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• Show flaws of existing multiplicative transitivity models of interval-valued fuzzy preference relations (IVFPRs). • Develop an and-like-uninorm-based functional transitivity equation for IVFPRs. • Find a closed-form solution for the optimal interval-valued fuzzy weights of IVFPRs. • Formulate geometric consistency indices of IVFPRs and propose a new acceptability checking model. • Devise an and-like-uninorm-based method to aggregate local interval-valued fuzzy weights. The framework of interval-valued fuzzy preference relations (IVFPRs) is adequate and effective to model human preference evaluations under indeterminacy. This paper analyzes three recently presented multiplicative transitivity models of IVFPRs and exposes their drawbacks. An and-like-uninorm-based functional transitivity equation is developed to introduce a multiplicative consistency notion for IVFPRs. Based on the transitivity logarithmic equation, a geometric-consistency index is further proposed to compute the inconsistency level of an IVFPR. The paper builds a logarithmic least squares model with row indeterminacy constraints and equivalently transforms it into a quadratic programming model for finding a closed-form solution of the normalized interval-valued fuzzy weights of IVFPRs. A novel method is subsequently presented to check the acceptability of an IVFPR by examining its acceptable consistency and acceptable indeterminacy. An approach including an and-like-uninorm-based maximization model is introduced to aggregate local interval-valued fuzzy weights and an interval fuzzy analytic hierarchy process is designed step-by-step. An illustrative example and a comparison study are utilized to demonstrate the performance and merits of the presented models. Meanwhile, an outstanding undergraduate student selection problem in international exchange is provided to show the application of the proposed decision method. [ABSTRACT FROM AUTHOR]

The good development of health care is conducive to improve the value and prospects of society. However, health sectors of Ghana are facing a challenge in providing medical services with expected quality for an ever-increasing number of patients in response to competitive pressures. In such circumstances, the proper evaluation of hospital health-care delivery quality becomes critical. Thus, to achieve this goal, this paper proposes an integrated medical triangular fuzzy MULTIMOORA approach (IMTFMA). We firstly construct the appropriate evaluation criteria system based on the analysis of Ghana's medical services. Then, to properly evaluate the weight of the criteria in a comprehensive manner, we determine the weight of criteria from subjective and objective perspectives. Meantime, we handle the fuzzy evaluation of experts for the criterion importance with the enhanced alpha-level sets method. According to the triangular fuzzy rating for hospitals provided by respondents, we further develop a novel evaluation method based on MULTIMOORA with the axiomatic design for accurately evaluating health-care delivery quality. The research is conducted on 8 selected hospitals, including 4 public and 4 private hospitals in the Greater Accra Region of Ghana, with 24 criteria. 15 experts with rich experience in related fields and 480 respondents assessed the above 8 selected hospitals by questionnaires. According to the outcome of the empirical analysis, even though public hospitals benefit subsidy from the government, they perform abysmally low, whereas private hospitals which are self-sponsored rather perform extremely better than expectation. [ABSTRACT FROM AUTHOR]

This paper focuses on how to find an analytic solution of optimal interval weights from consistent interval fuzzy preference relations (IFPRs) and obtain approximate-solution-based interval weights in analytic form from inconsistent IFPRs. The paper first analyzes the popularly used interval weight additive normalization model and illustrates its drawbacks on the existence and uniqueness for characterizing ]0, 1[-valued interval weights obtained from IFPRs. By examining equivalency of ]0, 1[-valued interval weight vectors, a novel framework of multiplicatively normalized interval fuzzy weights (MNIFWs) is then proposed and used to define multiplicatively consistent IFPRs. The paper presents significant properties for multiplicatively consistent IFPRs and their associated MNIFWs. These properties are subsequently used to establish two goal programming (GP) models for obtaining optimal MNIFWs from consistent IFPRs. By the Lagrangian multiplier method, analytic solutions of the two GP models are found for consistent IFPRs. The paper further devises a two-step procedure for deriving approximate-solution-based MNIFWs in analytic form from inconsistent IFPRs. Two visualized computation formulas are developed to determine the left and right bounds of approximate-solution-based MNIFWs of any IFPR. The paper shows that this approximate solution is an optimal solution if an IFPR is multiplicatively consistent. Three numerical examples including three IFPRs and comparative analyses are offered to demonstrate rationality and validity of the developed model. [ABSTRACT FROM AUTHOR]

