ICCMIT 2017 ROUGH STANDARD NEUTROSOPHIC SETS: An aplication on standard neutrosophic information systems Authors: Nguyen Xuan Thao Bui Cong Cuong Florentin Smarandache Poland, April 3-5, 2017 ROUGH STANDARD NEUTROSOPHIC SETS: An aplication on standard neutrosophic information systems Outlines I. Introduction

II. Basic notions of standard neutrosophic and rough set III. Rough standard neutrosophic set IV. The standard neutrosophic information systems (SNIF) V. The knowledge discovery on SNIF VI. The reduction and extension of SNIF VII. Conclucion I.Introduction Fuzzy set (L. Zadeh, 1965): a useful method study in the problems of imprecision and uncertainty. We denote ( is a fuzzy set A on universe set . Intuitionistic set (Atanassov, 1986): ( where

membership, is a non-membership of A and is a I. Introduction Neutrosophic set (NS) (F. Smarandache, 1999): where is a degree of truth (T), is a degree of indeterminacy (I) and is a degree of falsity (F) statisfy A tandard neutrosophic set (SNS) (Picture fuzzy set) (B.C. Cuong, 2013): in which 1. The family of all standard neutrosophic set in is denoted by Neutrosophic set and standard neutrosophic set have many application, see [7],[8],...

I. Introduction An information system (IS) is any organized system for the collection, organization, storage and communication of information. Rough set (Z. Pawlak, 1980s): a usefully mathematical tool for data mining, especially for information systems. A standard neutrosophic information system (SNIS) is an information system in which have using standard neutrosophic values, such as voting information systems,... Rough standard neutrosophic set (RSNS) is a usefully

mathematical tool for SNIS,... II. Basic notions of standard neutrosophic and rough set Definition 2. (Lattice ). Let . We define a relation on as follows: then iff (or or orand. We put ) II. Basic notions of standard neutrosophic and rough set Previous surveys of voters in the US presidential election of 2017. Many people believe that Mrs Clinton will win. But, when the election results

were announced, Mr Trumpt win. Those who carried out the survey has no statistical omission to those who have not been surveyed or comments about the survey. These people in the elections could actually participate very strong decision to actually vote results. It is where II. Basic notions of standard neutrosophic and rough set Standard neutrosophic set (SNS) in which 1. Level set of SNS: level of a SNS defined by II. Basic notions of standard neutrosophic and rough set

Let be a nonempty universe of discourse. A subset is referred to as a (crisp) binary relation on . Denote Rough set: Let be a crisp approximation space. For each crisp set , we define the upper and lower approximations of (w.r.t) denoted by and , respectively, are defined as follows III. Rough standard neutrosophic set RSNS: Let be a crisp approximation space. For , the upper and lower approximations of (w.r.t) denoted by and , respectively, are defined as follows: Where , , ,

and , , Some properties of RSNS are studied in full paper. IV. The standard neutrosophic information systems (SNIS) Information systems (IS) Let be a information system. Here is the (nonempty) set of objects, i.e., is the conditional attribute set, and is the relation set of and , i.e., where is the domain of the attribute ( is the decision attribute set; G is the relation set of and . The ) is called a classical information system. Relation (where , as follows, for all .

IV. The standard neutrosophic information systems (SNIS) SNIS: Let be the information system. If where is a standard neutrosophic subset of and G is the relation set of and , then is called a standard neutrosophic information system. Example: A SNIS (see Tabble 1) condition attribute set is and the decision attribute set is , where is a standarf neutrosophic subset of . IV. The standard neutrosophic information systems (SNIS) Table 1: A standard neutrosophic information system

U 3 3 1 1 2 2 3 3 1 1 2

2 (0.2,0.5,0.3) (0.2,0.5,0.3) (0.3,0.5,0.1) (0.3,0.5,0.1) (0.15,0.2,0.6) (0.15,0.2,0.6) (0.3,0.3,0.3) (0.3,0.3,0.3) (0.4,0.5,0.05) (0.4,0.5,0.05) (0.35,0.4,0.1)

(0.35,0.4,0.1) 3 3 3 3 2 2 2 2 1 1 2 2 3

3 1 1 2 2 3 3 2 2 3 3 3 3 2

2 2 2 3 3 1 1 1 1 4 4 4 4 2

2 4 4 1 1 2 2 (0.6,0.4,0) (0.6,0.4,0) (0.15,0.7,0.1) (0.15,0.7,0.1) (0.05,0.7,0.2) (0.05,0.7,0.2) (0.1,0.5,0.3)

(0.1,0.5,0.3) (0.25,0.4,0.3) (0.25,0.4,0.3) (0.1,0.2,0.6) (0.1,0.2,0.6) (0.45,0.45,0.1) (0.45,0.45,0.1) (0.05,0.9,0.05) (0.05,0.9,0.05) (0.3,0.6,0.05) (0.3,0.6,0.05) (0.1,0.8,0.05) (0.1,0.8,0.05) (0.2,0.3,0.4)

