Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment

Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision-Making

“…Two illustrative numerical examples were solved and comparisons with existing strategies were provided to demonstrate the feasibility, applicability, and efficiency of the proposed strategies. We hope that the proposed cross entropy measures can be effective in dealing with group decision-making, data analysis, medical diagnosis, selection of a suitable company to build power plants [94], teacher selection [95], quality brick selection [96], weaver selection [97,98], etc. In future, the cross entropy measures can be extended to other neutrosophic hybrid environments, such as bipolar neutrosophic soft expert sets, bipolar neutrosophic refined sets, etc.…”

Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-Algebras

“…Using the notions of subalgebras and ideals in BCK/BCI-algebras, Jun et al [8] introduced the notions of energetic subsets, right vanished subsets, right stable subsets, and (anti-)permeable values in BCK/BCI-algebras, as well as investigated relations between these sets. As a more general platform that extends the concepts of classic and fuzzy sets, intuitionistic fuzzy sets, and interval-valued (intuitionistic) fuzzy sets, the notion of NS theory has been developed by Smarandache (see [1,2]) and has been applied to various parts: pattern recognition, medical diagnosis, decision-making problems, and so on (see [3][4][5][6]). In this article, we have introduced the notions of neutrosophic permeable S-values, neutrosophic permeable I-values, (∈, ∈)-neutrosophic ideals, neutrosophic anti-permeable S-values, and neutrosophic anti-permeable I-values, which are motivated by the idea of subalgebras (s-values) and ideals (I-values), and have investigated their properties.…”

“…The notion of neutrosophic set (NS) theory developed by Smarandache (see [1,2]) is a more general platform that extends the concepts of classic and fuzzy sets, intuitionistic fuzzy sets, and interval-valued (intuitionistic) fuzzy sets and that is applied to various parts: pattern recognition, medical diagnosis, decision-making problems, and so on (see [3][4][5][6]). Smarandache [2] mentioned that a cloud is a NS because its borders are ambiguous and because each element (water drop) belongs with a neutrosophic probability to the set (e.g., there are types of separated water drops around a compact mass of water drops, such that we do not know how to consider them: in or out of the cloud).…”

An Iterative Algorithm for the Nonlinear MC2 Model with Variational Inequality Method

“…In addition, the mixed energy system was also obtained by using HOMER (Hybrid Optimization Model for Multiple Energy Resources) software (National Renewable Energy Laboratory (NREL), CO, Boulder, USA) and the TOPSIS multi criteria algorithm. In [3], a nonlinear programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS) was developed to solve decision-making problems. Suzdaltsev et al [4] developed the genetic, ant colony and bee algorithms for solving the printed circuit board (PCB) design multi criteria optimization problems.…”