Fault-tolerant enhanced bijective soft set with applications

Abstract

a b s t r a c tAs an extension of the soft set, the bijective soft set can be used to mine data from soft set environments, and has been studied and applied in some fields. However, only a small proportion of fault data will cause bijective soft sets losing major recognition ability for mining data. Therefore, this study aims to improve the bijective soft set-based data mining method on tolerate-fault-data ability. First some notions and operations of the bijective soft set at a ␤-misclassification degree is defined. Moreover, algorithms for finding an optimal ␤, reductions, cores, decision rules and misclassified data are proposed. This paper uses a real problem in gaining shoreline resources evaluation rules to validate the model. The results show that the proposed model has the fault-tolerant ability, and it improves the tolerate-ability of bijective soft set-based data mining method. Moreover, the proposed method can help decision makers to discover fault data for further analysis.

A Novel Approach to Decision Making Based on Interval-Valued Fuzzy Soft Set

“…There are rich variety of applications of soft set theory in many fields as diverse as game theory [4], operations research, decision making [5][6][7][8], data mining [9,10] Screening alternatives [11], resource discovery [12] and data filling [13] for incomplete datasets [14], and so on. In addition to the soft set theory, recently, scholars have developed and studied plenty of combination models of the soft set theory with other mathematical models such as fuzzy soft set [15][16][17], intuitionistic fuzzy soft set [18,19], belief interval-valued soft set [20], interval-valued intuitionistic fuzzy soft sets [21], hesitant N-soft sets [22], confidence soft sets [23], fault-tolerant enhanced bijective soft set [24], trapezoidal interval type-2 fuzzy soft sets [25], soft rough set [26], Z-soft fuzzy rough set [27], Z-soft rough fuzzy set [28], and so on.…”

Data Analysis Approaches of Interval-Valued Fuzzy Soft Sets Under Incomplete Information

“…After that fuzzy soft set theory has been successfully introduced into the application of decision making [21]- [26], [28]. Soft sets are further extended to intuitionistic fuzzy soft sets [29]- [33], Intuitionistic fuzzy parameterized soft set [34], intervalvalued intuitionistic fuzzy soft set theory [35]- [37], lattice ordered soft sets [38], Bijective soft set [39], [40], vague soft sets [41], [42], trapezoidal interval type-2 fuzzy soft sets [43], [44], soft rough set [45], Z-soft fuzzy rough set [46], [47], rough soft sets [48].…”

Soft Set Based Parameter Value Reduction for Decision Making Application

“…The associate editor coordinating the review of this manuscript and approving it for publication was Wajahat Ali Khan. fuzzy soft set [8], [35], [36], interval-valued intuitionistic fuzzy soft set theory [9], bijective soft set [11], [12], trapezoidal interval type-2 fuzzy soft sets [13], [14], soft rough set [15], hesitant N-soft set [10], Z-soft fuzzy rough set [16], [17], confidence soft sets [19], Belief interval-valued soft set [20] and rough soft sets [18] so on. Except for the development of theoretical research, soft set also fully express in the real life applications such as the smoothness of functions, game theory, operations research, Riemann integration, Perron integration, probability theory, and measurement theory [1], data analysis, screening alternative problem [21] and data mining [22], [23] so on.…”