The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

Abstract: In this paper, similar to the extension from intuitionistic fuzzy numbers (IFNs) to neutrosophic numbers (NNs), we propose the normal neutrosophic numbers (NNNs) based on the normal intuitionistic fuzzy numbers (NIFNs) to handle the incompleteness, indeterminacy and inconsistency of the evaluation information. In addition, because Heronian mean (HM) operators can consider capture the ...

Assessment specialists (experts) are sometimes expected to provide two types of information: knowledge rating domains and the performance objects (called confidence levels). Unfortunately, results previous information aggregation studies cannot be properly used combine categories data covered above. Additionally, a significant range symmetric/asymmetric events structures frequently included in ...

The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

Bipolar fuzzy set theory has been successfully applied in some areas, but there are situations real life which can’t be represented by bipolar sets. However, all the existing approaches unsuitable to describe positive and negative membership degree an element uncertain linguistic label have interval value, can reflect decision maker’s confidence level when they making evaluation. In order overc...

We present the generalized hybrid averaging (GHA) operator. It is a new aggregation operator that generalizes the hybrid averaging (HA) operator by using the generalized mean. Thus, we are able to generalize a wide range of mean operators such as the HA, the hybrid geometric averaging (HGA), the hybrid quadratic averaging (HQA), the generalized ordered weighted averaging (GOWA) operator and the...

Abstract The T-spherical uncertain linguistic (TSUL) sets (TSULSs) integrated by fuzzy and variables are introduced in this article. This new concept is not only a generalized form but also can integrate decision-makers’ quantitative evaluation ideas qualitative information. TSULSs serve as reliable comprehensive tool for describing complex decision paper focuses on an extended MARCOS (Measurem...