Abstract: To make the fuzzy mathematics get wider application in books and information fields, this research investigates the status quo of Yanshan University library and applies the fuzzy order-optimum theory to select the core periodicals of mathematics and physics in “The main contents for Chinese Core Periodicals”.
INTRODUCTION
With the increasing number of scientific and technological periodicals, it seems essentially important to identify core periodicals in a variety of concerned fields. The identification of core periodicals is a dynamic and random process. To avoid limitations and incompleteness, this paper applies the theory of fuzziness to get a fuzzy order of technological periodicals. The result is rather practical, thus it should be possible to identify core periodicals in a library as well as improve technicians' academic performance.
FUZZY ORDER-OPTIMUM THEORY AND CORE PERIODICALS
Fuzzy mathematics is an effective tool to do research and deal with fuzzy phenomena. Fuzzy order-optimum Theory is to apply similarity priority formula to measure the fuzziness distance between actual samples and desired samples. In this way, those of greater similarity will be selected (Zhongxiong, 1999). This is a step-by-step process of calculation and comparison.
Suppose there are m core periodicals in the whole system and n relatively selected participants to appraise the system. Consequently, the system index feature value matrix is (Shouyu, 2002):
i = 1, 2, 3,…m. j = 1, 2, 3,…,n
Of them, Xij is the feature value of object i and index j.
As for the most desired samples, their n index value is the highest. What is more, compared with the degree of similarity of each element in the desired samples in set m, we can get a relative fuzziness matrix. The sample selecting is based on their degree of similarity, that is, the similarity between any sample from set m and desired samples.
Suppose Xi and Xj are two samples selected at random. In order to compare the degree of similarity between them and the desired sample XR, we can calculate the Haming Distance di and dj of Xi, Xj and XR:
Then we can get priority selection proportion:
| (1) |
After getting fuzzy relative matrix (1) we select λ value according to the number, λε[0,1]. Those λ--cut matrixes whose diagonal lines are 1 enjoy most resemblance with desired samples. We mark their consequence number 1. Then we delete its whole row and the line whose row number is the same. The next step is to lower the λ value and to get their respective consequence number. Their number can be marker with number 2,3…. The smaller the number is, the greater the degree of resemblance is. Another way to examine this is to add all the numbers. The smaller the added number is, the greater the degree of resemblance is. If we grant all indexes weights, the result will be more accurate. If a is weight, a1+a2+…an = 1 = W. Through the formula X·W = Y, we can get Y, that is, the comment set.
APPLIED EXAMPLES
This research studies the core periodicals of mathematics and physics in “The main contents for Chinese Core Periodicals” (Shoujing, 2002). Thirteen kinds of physics periodicals are retrieved, their number being marker A1~A13.
| Table 1: | Finding of mathematics core periodicals |
| Table 2: | Finding of physics core periodicals |
| Notes: 1) CCP refers the consequence number in “The main contents for Chinese Core Periodicals”; 2) A* refers the journal published by the work unit for which the author works | |
| Table 3: | Finding of physics core periodicals and order |
The consequence is like Table 1 Mathematics periodicals are altogether 10 issues, marked from A1' to A10'. Its consequence is like Table 2. Suppose the most desired sample is Journal of Yanshan University, marked with A*. Four variables are selected to do the research:
| • | The index of circulation rate-the lending statistics of technological periodical library within a limited period; |
| • | The index of referred thesis-a statistics of references in “Journal of Yanshan University” and postgraduate thesis within the recent 4 years; |
| • | The index of issue quality-professors from mathematics department and physics department are invited to evaluate two core periodicals; |
| • | The index of library staff-purchasers and issue librarians are invited to evaluate the aforementioned two periodicals. The full mark is 10. |
| Table 4: | Finding of mathematics core periodicals and order |
The statistical finding is shown in Table 1 and 2:
According to Formula of Fuzzy Similarity Priority (1), taking C1 in Table 1 as an example, we can obtain the to the similar priority select proportion between A1\A2 and A*:
| (2) |
| Table 5: | Priority results sort for the mathematical and physical journal |
As is shown in (2): A2 is more likely to be resemble with A* than A1. Likewise, we can obtain all rij and rji (i, j = 1, 2, 3,…,13). When i = j, rij = rji = 0
In a similar way, the fuzzy relative matrix of Ci is R<1> (i = 1, 2, 3, 4).
We can conclude that the fuzzy relative matrix of C1 is R<1> (R<1> is the fuzzy relative matrix of referred time of physics periodicals); the fuzzy relative matrix of C2 (the circulation time) is R<2>; the fuzzy relative matrix of C3 (issue quality) is R<3>; the fuzzy relative matrix of C4 (staff comment) is R<4>. Here, we only demonstrate the matrix of physics periodicals R<1>:
Select λ value from the bigger to smaller in various matrixes R. In matrix R<1>, when λ = 0.49, A10 and A4 are the first two to reach the point λ 1. Therefore we define the consequence numbers of A10 and A4 are 1. Meantime, we delete row 10 and row 4, line 10 and line 4. Then we devalue λ one by one and decode the matrix. Likewise, we can also decode matrixes R<2>R<3>R<4> and obtain Table 3. The consequence number in Table 4 stands for the degree of similarity between individual index of core periodicals and desired samples and the added consequence number stands for the degree of similarity between the whole four indexes and the desired samples. The smaller the added consequence number is, the greater degree of similarity it will be.
The same calculative method can be used to calculate the fuzzy relative matrixes
of mathematics periodicals
CONCLUSIONS
The situation of periodicals varies from library to library. The applications of the Fuzzy Order-Optimum theory helps a lot to easily and accurately identify the core periodicals in a specific library. Thus this provides evidence to purchase new periodicals for the library, as well as reference for readers. It is also conducive to the quantitative management of periodicals.