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«VOLUM E 1 1, N UM B E R 1 I S SN 2 1 6 8 - 0 6 1 2 F L ASH DR I V E I S SN 1 9 4 1 - 9 5 8 9 ON L I N E T h e In s t it ut e f o r Bu s i n e s s an ...»

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() = t(12.5,15,20,22.5) () = t(20,25,30,30) Further fuzzy linguistic variables that are incorporated into SMEP efficiency analysis are Productivity (2 ) Cost (3 ), and Documentation(4 ). Using Table 3, the acceptable universes of discourse of Productivity, Cost, and Documentation are respectively, 2 =[.8 3.2], 3 =[0 50.0], and 4 =[0 100]. The baseline figures for Productivity, Cost, and Documentation are.905/kloc, k$25.0/kloc, and 30 pages/kloc, respectively. As H_, F_ and L_ for each variable , i=1,4 as presented in Figure 4. In order to allow management to play for the linguistic fuzzy subsets of the software Quality variable, we associate three linguistic fuzzy subsets an interactive role in evaluating the overall performance of the SMEP with respect to various base variables (not included in the fuzzy process), the linguistic variable "Trend" is added at all levels of the hierarchic structure of the evaluation process. The trend variable x, is associated with three fuzzy subsets HT, FT, and

LT expressed as follows:

HT="the overall base performance of the SMEP is now higher" FT="the overall base performance of the SMEP is now fair" LT="the overall base performance of the SMEP is now lower" Figure 4: Rule Base Segment Identified with 1 = HE HP="high software productivity" FP="fair software productivity" LP="low software productivity" HC="high software cost" FC="fair software cost" LC="low software cost" HD="high software documentation" FD="fair software documentation" = , = , = , = , = → = LD="low software documentation" = , = , = , = , = → = = , = , = , = , = → = = , = , = , = , = → = ...

= , = , = , = , = → = = , = , = , = , = → =

–  –  –

The SMEP database is useful in assessing membership functions associated with 3x5x4+3=63 linguistic variables. Membership functions are stared in the fuzzy database. The fuzzy database constitutes a universal relation where 4 columns are reserved to the coefficients a, b, c, and d. This relation may have 3x6x4=72 tuples. Management selects the base variables pertinent to evaluating the SMEP and may use bar charts to examine the evolution of base variables over the last five years. By looking at the trend, management will be able to judge if the SMEP performance, with respect to this variable, is improving, stable, or worsening.

A three-point scale may be used to rate the situation: 3="improving", 2="stable", and l="worsening".

Following analyzing the trends of all selected base variables, the overall performance of base variables may be obtained by averaging all rates collected. The universe of discourse of the linguistic fuzzy variable,

Trend, is therefore [1 3]. Its membership function is computed as follows:

= t(2.25,2.75,3.0,3.0) = t(1.5,1.75,2.25,2.75) = t(1,1,1.25,1.75) Inference Mechanism fuzzification function transforms the input vector e=(e1, e2, e3, e4 ) into 4 membership matrices, M (e ), The inference mechanism consists of three functions: fuzzification, inference, and defuzzification. The k=1,4 with n1 +n2 + n3 rows and 5 columns, each. In the inference process, for every knowledge segment skj, k=1,4 and j=1,3 in the rule base bk, a truth factor vkji, i=1, nkj is first attributed to every rule rkji of the segment skj. The value of vkji is computed as Minp=1,5{m(rkji,p)(ek)}, the minimum of all membership grades of the input vector ek in the fuzzy sets xp, p=1,5, forming the rule rkji. In a second step, every segment skj, is associated with a truth factor wkj computed as wkj= Maxi=1,nkj{ vkji } the highest truth factor attributed to the rules making the segment skj. In a third step, every segment skj is represented by a fuzzy variable is, = ∑=1,3 ∗ . The fuzzification function transforms the input vector e1=(u1, u2, u3, u4, u5) into defined as wkj * ykj. The rule base bk is represented by zk, the aggregation of the these fuzzy variables; that a membership matrix, M1(e1), that has n11+n12+n13 rows and 5 columns. The inference process applies ISBR to produce a compatibility function for the SMEP Efficiency variable associated with information system applications, as an aggregation of all its linguistic values. The defuzzification function will produce a scaler representative of the aggregated variable, computed in this system as the fuzzy set's center of gravity. Every rule r11i, i=1, n11, is mapped to v11i, in [0 1]. The scalar v11i represents the truth value of the rule r11i, or Minp=1,5{m(r11i,p)(e1)}. Among all v11i i=1, n11, identified with one rule base segment s11, only w11=Maxi=1,n11{v11i}, the maximum truth factor of the rule base segment s11 is selected. In the same manner for the remaining ISRB segments, the local truth factors for SMEP Efficiency (type=IS) are given as


Efficiency is High: w11, based on segment s11 or ISBR1 Efficiency is Fair: w12, based on segment s12 or ISBR2 Efficiency is Low: w13, based on segment s13 or ISBR3 Because of the fuzzy modus ponens employed in fuzzy logic, the input vector only partially satisfies the antecedents of rules. Using the maximum truth factors wij, j=1,3, the fuzzy sets Y1j, j=1,3 associated with

y1, may be redefined so that:

