On Interval-Valued Hesitant Fuzzy Soft Sets

Abstract

By combining the interval-valued hesitant fuzzy set and soft set models, the purpose of this paper is to introduce the concept of interval-valued hesitant fuzzy soft sets. Further, some operations on the interval-valued hesitant fuzzy soft sets are investigated, such as complement, “AND,” “OR,” ring sum, and ring product operations. Then, by means of reduct interval-valued fuzzy soft sets and level hesitant fuzzy soft sets, we present an adjustable approach to interval-valued hesitant fuzzy soft sets based on decision making and some numerical examples are provided to illustrate the developed approach. Finally, the weighted interval-valued hesitant fuzzy soft set is also introduced and its application in decision making problem is shown.

Comment on “Corrigendum to ‘On Interval‐Valued Hesitant Fuzzy Soft Sets’” and “Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis”

“…Definition 6 (cf. [9,10]). Each element Γ ∈ ([0, 1] ) (i.e., a family {Γ( )} ∈ of fuzzy sets on ) is called a fuzzy soft set on , and each element Φ ∈ ((2 (I) ) ) is called an interval-valued hesitant fuzzy soft set on ; we will use ( ) , to denote the -th largest element (it exists by Theorem 3) in (Φ( )( ), ⩽) ( ∈ , ∈ , ≤ |Φ( )( )|, and |Φ( )( )| denotes the cardinality of Φ( )( )).…”

Multi-Attribute Group Decision-Making Methods Based on Pythagorean Fuzzy N-Soft Sets

“…As a result, Maji et al made the study of soft sets by initiating the concept of fuzzy soft sets [21] and intuitionistic fuzzy soft set [22], and proceeded to solve various decision making problems by using these theories. Following the research ideas, many new fusion models have been produced [6], [8], [17], [23], [27], [29], [32], [33], [35], [41], [43]- [47]. For example, Majumdar and Samantha [23] proposed a generalized fuzzy soft set on the basis of fuzzy soft set and applied it to decision-making problems.…”

“…Recently, Peng et al [27] has extended fuzzy soft sets into Pythagorean fuzzy environment to handle decision making problems more effectively, and developed the concept of Pythagorean fuzzy soft sets. Later, the researchers successively came up with many fusion models for soft sets including generalized intuitionistic fuzzy soft sets [6], hesitant fuzzy soft sets [35], interval-value hesitant fuzzy soft sets [43], dual hesitation fuzzy soft sets [44], interval-value intuition hesitation fuzzy soft sets [32], soft rough sets [46], soft fuzzy rough sets [45] and soft rough fuzzy sets [47], etc.…”

Hesitant Bipolar-Valued Fuzzy Soft Sets and Their Application in Decision Making

“…e integration of the two theories has become one of the popular research directions. In recent years, some scholars presented fuzzy soft sets and various kinds of extended models [3][4][5][6][7][8][9][10][11], such as fuzzy soft sets, intuitionistic fuzzy soft sets, interval-valued fuzzy soft sets, interval-valued intuitionistic fuzzy soft sets, hesitant fuzzy soft sets, interval-valued hesitant fuzzy soft sets, and generalized hesitant fuzzy soft sets. e corresponding basic procedures and properties are also discussed.…”