Abstract
A single-valued neutrosophic multi-set is characterized by a sequence of truth membership degrees, a sequence of indeterminacy membership degrees and a sequence of falsity membership degrees. Nature of a single-valued neutrosophic multi-set allows us to consider multiple information in the truth, indeterminacy and falsity memberships which is pretty useful in multi-criteria group decision making. In this paper, we consider sequences of intuitionistic fuzzy values instead of numbers to define the concept of intuitionistic fuzzy-valued neutrosophic multi-set. In this manner, such a set gives more powerful information. We also present some set theoretic operations and a partial order for intuitionistic fuzzy-valued neutrosophic sets and provide some algebraic operations between intuitionistic fuzzy-valued neutrosophic values. Then, we develop two types of weighted aggregation operators with the help of intuitionistic fuzzy t-norms and t-conorms. By considering some well-known additive generators of ordinary t-norms, we give the Algebraic weighted arithmetic and geometric aggregation operators and the Einstein weighted arithmetic and geometric aggregation operators that are the particular cases of the weighted aggregation operators defined via general t-norms and t-conorms. We also define a simplified neutrosophic valued similarity measure and we use a score function for simplified neutrosophic values to rank similarities of intuitionistic fuzzy-valued neutrosophic multi-values. Finally, we give an algorithm to solve classification problems using intuitionistic fuzzy-valued neutrosophic multi-values and proposed aggregation operators and we apply the theoretical part of the paper to a real classification problem.
Highlights
Fuzzy sets (FSs) [1] are characterized by membership functions and a fuzzy set is a successful tool to handle uncertainties arising from partial belongingness of an element to a set
We study some particular cases of W A − intuitionistic fuzzy-valued neutrosophic multi-value (IFVNMV) and W G − IFVNMV by choosing particular additive generators
We introduce the concept of intuitionistic fuzzyvalued neutrosophic multi-set (IFVNMS) by considering the sequences of intuitionistic fuzzy values instead of numbers
Summary
Fuzzy sets (FSs) [1] are characterized by membership functions and a fuzzy set is a successful tool to handle uncertainties arising from partial belongingness of an element to a set. Theory of IFS has been extensively studied by many authors and it has been applied to vary fields such as decision making, image fusion and segmentation systems, classification and clustering (see e.g., [4,5,6,7,8,9]). Krawczak and Szkatula [10] have studied on IFSs’s perturbation and they have applied this concept to classification problems. He et al [11] have proposed some distance measures between IFSs via dissimilarity function and have given a pattern recognition application. Lohani et al [13] have carried out experimental study of intuitionistic fuzzy c-mean algorithm over machine learning dataset
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