SN-GDM) is put forward. Firstly, the concept of the type-2 linguistic trust function is defined to model direct trust relationship of group experts in SN-GDM. It adopts the bilattice structure with of trust/distrust values that are all described by distributed linguistic function. Secondly, the type-2 uninorm trust propagation operator is investigated to connect the indirect trust relationship between group experts. The path-ordering induced order weighted averaging (P-IOWA) operator is proposed to aggregate to multiple trust propagation paths into a collective one. Then, the completed trust relationship between group experts is constructed to estimate the incomplete preference information in decision matrix. Combining the social network trust with the collaborative filtering, a comprehensive estimation method for incomplete information is proposed. In detail, the estimation method based the social network trust uses the actual reputation between experts as ‘historic’ actions. While the estimation method by the collaborative filtering utilizes the similar degree of decision as ‘current’ information. Then, the proposed comprehensive estimation method resembles the Bayesian approach, and consequently it can enhance the reliability for the evaluation of the incomplete elements in GDM. Hence, a consensus reaching process for GDM with incomplete preference information is proposed. Finally, an example is given to illustrate the use of the proposed method.

Spatial multi-attribute decision analysis: Axiomatic foundations and incomplete preference information

This paper advances the theoretical foundations and the methodology of spatial decision analysis in which multi-attribute consequences of decision alternatives vary over a spatial region. First, we introduce necessary and sufficient conditions for representing the decision maker’s preferences among such decision alternatives with an additive spatial value function. This new axiomatization allows for the representation of preferences when the spatial region consists of an infinite number of locations, which is often the case in practical applications. Moreover, we show that spatial value functions suggested in the existing literature can be interpreted as special cases of our additive spatial value function. Second, motivated by the high effort required to elicit preferences in spatial decision problems, we develop a method for utilizing the additive spatial value function with incomplete preference information about spatial weights describing the importance of locations and attribute weights. This method provides defensible decision recommendations through the use of dominance concepts and decision rules. The applicability of the developed value function and analysis method is illustrated with a real-life application in air defense planning.

Selection of a sustainable third-party reverse logistics provider based on the robustness analysis of an outranking graph kernel conducted with ELECTRE I and SMAA

Pressure from legislation and customers has motivated companies to consider reverse logistics (RL) in their operations. Since it is a complex procedure that requires an adequate system, the recent trend consists in outsourcing RL to third-party reverse logistics providers (3PRLPs). This paper provides the background of sustainable triple bottom line theory with focus on economic, environmental, and social aspects under 3PRL concerns. The relevant sustainability criteria are used in a case study conducted in cooperation with an Indian automotive remanufacturing company. To select the most preferred service provider, we use a hybrid method combining a variant of ELECTRE I accounting for the effect of reinforced preference, the revised Simos procedure, and Stochastic Multi-criteria Acceptability Analysis. The incorporated approach exploits all parameters of an outranking model compatible with the incomplete preference information of the Decision Maker. In particular, it derives the newly defined kernel acceptability and membership indices that can be interpreted as a support given to the selection of either a particular subset of alternatives or a single option. The proposed ELECTRE-based method enriches the spectrum of multiple criteria decision analysis approaches that can be used to effectively approach the problem of the 3PRLP selection. As indicated by the extensive review presented in the paper, this application field was so far dominated by Analytic Hierarchy Process and TOPSIS, whose weaknesses can be overcome by applying the outranking methods.

Periodic benefit-risk assessment using Bayesian stochastic multi-criteria acceptability analysis

Benefit-risk (BR) assessment is essential to ensure the best decisions are made for a medical product in the clinical development process, regulatory marketing authorization, post-market surveillance, and coverage and reimbursement decisions. One challenge of BR assessment in practice is that the benefit and risk profile may keep evolving while new evidence is accumulating. Regulators and the International Conference on Harmonization (ICH) recommend performing periodic benefit-risk evaluation report (PBRER) through the product's lifecycle. In this paper, we propose a general statistical framework for periodic benefit-risk assessment, in which Bayesian meta-analysis and stochastic multi-criteria acceptability analysis (SMAA) will be combined to synthesize the accumulating evidence. The proposed approach allows us to compare the acceptability of different drugs dynamically and effectively and accounts for the uncertainty of clinical measurements and imprecise or incomplete preference information of decision makers. We apply our approaches to two real examples in a post-hoc way for illustration purpose. The proposed method may easily be modified for other pre and post market settings, and thus be an important complement to the current structured benefit-risk assessment (sBRA) framework to improve the transparent and consistency of the decision-making process.

