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In this paper, we investigate the multi-criteria group decision-making (MCGDM) problems with incomplete weight information under T-spherical fuzzy environment. Firstly, motivated by the idea of the intuitionistic fuzzy interaction method, we propose some operation laws of T-spherical fuzzy numbers (T-SFNs), as well as some T-spherical fuzzy interaction aggregation operators, such as the T-spherical fuzzy weighted averaging interaction (T-SFWAI) operator, the T-spherical fuzzy weighted geometric interaction (T-SFWGI) operator, the T-spherical fuzzy ordered weighted interaction aggregation operators and the generalized T-spherical fuzzy interaction aggregation operators. Then, some desirable properties of the proposed T-SFWAI and T-SFWGI operators and some special cases of the generalized T-spherical fuzzy interaction aggregation operators are discussed in detail. Secondly, for the situations where the information about the weights of criteria is partly known or completely unknown, we establish two optimization models to determine the weights of criteria based on the maximizing deviation method and Lagrange function method, respectively. Thirdly, the traditional TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) approach is extended to solve MCGDM problem under the T-spherical fuzzy environment by defining the distance between T-SFNs, score function and accuracy function of T-spherical fuzzy number. Finally, a numerical example is given to illustrate the application of the extended TODIM approach, and further the sensitivity analysis and comparison analysis are carried out to demonstrate the influence of parameter on the final result and the effectiveness of the extended method. [ABSTRACT FROM AUTHOR]

In the classical LINear programming technique for Multidimensional Analysis of Preference (LINMAP), the criteria are assumed to be independent, which may cause distorted results. The aim of this paper is to employ the LINMAP to develop an interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for multicriteria group decision making considering not only the importance of criteria and that of their ordered positions but also the interactions among criteria and those among their ordered positions. In the spirit of LINMAP, new group consistency and group inconsistency indices based on cross-entropy and Shapley values are firstly defined by considering the interactions among criteria and among their ordered positions. To simultaneously determine the fuzzy measures on criteria set and on ordered set, a bi-objective IVIF programming model is then constructed by minimizing the inconsistency index and maximizing the consistency index. The proposed IVIF programming model is subsequently solved by transforming it into a multiobjective programming model. Furthermore, some generalizations of the proposed programming model are investigated. Finally, two examples are given to illustrate the application of the proposed method, and its superiority is demonstrated by comparing the performance of the proposed method with that of the existing methods. [ABSTRACT FROM AUTHOR]

With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods. [ABSTRACT FROM AUTHOR]

With respect to multi-attribute group decision-making (MAGDM) problems in which the attribute values take form of intuitionistic trapezoid fuzzy linguistic numbers, some new aggregation operators are proposed, such as intuitionistic trapezoid fuzzy linguistic weighted geometric operator, intuitionistic trapezoid fuzzy linguistic ordered weighted geometric operator, intuitionistic trapezoid fuzzy linguistic hybrid weighted geometric operator, intuitionistic trapezoid fuzzy linguistic generalized weighted averaging operator, intuitionistic trapezoid fuzzy linguistic generalized ordered weighted averaging operator and intuitionistic trapezoid fuzzy linguistic generalized hybrid weighted averaging operator are proposed at first. Then, some desirable properties of these proposed operators are discussed, including monotonicity, idempotency, commutativity and boundedness. Furthermore, based on the proposed operators, some novel methods are developed to solve MAGDM problems with intuitionistic trapezoid fuzzy linguistic information under different cases. Finally, an illustrative example of emergency response capability evaluation is provided to illustrate the applicability and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]