MHQ’(y)=min(w11, mHQ(y)) MFQ’(y)=min(w11, mFQ(y)) MLQ’(y)=min(w11, mLQ(y))

–  –  –

The factors w1j, j=1,3 not only correspond to the largest partial match of the input vector with all rules for which y1=HQ, y1=FQ, and y1=LQ but also the truth of these respective conclusions. In fact, "y1=HQ’" means "y1=HQ with a truth of w11". An aggregate truth distribution that takes into account all rules of the rule base ISBR is then developed from the three new fuzzy subsets HQ’, FQ’, and LQ’. That is, z1=HQ’+FQ’+LQ’, for which mzl(v)=Max{mHQ’(v), mFQ’(v), mLQ’(v)}. In general, however, for every rule base bk, k=1,4, a truth factor wk,j represents a rule base segment skj, p=1,3. Truth factors for the current

fuzzification process are computed as follows:

–  –  –

SMEP efficiency is then represented by a new fuzzy set z computed as the product of SMEP efficiency fuzzy variables used in organizing various rule bases identified with various software applications. That is, z=∏k=1,4zk. The membership function of z is computed as mz=Mink=1,4zk. The defuzzification is performed by computing z's center of gravity as a scalar v* representing the fuzzy set z, v*=f01vmz(v)dv.


This article demonstrated how fuzzy logic offers a natural process for analyzing the imprecise declarations and managerial subjective judgment involved in the evaluation of a company's software engineering process. Human resources constitute an important factor in the success of the fuzzy logic system. For instance, the system required the involvement of a human expert for the construction of the rule bases and the fuzzy subsets and management for the fuzzification function. While the fuzzy logic system enforces the independence between the uncertainty management method and the rule base, since the rules and fuzzy sets are stored in two different subsystems, the success of inference process depends on both structures. The proposed fuzzy evaluation system remains partial without including definition and maintenance analyzes and a direct query system for management to keep track of changes in base variables incorporated in this system as trend analyses. However, this article demonstrates how fuzzy logic is effective in modeling managerial heuristic processes in the evaluation of SMEP efficiency.


Upon request


S. L. Boumediene, Corresponding author, has a PhD in Business Administration (Accounting) from the University of El Manar, Tunisia. Before Joining Montana State University Billings, Dr. Boumediene taught both financial and managerial accounting in both undergraduate and graduate levels at the top business schools in Tunisia. Dr. Boumediene has been publishing his research work in academic journals such as Journal of Modern Accounting, Accounting & Taxation and Auditing and the Journal of Management and Business Research among others. Dr. Boumediene published a book on statistical characteristics and quality of accounting information in 2013 GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 351 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 S. Boumediene Has a Master in Management Information System (MIS) from the University of Tunis, Tunisia. Before Joining Montana State University Billings as an Adjunct professor, Salma taught Administering and Programming Databases, Management Information Systems and Computer Programming at the top business schools in Tunisia. Salma has been presenting papers in the Western Decision Sciences Institute (WDSI). She formerly was Senior Project Manager for several project related to software engineering. She is Microsoft Certified Professional (MCP) in SQL Server.

GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 352 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1




Mirzoanvar Bahodirov, ROADMAX Group of Company

–  –  –

In today’s world, foreign investments remains as important financial resources for development of economics, in its place improving the investment climate – is a guarantee of investments flow. In order to create favorable conditions for foreign investors, as well as to protect their interests, a legal framework, which is constantly being improved and modified, has been established in Uzbekistan.


Among the most important laws of the Republic of Uzbekistan in the sphere of foreign investments protection, guarantees and rights of investors, the laws such as “On foreign investments”, “On guarantees and measures to protect the rights of investors” must be noted. This kind of laws are laid the foundation for the formation of favorable investment climate.

In addition, there are more that 50 bilateral agreements, as well as a number of multilateral international legal agreements, which are signed by Uzbekistan with different countries in the field of mutual encouragement and protection of the investments.

The practical result of improving the legal framework may be noted in the area of the growth of the GDP of Uzbekistan, which over the past five years has averaged 8 (eight) %, and which is higher than the average growth in CIS. The stable GDP growth within the country is one of the main indicators (factors) of attracting foreign investments and assets.

The analysis of the causes which contributes to the dynamic growth both of the GDP and tax revenues (to the budget) shows, that it depends on the state policies, which are held in the country, and which is aimed to attracting foreign assets to the various spheres of industrial production, primarily by providing the tax incentives.


Some British and US experts argue that investments are a highly profitable source of the taxes and ensure of the society maintenance, development of all its spheres, satisfaction of new, more complex and diverse needs of people (Atkinson & Stiglitz, 1995) The major investments within Uzbekistan are carried out by the foreign legal entities, through the creation of joint ventures or foreign companies, through the acquisition of shares in the Charter Capital of the existing company or through permanent institutions.

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