• Obtain uncertainty constraints among assessments in an additively consistent IVFPR. • Acquire an analytical solution of interval fuzzy utility vectors from IVFPRs. • Propose a novel acceptability checking method for IVFPRs. • Develop MCDM with highlighting individual characteristics of alternatives. Acquiring an analytical solution of interval fuzzy utility vectors (IFUVs) from interval-valued fuzzy preference relations (IVFPRs) plays a key role in improving the efficiency and performance of decision making with IVFPRs. This study devises formulas to compute uncertainty indices of interval-valued fuzzy assessments and IVFPRs, and builds uncertainty constraints among fuzzy assessments in an additively consistent IVFPR. By dividing all IVFPRs with the same size into two categories, least square models with constraints of uncertainty indices are set up and their analytical solutions are found to respectively acquire normalized IFUVs from the two categories of IVFPRs. The analytical solutions are then integrated into unified computational formulas acquiring normalized IFUVs from IVFPRs. On the basis of analytical-solution-based IFUVs, a distance based additive consistency index is devised and a novel acceptability concept is presented by taking both additive inconsistency acceptability and uncertainty acceptability into account. Subsequently, this paper proposes a multi-criteria decision making method with highlighting individual characteristics of alternatives. An illustration with one consistent IVFPR and three inconsistent IVFPRs is offered and a comparative study is implemented to validate the models presented. An annual-performance-evaluation-based outstanding teacher recommendation problem is utilized to show the practicality of the decision method proposed. [ABSTRACT FROM AUTHOR]

• We propose a knee based evolutionary algorithm, named MMO-EvoKnee, which incorporates MCDM strategy into solving MMOPs. The proposed algorithm can find a complete set of global knee solutions accurately instead of an entire Pareto front and Pareto sets. • The EvoKnee selection aims to find target global knee solutions and boundary individuals in the objective space. After that, the other three procedures would turn the search direction into the decision space for multiple equivalent optimal knee and boundary solutions. • The Knee Multimodal Solutions Selection focuses on searching for well-converged knee solutions. Furthermore, the Maximum Spanning Subset Selection can accurately identify a complete set of global knee solutions from overcrowded solutions, which can relieve the burden for decision makers. Recently, many advanced multimodal multi-objective evolutionary algorithms (MMOEAs) have been presented to solve multimodal multi-objective optimization problems (MMOPs). However, most of these approaches struggle not only to find the entire Pareto sets and Pareto front, but also ignoring the problem of Multi-Criteria Decision Making (MCDM) to be handled at a later stage. As a matter of fact, it is a very eclectic and challenging burden for decision makers to choose some trade-off optimal solutions from an enormous collection of non-dominated Pareto-optimal individuals. In this paper, we propose a knee based evolutionary algorithm, named MMO-EvoKnee, which incorporates MCDM strategy into solving MMOPs. The proposed algorithm is designed to search for a complete set of global knee solutions instead of an entire Pareto front and Pareto sets. Firstly, the EvoKnee Selection is adopted to find target global knee solutions and boundary individuals. Secondly, the Knee Multimodal Solutions Selection focuses on decision space exploitation to obtain well-converged multiple Pareto-optimal knee solutions. Thirdly, the Maximum Spanning Subset Selection is designed to accurately identify a complete number of knee solutions from overcrowded Pareto regions. Fourthly, the Boundary Multimodal Solutions Selection can find and maintain well-diversified and well-converged boundary solutions. As a result, MMO-EvoKnee can consistently find all knee solutions of interest quickly, and it relieves the burden for decision makers. Finally, the performance of the proposed algorithm is evaluated on thirteen benchmark MMOPs. The experiment results clearly show that the proposed MMO-EvoKnee provides a competitive edge over the chosen state-of-the-art MMOEAs. [ABSTRACT FROM AUTHOR]