(0.2,0.3,0.4) (0.2,0.4,0.3) (0.2,0.4,0.3) (1,0,0) (1,0,0) (0.25,0.4,0.3) (0.25,0.4,0.3) (0.25,0.3,0.4) (0.25,0.3,0.4) (0.4,0.3,0.2) (0.4,0.3,0.2) (0.1,0.4,0.45) (0.1,0.4,0.45) (0.2,0.3,0.4)

(0.2,0.3,0.4) (0.05,0.5,0.4) (0.05,0.5,0.4) (1,0,0) (1,0,0) (0.3,0.4,0.3) (0.3,0.4,0.3) (0.4,0.6,0) (0.4,0.6,0) (0.2,0.3,0.5) (0.2,0.3,0.5) (0.05,0.2,0.7) (0.05,0.2,0.7) V. The knowledge discovery in SNIS

Let be the NSIS and we denote is the lower rough SN approximation of on approximation space . Theorem 5: Let be the SNIS and . If for any , then and where . V. The knowledge discovery in SNIS Let be a SNIS, The universe is divided by as following: . Then the approximation of the SN decision denoted as, for all , Example 3. The SNIS in Table 1. The equivalent classes The approximation of the standard neutrosophic decision is in Table 2.

V. The knowledge discovery in SNIS (0.15,0.6,0,05) (0.1,0.5,0.05) Table 2: (0.05,0.9,0.05) (0.05,0.4,0.1) (0.15, 0.7, 0.1) (0.1,0.8,0.05) (0.2,0.3,0.4)

(0.05,0.7,0.2) (0.2,0.4,0.3) (0.05,0.6,0) (0.1,0.5,0.3) (0.2,0.4,0.3) (1,0,0) The approximation of the Standard neutrosophic decision VI. The knowledge reduction and extension

of SNIS Definition 7. Let be the classical IS and . (i) is called the SN reduction of , if is the minimum set which satisfies the following relations: (ii) is called the SN lower approximation reduction of , if is the minimum set which satisfies the following relations: : (iii) is called the SN upper approximation reduction of , if is the minimum set which satisfies the following relations: Where are SN lower and SN upper approximation sets of SN set based on , respectively VI. The knowledge reduction and extension of

SNIS Definition 8. Let be the SNIS is called the discernibility matrix of (where is the maximum of obtained at , i.e., VI. The knowledge reduction and extension of SNIS Definition 9. Let be the standard neutrosophic information system, for any , if the following relations holds, for any : then is called the consistent set of . Theorem 6. Let be the standard neutrosophic information system. If there exists a subset such that , then is the consistent set of .

VI. The knowledge reduction and extension of SNIS Definition 11. Let be the classical IS and . (i) is called the SN extension of , if satisfies the following relations: (ii) is called the SN lower approximation extension of , if satisfies the following relations: (iii) is called the SN upper approximation extension of , if satisfies the following relations: for any Theorem 8. Let be the classical IS, for any hyper set , such that , if is the SN reduction of the classical IS , then is the SN extension of , but not conversely necessary.

VI. The knowledge reduction and extension of SNIS Example 4. In the approximation of the SN decision in Table 1, Table 2. Let , then we obtained the family of all equivalent classes of based on the equivalent relation as follows We can get the approximation value given in Table 3. It is samed to the approximation value given in Table 2. It mean is a reduction of ) The discernibility matrix of the standard neutrosophic information system will be presented in Table 4. VI. The knowledge reduction and extension of SNIS (0.15,0.6,0,05)

(0.05,0.9,0.05) (0.15,0.6,0,05) (0.15, 0.7, 0.1) (0.1,0.8,0.05) (0.05,0.9,0.05) (0.05,0.7,0.2) (0.2,0.4,0.3) (0.15, 0.7, 0.1) (0.1,0.8,0.05) (0.1,0.5,0.3) (0.2,0.4,0.3) (0.05,0.7,0.2) (0.2,0.4,0.3) (0.1,0.5,0.3) Table 3: (0.2,0.4,0.3)

(0.1,0.5,0.05) (0.1,0.5,0.05) (0.05,0.4,0.1) (0.2,0.3,0.4) (0.05,0.4,0.1) (0.05,0.6,0) (0.2,0.3,0.4) (1,0,0) (0.05,0.6,0) (1,0,0) The approximation of the standard neutrosophic decision VI. The knowledge reduction and extension of SNIS

Table 4: The discernibility matrix of the standard neutrosophic information system Conclusion We introduce the concept of standard neutrosophic information system We study the knowledge discovery of standard neutrosophic information system based on rough standard neutrosophic sets knowledge reduction and extension of the standard neutrosophic information system THANK YOU FOR

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