Cotangent Similarity Measure of Consistent Neutrosophic Sets and Application to Multiple Attribute Decision-Making Problems in Neutrosophic Multi-Valued Setting

A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and consistency degree of true,false,and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS.However,there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature.This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting.The cosine similarity measures showthe cosine of the angle between two vectors projected into amultidimensional space,rather than their distance.The cotangent similaritymeasures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent.Then,a decisionmaking approach is presented in viewof the established cotangent similarity measures in the case of NMVSs.Finally,the developed decision-making approach is applied to selection problems of potential cars.The proposed approach has obtained two different results,which have the same sort sequence as the compared literature.The decision results prove its validity and effectiveness.Meantime,it also provides a new manner for neutrosophic multi-valued decision-making issues.

MCGDM model using uncertain linguistic consistency sets of single andinterval linguistic term multivalued sets

This paper presents hybrid linguistic expressions and operations for the hybridlinguistic multiple criteria group decision making (MCGDM) issue withidentical and/or different single and interval linguistic term values. First, wepropose a single and interval linguistic term multivalued set/element (SILTMS/SILTME) and develop a consistency measure of SILTMEs based on Shannonentropy to measure the consistency degree of single and interval linguistic termvalues in SILTME. Second, we converse SILTMS/SILTME into an uncertainlinguistic consistency set/element (ULCS/ULCE) in terms of the mean andconsistency measure of SILTMEs to reasonably perform operations betweendifferent information forms/sequence lengths in SILTMSs. Third, we definesome operations of ULCEs and the expected values and sorting rules ofULCEs. Fourth, we present the ULCE weighted mean and geometric operatorsand their characteristics. Finally, we develop a MCGDM model using theweighted mean operation of the two operators and apply it in the mine safetyassessment.