Fuzzy approach to analyzing processes in the software market
When evaluating software products, a number of difficulties usually arise, the main of which is the inability to define a clear segmentation of the software market into independent markets, both due to the large degree of influence of sectors and due to the variety of functions and integrated solutions. In addition, due to easy copyability and wide variation in output, traditional costly pricing methods are very limited. It is most advisable to use price-based pricing methods in the buyer's market.
The purpose of the study is to propose an approach to modeling pricing processes and evaluating a product on the software market based on user preferences as a ratio of product properties to consumers' expectations, taking into account weakly formalized factors, such as the quality of a software product, using a fuzzy logic apparatus.
Obviously, this can be achieved by formalizing and quantifying the quality indicators of a software product and the user's expectations as fuzzy objects.
The object of the research is the market of software products in its variety of functions, products and mechanisms. However, the emphasis is on the market for custom software for a wide range of consumers.
The subject of consideration were such issues as: the applicability of fuzzy calculations, sets and fuzzy logic in the evaluation of the quality of IP; qualimetry, fuzzy qualifiers of quality, methods and criteria for assessing the quality of IP.
The first stage of modeling is the construction of an integrated system of indicators of software systems. Let U be a universal set of property indices, representing a discrete set or an n-dimensional vector; The variable u taking values ​​on this set is interpreted as a “quality indicator”. Fuzzy subset A of U, corresponding to a specific software product is determined by the characteristic function
Where 
- the value of the i-th metric of the vector U. A comparative study of a number of similar products gives rise to an array 
where j - conditional number of a specific product. The decisive characteristic of such a set can be the completeness with which it describes the whole variety of software markets. The criteria system of PS properties has weight characteristics indicating the degree of importance of this property according to a specific set of goals.
Market segmentation is represented as a process of assigning to each parameter from the set U a weighting factor M (U) = V. Each separate software market (software category) will then have a certain set of weights. Methods for obtaining quantitative estimates of these weights, interpreted as segment data can vary from expert to statistical. Since each of these methods has its drawbacks, it makes sense to combine them with each other and using fuzzy logic to take into account the uncertainty of the segments. We introduce a linguistic variable (X, T (X), U, G, M), where X can be interpreted as “software category”, U = [1, n], where n is the number of indicators of properties, T (X) is defined as a set all segments or categories of the software market,
where 
- the weight of the i-th index of the property set for the segment X. The operation of weighing the tree in such a model is reduced to multiplying the sets A and X. Then the expression 
interpreted as product presentation 
in the context of the j-th category of software. This operation allows to take into account the vagueness of the segmentation of the software market and the multi-functionality, diversity of modern RFP in terms of 
. The net power assessment of the product quality will serve as a power function: 
.
We proceed from the assumption that each potential consumer of software has some unmet need, which, in fact, defines him as a consumer. This need is complex and can be expressed using a vector or semantic differential through properties that are relevant to a specific category of the software market. You can formalize user expectations as a fuzzy subset B, which is defined similarly to subset A. The expression quantitative components of vector B can serve as an estimate.
- identification of needs through the 'perfect' product.
- the condition of full satisfaction of needs;
- preference product k product i;
Due to the peculiarities of the process of developing and distributing software products, as well as market trends, it is impossible to set a clear segmentation of the software market into independent markets, both due to the large degree of influence of sectors and due to the variety of functions and integrated solutions.
This uncertainty of the type of fuzziness makes it possible to say with confidence that when modeling the software market it will find its use of a fuzzy logic apparatus provided that the main parameters are formalized, primarily those that together give a comprehensive concept of software quality.
According to the results of the analysis performed, it can be concluded that the existing methods are either narrowly specialized or do not take into account a number of significant parameters (demand factors, projected revenue or information about competitors).
Literature
Piryazev M.S. Features of the pricing methodology for software products // “Russian Entrepreneurship” No. 12 2004.
S.A. Ayvazyan, V.S. Stepanov. Tools for statistical data analysis // PC World, No. 8, 1997, p. 32-41.
Ryzhov AP Elements of the theory of fuzzy sets and its applications. M., 2003
GOST R ISO / IEC 9126-93. Evaluation of the software product. Quality characteristics and guidelines for their use.
