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In this paper, we demonstrate that the Theorem 3.1 in a recently published paper by Garg [Appl. Soft Comput. 38 (2016) 988–999] is incorrect by a counterexample. Further, we point out the shortcomings of Garg's proposed generalized improved score function for practical decision making. [ABSTRACT FROM AUTHOR]

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some 'false' or 'biased' arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

Most real-world decisions practically occur in extremely complex environments characterized by both fuzziness and randomness. This phenomenon highlights the requirement for new evaluation methods in a fuzzy random environment and new ways to address fuzzy random multiple-criteria decision-making (MCDM) problems. This study reviews fuzzy random variable (FRV) to evaluate fuzzy random decision-making environment. Given the inaccuracy of certain precision formulas proposed in previous studies for the variance of a triangular FRV, this work presents the detailed process of calculating precision variance formulas and discusses several properties of the expectation and variance of triangular FRVs (TFRVs). The united variance of a TFRV vector is also proven to possess non-additive properties. Thus, an ordered weighted averaging (OWA) operator is extended to aggregate fuzzy random data by proposing a triangular fuzzy random OWA operator. Motivated by the idea of mean-variance analysis, an expectation-variance-based method is employed to rank TFRVs. Furthermore, a novel triangular fuzzy random MCDM method is developed, and certain numerical examples are provided to demonstrate the ability of TFRVs to comprehensively assess the performance of a specific alternative. This work also illustrates how the triangular fuzzy random MCDM framework can be extended to any fuzzy random decision-making process. [ABSTRACT FROM AUTHOR]

In this note, we point out an error to the proof of Theorem 3.4 in Zhang and Xu (Int J Intell Syst 2014;29(12):1061-1078) by a counterexample. We find that the inequality (i.e. [ABSTRACT FROM AUTHOR]

The process of bid evaluation is subject to indetermination, imprecision, and uncertainty in terms of their alternative-criterion decision appraisals. To address this issue, this paper develops a novel ELECTRE III-based MCGDM approach for bid evaluation, in which generalized comparative linguistic expressions (GCLEs) are used to evaluate bidder performance. The collected GCLEs are further transformed into possibility-distribution-based hesitant fuzzy linguistic-term sets (HFLTSs) to facilitate the qualitative construction of individual expertise. A consensus-reaching process is introduced to promote decisions that are agreed upon by experts and thereby ensure an enhanced state of mutual agreement among the experts. Subsequently, an integrated subjective-objective approach is proposed to calculate criterion weights and to implement an ELECTRE III-based method that incorporates HFLTS possibility distributions, which allows us to treat the indetermination, imprecision, and uncertainty embedded in appraisals of alternative-criterion decisions when evaluating bids. The potential advantages of the proposed approach are validated by a real-life contractor-selection case. • This paper develops a generalized comparative linguistic ELECTRE III frame-work for bid evaluation. • The framework integrates novel expertise characterizations for weighing experts selected for evaluating bids. • This paper establishes a comprehensive criteria system for bid evaluation that includes qualitative and quantitative aspects. • A consensus-reaching process with possibility-distribution-based hesitant fuzzy linguistic information is introduced. • A novel weighting procedure on the basis of distance-based entropy for HFLTS possibility-distribution is presented. [ABSTRACT FROM AUTHOR]

Increasing growth and development of building industry and civil engineering motivates enterprises to advance bid evaluation process in an effort to ameliorate building quality and diminish construction cost. The selection of qualified construction contractor has been generally formulated and addressed as a multi-attribute group decision-making problem. However, few existing studies have taken the reasoning logic pattern in human cognition process and the compensatory among attributes into account. Therefore, a two-stage logic scoring of preference-ELECTRE III-based approach is established for the management and manipulation of bidder selection. In a bid to facilitate expert evaluation articulation, alternative-attribute assessments in this approach take the form of generalized comparative linguistic expressions, which are subsequently converted into possibility-distribution-based hesitant fuzzy linguistic term set via the similarity measure-based generation approach to enhance information quality and reliability. Then, nonlinear optimization-based direction rules are introduced to advance the automatic minimum-distance-based consensus reaching model and based on which, the individual semantic-embedded assessments are algorithmically adjusted to reach acceptable consensus. Furthermore, the expert and attribute importance degrees are extracted from both semantic and formal logic aspects, and the modified individual assessments are gathered by integrating the two-stage logic scoring of preference aggregation structure and the ELECTRE III method. The present approach provides a solution to bid evaluation problems considering the reasoning logic pattern in human cognition process and the compensatory among attributes. A practical case study and a comparative analysis are performed to demonstrate the feasibility and effectiveness of the established multi-attribute group decision-making approach. • A consensus reaching model is proposed to minimize opinion adjustment. • A novel collective opinion generation approach is developed. • Establish a comprehensive bid evaluation attribute tree. • Construct a LSP- and ELECTRE III-integrated bid evaluation framework. • Introduce the two-stage aggregation paradigm for preference assessments. [ABSTRACT FROM AUTHOR]