Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation

Abstract

From the perspective of the degrees of classification error, we proposed graded rough intuitionistic fuzzy sets as the extension of classic rough intuitionistic fuzzy sets. Firstly, combining dominance relation of graded rough sets with dominance relation in intuitionistic fuzzy ordered information systems, we designed type-I dominance relation and type-II dominance relation. Type-I dominance relation reduces the errors caused by single theory and improves the precision of ordering. Type-II dominance relation decreases the limitation of ordering by single theory. After that, we proposed graded rough intuitionistic fuzzy sets based on type-I dominance relation and type-II dominance relation. Furthermore, from the viewpoint of multi-granulation, we further established multi-granulation graded rough intuitionistic fuzzy sets models based on type-I dominance relation and type-II dominance relation. Meanwhile, some properties of these models were discussed. Finally, the validity of these models was verified by an algorithm and some relative examples.

Ranking Method of Intuitionistic Fuzzy Numbers and Multiple Attribute Decision Making Based on the Probabilistic Dominance Relationship

“…Therefore, many scholars have conducted researches on IFS, such as distance measure [24][25][26] and similarity measure [27]. In addition, the model generalization of IFS is also studied, such as interval type IFS [28], Atanassov-type intuitionistic fuzzy [29], intuitionistic fuzzy soft sets [30,31], intuitionistic fuzzy rough sets [32,33], intuitionistic fuzzy set and three-way decision [34][35][36][37], intuitionistic fuzzy set and dominance relationship [38,39], and other series of achievements. At present, IFS have achieved good application results in fault diagnosis [40], multi-attribute decision-making [41], incomplete data decision-making [42], deep learning [43], imbalance learning [44], and other fields.…”

Multiple-Attribute Decision Making Based on the Probabilistic Dominance Relationship with Fuzzy Algebras

“…These methods aim to tackle the challenges posed by the uncertainty of information expression and applicability in practical problems, as the uncertainty of fuzzy sets is described by the degree of membership (DM) and degree of non-membership (DN). Scholarly efforts have been dedicated to various aspects of IFS research, including distance measure [5][6][7][8][9], similarity measure [10], model generalization, such as interval-type IFS and Atanassov-type intuitionistic fuzzy [11], and other achievements, such as intuitionistic fuzzy soft sets [12], intuitionistic fuzzy rough sets [13,14], intuitionistic fuzzy set and threeway decision [15][16][17][18][19], and intuitionistic fuzzy set and dominance relationship [20,21]. These advancements in IFS research have found practical applications in fault diagnosis [22], multi-attribute decision-making [23], deep learning [24], imbalance learning [25], and other fields.…”

Object-First Incremental Algorithms for Updating Approximations in Multi-Granulation Fuzzy Probabilistic Rough Sets Over Two Universes

“…RS theory is a mathematical tool for depicting imperfection and imprecision. To apply RS theory to various complex application fields, such as pattern recognition [2], [3], machine learning [4], [5], image processing [6], and data mining [7], [8], some scholars did in-depth research on RS theory and proposed many extension RS models, such as fuzzy rough set model [9], fuzzy probabilistic rough set model [10]. In 1995, Yao et al [11] proposed a twodomain RS model based on precise binary relations, which extended the RS theory to the information system over two universes.…”

“…In this regard, Qian et al [19], [20] proposed multi-granulation rough set (MRS) model by using multiple equivalence relations to define the approximation of a group of objects. MRS model extended applications of RS theory in the multi-granulation structure, such as decision making [21], [22] and feature selection [23], [24]. Therefore, so as to extend the model of the fuzzy probabilistic rough set over two universes from single granulation into multiple granulations, Mandal et al [25] proposed a model of multi-granulation bipolar-valued fuzzy probabilistic rough set over two universes.…”