Interval type-2 fuzzy sets are more valuable than conventional type-1 fuzzy sets in terms of covering more uncertain and complex preference information. Interval type-2 trapezoidal fuzzy sets, as a particular form of interval type-2 fuzzy sets, can precisely express subjective evaluations and qualitative assessments. In this paper, the concept of the likelihoods of interval type-2 fuzzy preference relations are utilized to propose a novel multi-criteria decision-making model for the sustainable supplier selection problems in which the weights of criteria and performance ratings are expressed as interval type-2 trapezoidal fuzzy sets. A new likelihood-based multi-criteria sustainable supplier selection model is proposed by encapsulating assorted sustainability triple bottom line criteria, collected from the state-of-the-art literature, which turns this framework into a benchmark approach for the evaluations of sustainable suppliers. The practical effectiveness of the proposed likelihood-based method is illustrated by the applications to four real cases and the comparative analysis demonstrates the validation and advantages of the proposed method over conventional multi-criteria sustainable supplier selection methods. [ABSTRACT FROM AUTHOR]

The Social Web promotes social interactions among people through Web 2.0 technologies. In this context, User-Generated Content (UGC) spreads across social media platforms in the absence of traditional intermediaries that can verify both the believability of the content and the reliability of the sources that generated it. For this reason, the problem of how to assess the credibility of UGC is receiving nowadays increasing attention. In the literature, several approaches have tackled this issue mainly as a classification problem, by categorizing information into genuine and fake. The majority of the proposed solutions follows a data-driven approach, by employing supervised or semi-supervised machine learning techniques that act on multiple features related to credibility. Despite its effectiveness, however, machine learning may present some possible drawbacks, including data-dependency and the possible inscrutability of the contribution that single or interacting features have in the final classification process. In this paper, a Multi-Criteria Decision Making approach is proposed, aimed to assess the credibility of UGC. A given information item (alternative) is evaluated with respect to the considered credibility features (criteria) based on prior domain knowledge, where an overall credibility estimate is obtained by means of a suitable model-driven approach based on aggregation operators. The credibility estimate allows to classify credible UGC with respect to non-credible one, and can also be used to provide a ranking of the alternatives with respect to credibility. To consider interactions among features, the Choquet integral is employed. [ABSTRACT FROM AUTHOR]

In recent decades, sustainable investing has caught on with investors, and it has now become the norm. In the age of start-ups, with scant information on the sustainability aspects of an asset, it becomes harder to pursue sustainable investing. To this end, this paper proposes a sustainable financial portfolio selection approach in an intuitionistic fuzzy framework. We present a comprehensive three-stage methodology in which the assets under consideration are ethically screened in Stage-I. Stage-II is concerned with calculating the sustainability scores, based on various social, environmental, and economic (SEE) criteria and an evaluation of the return and risk of the ethical assets. Intuitionistic fuzzy set theory is used to gauge the linguistic assessment of the assets on several SEE criteria from multiple decision-makers. A novel intuitionistic fuzzy multi-criteria group decision-making technique is applied to calculate the sustainability score of each asset. Finally, in Stage-III, an intuitionistic fuzzy multi-objective financial portfolio selection model is developed with maximization of the satisfaction degrees of the sustainability score, return, and risk of the portfolio, subject to several constraints. The ϵ -constraint method is used to solve this model, which yields various efficient, sustainable financial portfolios. Subsequently, investors can choose the portfolio best suited to their preferences from this pool of efficient, sustainable financial portfolios. A detailed empirical illustration and a comparison with existing works are given to substantiate and validate the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: The hesitant fuzzy linguistic term sets (HFLTSs), which can be used to represent an expert’s hesitant preferences when assessing a linguistic variable, increase the flexibility of eliciting and representing linguistic information. The HFLTSs have attracted a lot of attention recently due to their distinguished power and efficiency in representing uncertainty and vagueness within the process of decision making. To enhance and extend the applicability of HFLTSs, this paper investigates and develops different types of distance and similarity measures for HFLTSs. The paper first proposes a family of distance and similarity measures between two HFLTSs. Then a variety of weighted or ordered weighted distance and similarity measures between two collections of HFLTSs are proposed and analyzed for discrete and continuous cases respectively. After that, the application of these measures to multi-criteria decision making problems is given. Based on the proposed distance and similarity measures, the satisfaction degrees for different alternatives are established and are then used to rank alternatives in multi-criteria decision making. Finally a practical example concerning the evaluation of the quality of movies is given to illustrate the applicability and advantage of the proposed approach and the differences between the proposed distance and similarity measures. [Copyright &y& Elsevier]

