Article

Xiao, Z.: Data analysis approaches of soft sets under incomplete information. Knowledge-Based Syst. 21(8), 941-945

College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
Knowledge-Based Systems (Impact Factor: 2.95). 12/2008; 21(8):941-945. DOI: 10.1016/j.knosys.2008.04.004
Source: DBLP

ABSTRACT

In view of the particularity of the value domains of mapping functions in soft sets, this paper presents data analysis approaches of soft sets under incomplete information. For standard soft sets, the decision value of an object with incomplete information is calculated by weighted-average of all possible choice values of the object, and the weight of each possible choice value is decided by the distribution of other objects. For fuzzy soft sets, incomplete data will be predicted based on the method of average-probability. Results of comparison show that comparing to other approaches for dealing with incomplete data, these approaches presented in this paper are preferable for reflecting actual states of incomplete data in soft sets. At last, an example is provided to illuminate the practicability and validity of the data analysis approach of soft sets under incomplete information.

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    • "Evaluating the need and importance of the soft sets in applied field, the names of Maji [26], Ali [6] [8] [9] and, Sezgin and Atagun [30], are note worthy among the researchers who accelerated the preliminaries of the very work. On this, the logic defined in soft set started to be used in programming the various complex problems in the fields of decision making [10] [11] [13] [14] [18] [25] [29], approximation and data analysis [33] [40], description logic [19], etc., into formal languages. "
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    ABSTRACT: To discuss the problems involving uncertainties using soft sets and semirings is very common now a days. Keeping in view this point in this paper we discuss soft intersectional sets in semirings using k-ideals of the algebraic structure. We introduce the concept of (X,Y)-SI-k-subsemirings, (X,Y)-SI-k-bi-ideals and (X,Y)-SI-k-quasi-ideals of semirings. We discuss (X,Y)-soft-union-intersection sum and (X,Y)-soft-union-intersection product and investigate some related results. Finally, we characterize k-semisimple semirings, k-regular semirings and k-intra-regular semirings by using their (X,Y)-SI-k-ideals.
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    • "In 1999, Molodtsov [18], [19], [20] introduced a soft set theory as a new tool for investigation of uncertainties where we can find a large range of applications of soft sets in many different fields. There has been a rapid growth of interest in soft set theory, its applications and its connection with another mathematical branches [1], [2], [4], [5], [7], [8], [12], [13], [14], [15], [16], [23]. Moreover, there are many papers devoted to soft topological spaces [3], [6], [9] ,[10], [11], [17], [21], [22]. "
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    ABSTRACT: The paper deals with a soft topological space which is defined over an initial universe set U with a fixed set of parameters E. The main goal is to point out that any soft topological space is homeomorphic to a topological space (E × U, τ) where τ is an arbitrary topology on the product E × U , consequently many soft topological notions and results can be derived from general topology. Furthermore, in many papers some notions are introduced by different ways and it would be good to give a unified approach for a transfer of topological notions to a soft set theory and to create a bridge between general topology and soft set theory.
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    • "They showed that soft sets are a class of special information systems. In recent years, many interesting applications of soft set theory have been expanded by embedding the ideas of fuzzy sets [2] [3] [5] [18] [19] [20] [21] [23] [24] [31]. To develop soft set theory, the operations of the soft sets are redefined and a uni-int decision making method was constructed by using these new operations [6]. "
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    ABSTRACT: Shabir and Naz in [27] introduced the notion of soft topological spaces. They defined soft topology on the collection t of soft sets over X. Consequently, they defined soft separation axioms, soft regular spaces and soft normal spaces and established their several properties. Min in [30] investigate some properties of these soft separation axioms. Kandil et al. [12] introduce the notion of soft semi separation axioms. In particular they study the properties of the soft semi regular spaces and soft semi normal spaces. In the present paper, we introduce the notions of soft regular (normal) spaces based on the notions of semi open soft sets and soft ideals. Also, we discuss some properties of these notions and introduce an alternative descriptions of the notions of soft regular spaces via soft ideals [7], which is more general.
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