An extended TODIM method for multiple attribute group decision‐making based on 2‐dimension uncertain linguistic Variable

Abstract

The significant characteristic of the TODIM (an acronym in Portuguese of Interactive and Multiple Attribute Decision Making) method is that it can consider the bounded rationality of the decision makers. However, in the classical TODIM method, the rating of the attributes only can be used in the form of crisp numbers. Because 2-dimension uncertain linguistic variables can easily express the fuzzy information, in this article, we extend the TODIM method to 2-dimension uncertain linguistic information. First of all, the definition, characteristics, expectation, comparative method and distance of 2-dimension uncertain linguistic information are introduced, and the steps of the classical TODIM method for Multiple attribute decision making (MADM) problems are presented. Second, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MADM problems in which the attribute values are in the form of 2-dimension uncertain linguistic variables, and detailed decision steps are given. Its significant characteristic is that it can fully consider the bounded rationality of the decision makers, which is a real action in real decision making. Finally, a numerical example is provided to verify the developed approach and its practicality and effectiveness.

Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

“…Then, Chen et al proposed the linguistic intuitionistic fuzzy number (LIFN), which is composed of the intuitionistic fuzzy number (the basic element in IFS) and the linguistic variable [6]. On the other hand, some methods for multiple attribute group decision-making (MAGDM) were proposed based on two-dimension uncertain linguistic variable [7,8]. Some improved linguistic intuitionistic fuzzy aggregation operators and several corresponding applications were given in decision-making [9].…”

A Novel Method for Interval-Value Intuitionistic Fuzzy Multicriteria Decision-Making Problems with Immediate Probabilities Based on OWA Distance Operators

“…To sum up, there are mainly four aspects on the decision-making under IVIF environment: (1) some decision-making methods are developed based on information measures (specially, distance, similarity, and entropy) because information measures for IVIFSs have great effects on the development of the IVIFS theory and its applications. For example, similarity measures [4][5][6], inclusion measure [7], entropy measure [8], cross-entropy measure [9], and distance measures [10] are developed and applied to corresponding MCDM and MADM problems; (2) many new aggregation operators are also investigated in the IVIFSs and applied to some decision-making problems, such as linguistic intuitionistic fuzzy power Bonferroni Mean operators [11], Hamacher aggregation operators [12], fuzzy power Heronian aggregation operators [13], fuzzy generalized aggregation operator [11,[14][15][16][17][18], (fuzzy Einstein) hybrid weighted aggregation operators [19,20], fuzzy prioritized hybrid weighted aggregation operator [21], and fuzzy Hamacher ordered weighted geometric operator [22]; (3) other methods for decisionmaking with IVIF information are also explored, such as evidential reasoning methodology [23], particle swarm optimization techniques [4], transform technique [24], nonlinear programming methods [25], and VIKOR methods in IVIFS [26], and others methods [27][28][29][30][31][32] are also developed for decision-making problems. Distance measure has great effects on obtaining the desirable choice in some decision problems.…”

Existence and boundary behavior of weak solutions for Schrödingerean TOPSIS equations

“…We call it a cylinder (see [3]). On that basis, the theory and applications of the Schrödingerean TOPSIS equation have been developed rapidly (see [2,[4][5][6][7][8][9][10][11] and the references therein).…”

“…Moreover, Liu (see [8]) has studied the Markov chains when coefficients are integral-Lipschitz, Zhang and Wu (see [9]) considered the modified Laplace equations with some good boundaries, Wang et al…”