In the process of multi-criteria decision making (MCDM), decision makers or experts usually exploit quantitative or qualitative methods to evaluate the comprehensive performance of all alternatives on each criterion. How the decision-makers or the experts make the evaluations relies on their professional knowledge and the actual performances on the criteria characters of the alternatives. However, because of both the objective complexity of decision making problem and the uncertainty of human subjective judgments, it is sometimes too hard to get the accurate evaluation information. Intuitionistic fuzzy set (IFS) is a useful tool to deal with uncertainty and fuzziness of complex problems. In this paper, we propose a new distance measure between IFSs and prove some of its useful properties. The experimental results show that the proposed distance measure between IFSs can overcome the drawbacks of some existing distance and similarity measures. Then based on the proposed distance measure, an extended intuitionistic fuzzy TOPSIS approach is developed to handle the MCDM problems. Finally, a practical application which is about credit risk evaluation of potential strategic partners is provided to demonstrate the extended intuitionistic fuzzy TOPSIS approach, and then it is compared with other current methods to further explain its effectiveness. [ABSTRACT FROM AUTHOR]

Thermodynamics has a knowledge structure to effectively depict the stability (or instability) of a system. Considering the increasing complexity of the application problems and the fuzzy nature of human thought, intuitionistic fuzzy sets were proposed by Atanassov [Intuitionistic fuzzy set, Fuzzy Sets and Systems, vol. 20, pp: 87–96, 1986] and have become a powerful tool to portray the uncertainty of things. In order to better solve the multi-criteria decision making (MCDM) problems in an intuitionistic fuzzy environment, the paper first proposes a thermodynamic method for MCDM with intuitionistic fuzzy numbers (IFNs), which can consider both the quantity and the quality of decision information in decision making process. Then, we conduct simulations to compare the decision making results derived by the proposed method and other two commonly used decision making methods (i.e., the weighted averaging operator and the TOPSIS) in the intuitionistic fuzzy environment. Furthermore, the thermodynamic method for MCDM with IFNs is applied to assist the hierarchical medical system in West China Hospital as a case study. We can get some empirical results from the simulations and applications: (1) if the optimal selections obtained by the proposed method and one of the two commonly used methods are the same, then it is likely that the three decision making methods would obtain the same results; (2) if the optimal selections by the three methods are different, then it is often the cases that the selection by the proposed method is different from those by the two other methods. These empirical studies demonstrate that the quality of decision information has significant impacts on decision making results, which indicates that the proposed method can effectively solve the practical decision making problems. [ABSTRACT FROM AUTHOR]

This paper investigates consistency and uncertainty measurements as well as acceptability checking for triangular fuzzy multiplicative preference relations (TFMPRs). A geometric consistency index is proposed to measure the consistency degree of a TFMPR, and thresholds of acceptable consistency are discussed for TFMPRs. Uncertainty indices are introduced to measure indeterminacy degrees of triangular fuzzy judgments and of TFMPRs and a notion of acceptable TFMPRs are put forward by considering both acceptable consistency and acceptable uncertainty in TFMPRs. We also explore the elicitation of triangular fuzzy weights from acceptable TFMPRs and the aggregation of local triangular fuzzy weights for solving hierarchical multi-criteria decision-making problems. A geometric mean-based equation and a logarithmic least square model are developed to elicit normalized acceptable triangular fuzzy multiplicative weights from an acceptable TFMPR. An equation and a linear program are established to transform triangular fuzzy multiplicative weights into triangular fuzzy additive weights. A geometric weighting-based equation and a pair of linear programs are devised to generate global priority fuzzy weights from local triangular fuzzy multiplicative weights. Three numerical examples, including a hierarchical multi-criteria decision-making problem, are used to illustrate how to apply the developed framework, and comparative studies are provided to show its availability and advantages. [ABSTRACT FROM AUTHOR]

