Similarity Measures between Intuitionistic Fuzzy Credibility Sets and Their Multicriteria Decision-Making Method for the Performance Evaluation of Industrial Robots

To enhance the credibility level/measure of an intuitionistic fuzzy set (IFS), this study proposes the notion of an intuitionistic fuzzy credibility set (IFCS) to express the hybrid information of a pair of a membership degree and a credibility degree and a pair of a nonmembership degree and a credibility degree. Next, we propose generalized distance and similarity measures between IFCSs and then further generalize the weighted generalized distance measure of IFCSs to the trigonometric function-based similarity measures of IFCSs, including the cosine, sine, tangent, and cotangent similarity measures based on the weighted generalized distance measure of IFCSs. Then, a multicriteria decision making (MCDM) method using the proposed similarity measures is developed in the environment of IFCSs. An illustrative example about the performance evaluation of industrial robots and comparative analysis are presented to indicate the applicability and efficiency of the developed method in the setting of IFCSs.

Assessment of national innovation capabilities of OECD countries using trapezoidal interval type-2 fuzzy ELECTRE III method

PurposeFor a nation to become a superpower, it's scientific and technological advancement is essential. Each country is exploring how to improve themselves in terms of science and technology. The authors analyzed the innovation capabilities of 35 OECD countries that have not recently joined Lithuania.Design/methodology/approachIn recent years, a lot of research work has been done on trapezoidal interval type-2 fuzzy sets (TIT-2 FS), and many research works have been published. The trapezoidal interval type-2 fuzzy set helps effectively to represent the uncertainty comparatively than the type-1 fuzzy set. Taking advantage of this effectiveness, the authors extend the best multi-criteria decision making method (MCDM) for trapezoidal interval type-2 fuzzy sets. Here, ELimination and Choice Expressing REality III (ELECTRE III) method in the trapezoidal interval type-2 fuzzy set environment is proposed.FindingsThis analysis helps to the OECD countries to develop their level of innovation in the criteria. The authors are making this evaluation for the year 2018 based on the 31 criteria. Application of the proposed method expressed by evaluation of the national innovation capability problem. Based on the obtained results, the top five countries are United States, Switzerland, Canada, Germany and Japan.Originality/valueThe authors collected required data from different available data sources like OECD, IMD, USPTO, ITU and surveyed data reported by KISTEP. After collecting all the data from different sources, the authors calculated the standard values as KISTEP. After converting the standard values into trapezoidal interval type-2 fuzzy values, the authors construct a decision matrix based on these values. Then, the authors determined the possibility mean values and preference. Then, they calculated the concordance and discordance credibility degree values. Finally, they ranked OECD countries by the net credibility degree. The results are computed by using the MATLAB software.

A cosine similarity measure for multi-criteria group decision making under neutrosophic soft environment

In actual life, uncertain and inconsistent information exists widely. How to deal with the information so that it can be better applied is a problem that has to be solved. Neutrosophic soft sets can process uncertain and inconsistent information. Also, Dempster-Shafer evidence theory has the advantage of dealing with uncertain information, and it can synthesize uncertain information and deal with subjective judgments effectively. Therefore, this paper creatively combines the Dempster-Shafer evidence theory with the neutrosophic soft sets, and proposes a cosine similarity measure for multi-criteria group decision making. Different from the previous studies, the proposed similarity measure is utilized to measure the similarity between two objects in the structure of neutrosophic soft set, rather than two neutrosophic soft sets. We also propose the objective degree and credibility degree which reflect the decision makers’ subjective preference based on the similarity measure. Then parameter weights are calculated by the objective degree. Additionally, based on credibility degree and parameter weights, we propose the modified score function, modified accuracy function, and modified certainty function, which can be employed to obtain partial order relation and make decisions. Later, we construct an aggregation algorithm for multi-criteria group decision making based on Dempster’s rule of combination and apply the algorithm to a case of medical diagnosis. Finally, by testing and comparing the algorithm, the results demonstrate that the proposed algorithm can solve the multi-criteria group decision making problems effectively.