Double Hierarchy Hesitant Fuzzy Linguistic Mathematical Programming Method for MAGDM Based on Shapley Values and Incomplete Preference Information

This paper investigates a double-hierarchy hesitant fuzzy linguistic mathematical programming method to multiple attribute group decision making (MAGDM) problems, where the assessment values of alternatives and the truth degrees of pairwise comparisons between alternatives are denoted by double-hierarchy hesitant fuzzy linguistic elements (DHHFLEs) and the inter-dependent or interactive characteristics among attributes and the incomplete preference information are taken into account. First, based on the distance measure between DHHFLEs, the double-hierarchy hesitant fuzzy linguistic positive ideal group consistency index (DHHFLPIGCI), double-hierarchy hesitant fuzzy linguistic positive ideal group inconsistency index (DHHFLPIGII), double-hierarchy hesitant fuzzy linguistic negative ideal group consistency index (DHHFLNIGCI), and double-hierarchy hesitant fuzzy linguistic negative ideal group inconsistency index (DHHFLNIGII) are defined, respectively. Then, to determine the positive ideal solution (PIS), negative ideal solution (NIS), and Shapley values of attributes simultaneously, a four-objective double-hierarchy hesitant fuzzy linguistic mathematical programming model is constructed by minimizing the DHHFLPIGII and DHHFLNIGII as well as maximizing the DHHFLPIGCI and DHHFLNIGCI. Subsequently, the relative closeness degrees (RCDs) of all feasible alternatives for each decision maker (DM) are obtained and the individual ranking order of alternatives for each DM is derived according to the descending order of RCDs, and thus a single-objective assignment model is established to generate the group ranking order of alternatives. Finally, a numerical example is given to illustrate the application of the proposed method and its effectiveness is demonstrated by comparison analysis.

A mathematical programming-based method for heterogeneous multicriteria group decision analysis with aspirations and incomplete preference information

Abstract Aspirations, which serve as a performance target and simplify cognitive processes associated with decision making, are an important decision factor for individuals and organizations. However, this factor is usually ignored in traditional multicriteria decision making. This paper considers a multicriteria group decision making problem with aspirations and incomplete preference information, in which criteria values and aspirations accept multiple formats. To solve this problem, new consistency and inconsistency indices considering importance and interaction as well as aspirations of criteria are defined. Then, we propose a bi-objective intuitionistic fuzzy programming model to identify importance and interaction parameters, based on which, an individual ranking of alternatives can be elicited. Next, to elicit a group ranking of individuals, a flexible mix 0–1 nonlinear programming model of minimizing the inconsistencies between the group final ranking and the individual ranking is established by comprehensively considering both the majority and the minority principles. Finally, an example of selecting the best strategic freight forwarder is used to illustrate the feasibility of the proposed method, followed by a sensitivity analysis and a comparison analysis. The prominent advantages of the developed method are its ability to handle multiple preference information characterizing bounded rationality and nonadditive behaviors of decision makers as well as improve a cardinal inputs-based group decision making model.

Portfolio decision analysis methods in environmental decision making

Environmental modellers recurrently work with decisions where a portfolio of actions has to be formed to effectively address the overall situation at hand. When creating the portfolio, one needs to consider multiple objectives and constraints, identify promising action candidates and examine interactions among them. The area of portfolio decision analysis deals with such tasks. This paper reviews portfolio modelling approaches and software that are applicable in environmental management. A framework for environmental portfolio decision analysis is provided that consists of steps ranging from problem framing to modelling and optimization, as well as to the analysis of results. The use of this framework is demonstrated with an illustrative case describing planning of urban water services. The problem is analyzed with a recently introduced portfolio decision analysis method called Robust Portfolio Modelling, which enables the use of incomplete preference information and consequence data. This feature can be particularly useful in environmental applications.

A testbed to enable comparisons between competing approaches for computational social choice

Within artificial intelligence, the field of computational social choice studies the application of AI techniques to the problem of group decision making, especially through systems where each agent submits a vote taking the form of a total ordering over the alternatives (a preference). Reaching a reasonable decision becomes more difficult when some agents are unwilling or unable to rank all the alternatives, and appropriate voting systems must be devised to handle the resulting incomplete preference information. In this paper, we present a detailed testbed which can be used to perform information analytics in this domain. We illustrate the testbed in action for the context of determining a winner or putting candidates into ranked order, using data from realworld elections, and demonstrate how to use the results of the testbed to produce effective comparisons between competing algorithms.