Hesitant fuzzy set (HFS) permits the membership degrees of an element to a set represented by several possible values. Thus, it provides a suitable means to express uncertain information of different group members within the process of multi-criteria decision making (MCDM). In this paper, we suggest a new approach, named HF-ELECTRE II approach that combines the idea of HFSs with the ELECTRE II method, to efficiently handle different opinions of group members that are frequently encountered when handling the MCDM problems. We formulate the approach by defining the concepts of hesitant fuzzy concordance and discordance sets and by constructing the strong and weak outranking relations, which are employed to decide the ranking for a set of alternatives. Numerical examples are presented to exhibit the applications of the proposed method. Furthermore, a comparison of the alternatives’ rankings derived from the HF-ELECTRE II method with those derived from the aggregation operators and the fuzzy group ELECTRE approach is made. After that, a decision supporting system based on the HF-ELECTRE II method is constructed to aid decision making, and the prominent characteristics of the HF-ELECTRE II method and future research challenges are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Decision support is one of the main objectives of ontology-based knowledge management systems. However, there is no standard method that would define how to model decisions in ontologies. Despite many research efforts and established methods for decision modelling and support, they have not yet been systematically applied to the field of ontologies. This paper proposes an ontology based multi-criteria decision making method that enables one to define decision models using ontology as the base construct. It structures decision models in such a way that the problem solution can be obtained by reasoning upon the ontology. We propose a generic approach that can be applied to an arbitrary domain. The proposed method is based on qualitative multi-criteria decision making, which is applied to the field of ontologies. OWL is used as the ontology representation language. As a proof of concept we have developed an ontology-based decision support system for an electric power transmission company. The proposed method represents an important step forward in the field of ontologies. Its main advantages are: a higher level of decision support provided by the ontology, direct use of information captured in ontology for decision making, a higher level of business process automation, and reuse of decision model concepts in definitions of more complex ontology concepts. [Copyright &y& Elsevier]

Abstract: The Bonferroni mean (BM) can capture the interrelationships among arguments, which plays a crucial role in multi-criteria decision making problems. In this paper, we explore the geometric Bonferroni mean (GBM) considering both the BM and the geometric mean (GM) under hesitant fuzzy environment. We further define the hesitant fuzzy geometric Bonferroni mean (HFGBM) and the hesitant fuzzy Choquet geometric Bonferroni mean (HFCGBM). Then we give the definition of hesitant fuzzy geometric Bonferroni element (HFGBE), which is considered as the basic calculational unit in the HFGBM and reflects the conjunction between two aggregated arguments. The properties and special cases of the HFGBM are studied in detail based on the discussion of the HFGBE. In addition, the weighted hesitant fuzzy geometric Bonferroni mean (WHFGBM) and the weighted hesitant fuzzy Choquet geometric Bonferroni mean (WHFCGBM) are proposed considering the importance of each argument and the correlations among them. In the end, we apply the proposed aggregation operators to multi-criteria decision making, and give some examples to illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper, we develop mathematical models for simultaneous consideration of suitability and optimality in asset allocation. We use a hybrid approach that combines behavior survey, cluster analysis, analytical hierarchy process and fuzzy mathematical programming. [Copyright &y& Elsevier]

Abstract: This paper will demonstrate a strong relationship between the Compromise Programming (CP) method and the Ordered Weighted Averaging (OWA) operator. We will mathematically prove that the application of the CP method reflects the pessimistic view of the Decision Maker (DM), if the distance from the ideal point is minimized. It will however present an optimistic DM, if the distance from the nadir is maximized. The OWA operator may cover all of the optimistic, neutral and pessimistic views. A practical relationship will be developed between the power value of the CP method and the optimism degree of the DM based on fuzzy quantifiers. The theoretical results will be illustrated by a real case study of a water resources management problem. [Copyright &y& Elsevier]

Abstract: Skyline queries have been increasingly used in multi-criteria decision making and data mining applications. They retrieve a set of interesting points from a potentially large set of data points. A point is said to be interesting if it is not dominated by any other point. Skyline cube (skycube) consists of skylines of all possible non-empty subsets of a given set of dimensions. In this paper, we propose two algorithms for computing skycube using bitmaps that are derivable from indexes. The Point-based skycube algorithm is an improvement over the existing Bitmap algorithm, extended to compute skycube. The Point-based algorithm processes one point at a time to check for skylines in all subspaces. The Domain-based skycube algorithm views points as value combinations and probes entire search space for potential skyline points. It significantly reduces bitmap access for low cardinality dimensions. Our experimental study shows that the two algorithms strictly dominate, or at least comparable to, the current skycube algorithm in most of the cases, suggesting that such an approach could be a useful addition to the set of skyline query processing techniques. [Copyright &y& Elsevier]