Soft Set Based Parameter Value Reduction for Decision Making Application

Abstract

The soft set theory is a completely new mathematical tool for modeling vagueness and uncertainty, which can be applied to decision making. However, in the process of making decision, there are some unnecessary and superfluous information which should be reduced. Normal parameter reduction is a good way to reduce superfluous information, which keeps the entire decision ability. However, the algorithm has a low redundant degree, which involves a great amount of computation. It is not certain that normal parameter reduction has the solution, that is, it has a low success rate of finding reduction. Parameterization value reduction is another reduction method, which improves redundant degree, amount of computation, and success rate of finding reduction. However, this method only considers the best choice, but it does not concern the suboptimal choice, the sequence of choice, and added parameter, that is, it loses some part of decision ability. In order to settle these problems, in this paper, we introduce the parameter value reduction which keeps the entire decision ability while having a very high redundant degree and success rate of finding reduction and low amount of computation. Maximal parameter value reduction is defined as the special cases of parameter value reduction and the related heuristic algorithms are presented, which reaches an extreme degree to reduce the redundant information. The comparison result among maximal parameter value reduction, parameterization value reduction, and normal parameter reduction on 30 datasets shows that the proposed algorithm outperforms parameterization value reduction and normal parameter reduction.

On Soft ωδ-Open Sets and Some Decomposition Theorems

“…Soft set theory and related fields have advanced greatly as a result very soon. As may be observed in [6][7][8][9][10][11][12], this has led to several applications of soft sets in real-world fields.…”

Soft Faint Continuity and Soft Faint Theta Omega Continuity between Soft Topological Spaces

“…The relationship between parameter sets and soft sets provides a standardized framework for modeling uncertain data. This has led to rapid advancements in soft set theory and related topics, as well as practical applications (see [6][7][8][9][10][11][12]).…”

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

“…Molodtsov initiated the concept of soft set theory [4] which is an effective mathematical tool in handling uncertainty. 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.…”