Hesitant fuzzy preference envelopment analysis and alternative improvement

TODIM method based on the CRITIC method for multi-attribute group decision making with dual probabilistic linguistic information

The main research of this paper is decision making under the dual probabilistic linguistic term sets (DPLTSs). This paper introduces a method, which combined TODIM method and CRITIC method. In this research, the CRITIC method is used to determine the weight, and the distance formula of TODIM method has been modified in order to adapt to DPLTS situation. Then, the TODIM method is used for multi-attribute group decision making (MAGDM) problem. Finally, a case study concerning investment project selection is given to demonstrate the merits of the developed methods. This combined method can be used for the automatic areal feature matching, medical quality assessment, and ranking of matching processes. There are very few papers about using TODIM method under DPLTS situation at present, so this is a new perspective on MAGDM. The DPLTS-TODIM-CRITIC method was compared with correlation coefficient method and closeness coefficient method, and it is easy to find the advantage of this new method over the other two existing methods.

The Fourth Axiom of Similarity Measures

In this research, the fourth axiom to improve the well-defined examination of similarity measures is studied, where the measures have a symmetric structure. We first provide a theoretic enhancement of three correlation coefficient similarity measures that were proposed by a source paper. Second, we use the same numerical example proposed by the source paper for pattern recognition problems to illustrate that the weighted correlation coefficient similarity measure is dependent on the set of weights. Finally, we demonstrate that the correlation coefficient similarity measure in the intuitionistic fuzzy set environment can address the issue of practical fault diagnosis when solving the turbine engine problems using similarity measures with symmetric characteristics.

Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

In this article, we propose another form of ten similarity measures by considering the function of membership degree, non-membership degree, and indeterminacy membership degree between the q-ROFSs on the basis of the traditional cosine similarity measures and cotangent similarity measures. Then, we utilize our presented ten similarity measures and ten weighted similarity measures between q-ROFSs to deal with multiple attribute decision-making (MADM) problems including pattern recognition and scheme selection. Finally, two numerical examples are provided to illustrate the scientific and effective of the similarity measures for pattern recognition and scheme selection.