Lipaev V.V. Software Quality Assessment. // "Network Journal" â„–3.2002
Azgaldov G.G. On the issue of evaluation of computer programs and databases // Intellectual property: management and evaluation. Tez. report International Scientific and Practical Conference May 22-23, 2008 - Pavlodar, 2008. - P.69 - 85.
The purpose of the study is to propose an approach to modeling pricing processes and evaluating a product on the software market based on user preferences as a ratio of product properties to consumers' expectations, taking into account weakly formalized factors, such as the quality of a software product, using a fuzzy logic apparatus.
Obviously, this can be achieved by formalizing and quantifying the quality indicators of a software product and the user's expectations as fuzzy objects.
The object of the research is the market of software products in its variety of functions, products and mechanisms. However, the emphasis is on the market for custom software for a wide range of consumers.
The subject of consideration were such issues as: the applicability of fuzzy calculations, sets and fuzzy logic in the evaluation of the quality of IP; qualimetry, fuzzy qualifiers of quality, methods and criteria for assessing the quality of IP.
The first stage of modeling is the construction of an integrated system of indicators of software systems. Let U be a universal set of property indices, representing a discrete set or an n-dimensional vector; The variable u taking values ​​on this set is interpreted as a “quality indicator”. Fuzzy subset A of U, corresponding to a specific software product is determined by the characteristic function
Where - the value of the i-th metric of the vector U. A comparative study of a number of similar products gives rise to an array where j - conditional number of a specific product. The decisive characteristic of such a set can be the completeness with which it describes the whole variety of software markets. The criteria system of PS properties has weight characteristics indicating the degree of importance of this property according to a specific set of goals.Market segmentation is represented as a process of assigning to each parameter from the set U a weighting factor M (U) = V. Each separate software market (software category) will then have a certain set of weights. Methods for obtaining quantitative estimates of these weights, interpreted as segment data can vary from expert to statistical. Since each of these methods has its drawbacks, it makes sense to combine them with each other and using fuzzy logic to take into account the uncertainty of the segments. We introduce a linguistic variable (X, T (X), U, G, M), where X can be interpreted as “software category”, U = [1, n], where n is the number of indicators of properties, T (X) is defined as a set all segments or categories of the software market,
where - the weight of the i-th index of the property set for the segment X. The operation of weighing the tree in such a model is reduced to multiplying the sets A and X. Then the expression interpreted as product presentation in the context of the j-th category of software. This operation allows to take into account the vagueness of the segmentation of the software market and the multi-functionality, diversity of modern RFP in terms of . The net power assessment of the product quality will serve as a power function: .We proceed from the assumption that each potential consumer of software has some unmet need, which, in fact, defines him as a consumer. This need is complex and can be expressed using a vector or semantic differential through properties that are relevant to a specific category of the software market. You can formalize user expectations as a fuzzy subset B, which is defined similarly to subset A. The expression quantitative components of vector B can serve as an estimate.
- identification of needs through the 'perfect' product. - the condition of full satisfaction of needs; - preference product k product i;Due to the peculiarities of the process of developing and distributing software products, as well as market trends, it is impossible to set a clear segmentation of the software market into independent markets, both due to the large degree of influence of sectors and due to the variety of functions and integrated solutions.
This uncertainty of the type of fuzziness makes it possible to say with confidence that when modeling the software market it will find its use of a fuzzy logic apparatus provided that the main parameters are formalized, primarily those that together give a comprehensive concept of software quality.
According to the results of the analysis performed, it can be concluded that the existing methods are either narrowly specialized or do not take into account a number of significant parameters (demand factors, projected revenue or information about competitors).
Literature
Piryazev M.S. Features of the pricing methodology for software products // “Russian Entrepreneurship” No. 12 2004.
S.A. Ayvazyan, V.S. Stepanov. Tools for statistical data analysis // PC World, No. 8, 1997, p. 32-41.
Ryzhov AP Elements of the theory of fuzzy sets and its applications. M., 2003
GOST R ISO / IEC 9126-93. Evaluation of the software product. Quality characteristics and guidelines for their use.
Lipaev V.V. Software Quality Assessment. // "Network Journal" â„–3.2002
Azgaldov G.G. On the issue of evaluation of computer programs and databases // Intellectual property: management and evaluation. Tez. report International Scientific and Practical Conference May 22-23, 2008 - Pavlodar, 2008. - P.69 - 85.
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