“Measuring the commercial potential of new product ideas using fuzzy set theory”

The stage of selecting creative ideas that have the prospect of further commercial use and can be used to create new products, services, or startups is one of the most complex and important stages of the innovation process. It is essential to take into account expert opinions and evaluations, often vague and ambiguous. The study aims to develop a methodological approach to measure the commercial potential of new product ideas based on fuzzy set theory and fuzzy logic. To this end, three calculation schemes are developed: the first two are based on fuzzy multicriteria analysis using Fuzzy SAW and Fuzzy TOPSIS methods, respectively; the third is based on building a logical-lin-guistic model with fuzzy expert knowledge bases and applying fuzzy inference using the Mamdani algorithm. Fuzzy numbers in triangular form with triangular membership functions are used to present linguistic estimates of experts and fuzzy data; the CoA (Center of Area) method is used to dephase the obtained values. For practical application of the proposed algorithm, the model is used as an Excel framework con- taining a general set of input expert information in the form of linguistic estimates and fuzzy data, a set of calculations using three schemes, and a set of defuzzification of the obtained results. The framework allows for simulation modeling depending on the modification of the list of defined evaluation criteria and their partial criteria, and adjustments to expert opinions. The developed methodological approach is suggested for the initial stages of the innovation process to facilitate the assessment of creative ideas and improve their implementation.


INTRODUCTION
Innovation is an extremely important component in achieving a competitive advantage. According to Drucker and Maciariello (2008), the organization must adhere to three principles in its work: continuous product improvement, knowledge use for its development, and systematic innovation. The need for continuous effort in innovations is also emphasized by Porter and Millar (1985), who claimed that a company achieves competitive advantage through innovation by using both new technologies and new working methods. Once a company achieves competitive advantage through innovation, the retention of this advantage is possible only through continuous improvement because competitors will overtake the company once it ceases to innovate.
One of the most responsible and critical stages in innovation is the cognitive stage, associated with the evaluation and selection of creative ideas that may become the basis for new products, goods, and services in the future. Difficulties that arise at this stage stem from its phenomenological characteristics. They include the informal nature of evalu-

THEORETICAL BASIS
Innovation is the driving force of the economy and the key to the successful development of a business. Barsh et al. (2007) revealed that more than 70% of executives believe that innovation is a top strategic priority for their companies. A creative idea is the starting point of any innovation. There are several types of ideas: • an old idea -an idea of the 'past experience' (i.e. an idea that has already been used to create new products, new knowledge, new ideas, etc.); • a new idea, which is a development or improvement of an old idea; • an integrated new idea based on: a) several old ideas or approaches from one field of knowledge or field of application; b) a few old ideas or approaches from different fields of knowledge or areas of application.
In particular, Sutton (2013) while researching innovative activities of companies such as Play-Doh and Apple iPod, normally focused only on the integrated new ideas. It was argued that "innovation and creativity is first and foremost the ability to create something new based on old things and ideas, not the ability to create something new out of nothing".
• and, a 'completely new (revolutionary), unique idea' that had no analogs, not even close ones in the past; and such an idea has the potential to become a driver that may uncover a whole layer of previously unresolved issues and suggest new technologies and methods for solving them. Stevanović et al. (2016) discovered that most companies prioritize developing new product ideas, but only in response to consumer requests, as this study was constrained by limited investment resources and issues related to human resources. Accordingly, the role of proper selection that saves effort and resources is growing as, according to recent studies, the failure is to be expected in at least 95% of the total number of new products in the US market and 90% of those in European markets. Thus, measuring the potential of creative ideas is a critical stage in innovation management as mistakes and errors at this stage may later lead to serious losses and strategic failures.
In this study, the ideas of Siegel et al. (1995), Jain et al. (2003), as well as the commercial potential of creative ideas are considered as an integral indicator of the promise.
An important aspect of measuring the commercial potential of a new product idea comprises a range of questions related to finding optimal evaluation procedures and their methodological support, including the development of evaluation criteria. For example, Messerle et al. (2012) developed a model for selecting and evaluating ideas that consists of eight stages: idea generation, idea capture, initial evaluation and selection, initial idea detailing, rough evaluation and selection, second idea detailing, detailed valuation, and selection, and implementation of the product idea. Westerski et al. (2011) suggested five stages of idea selection management: idea generation, idea im-provement, idea selection, idea implementation, and idea deployment. These stages are meant to ensure the integrity of cyclicity of the computer-assisted idea management process. At the initial stages of the idea generation process, this methodology provides for interaction between the stakeholders and the telecommunications infrastructure. Miloud et al. (2012) conducted an empirical study of idea evaluation in terms of ideas attractiveness for investment and developed several groups of evaluation factors: industry attractiveness, the organizational and entrepreneurial experience of the founder and the team, which are important for obtaining positive evaluation results. A systemic approach was used to identify factors and their selection for new product idea evaluation. Riel et al. (2013) developed a benchmark model for the ideation process based on fuzzy interface and expert evaluations. Based on that six critical success factors for ideas were singled out: ideation starts at the top management, ideation needs a clearly defined focus, ideation happens in networks, ideation demands creativity, ideation needs entrepreneurship, and ideation requires organizational orientation. It was suggested to select ideas using managerial decision-making frameworks, or "a set of tools for ideation". Trolle et al. (2020) studied the problems of using fuzzy evaluations at the stage of new product idea implementation and singled out the following evaluation factors: project, team, organization, and external environment impact factors. Gors et al. (2012) suggested sorting out innovative product ideas by combining individual and team-based methods of managerial decision-making and setting several requirements, such as speed, acceptance, computer support, minimizing cognitive load, and minimizing selection errors. The algorithm is based on FEoI decision-making method, single-criteria, and multi-criteria methods. Travessini et al. (2015) used the АНР support method for making decisions in the process of selecting new product ideas. Forde and Fox (2016) described the idea evaluation process based on the development of requirements for such a process and used the notion of utility to measure the probability of an idea being executed.
The most effective tools for evaluating new ideas are approaches that take into account the subjective and qualitative (linguistic) nature of expert evaluations, their vagueness, and fuzziness. In particular, Soukhoroukova et al. (2010) suggested using fuzzy methods to study the effectiveness of idea markets in three stages: selection, filtering, and evaluation. It is crucial to create a platform where it will be possible not only to place ideas but also to share experiences and express opinions. Huynh and Nakamori (2011) suggested the use of linguistic estimates to select ideas but identified a key drawback of the approach, namely the loss of information through approximation. At the same time, a model was proposed in which calculations are performed on the basis of the semantics of linguistic terms and the two-tune transformation, which is necessary for the unification of linguistic information. Malyar et al. (2016) developed a two-level model for evaluating startups (creative ideas) in conditions of uncertainty using fuzzy mathematics, which involves the use of experts' linguistic estimates of various membership functions, which may lead to certain ambiguity of the outcomes.
The variety of ideas and the complexity of the process of measuring their commercial potential call for the search of flexible and adaptive tools for comparative analysis and the development of effective algorithms and procedures to better take into account subjective, informal, fuzzy inputs, experts' opinions, and assumptions. Accordingly, this study uses fuzzy economic and mathematical modeling techniques to assess the commercial potential of creative ideas for a new product. The foundations of the fuzzy logic theory, based on the mathematical theory of fuzzy sets, were proposed by Zadeh (1965) and Zadeh (1978). Kosko (1993) made a very important step in the development of 'fuzzy' methodology, where any mathematical system can be approximated by a system built on fuzzy logic. This gave a powerful impetus to continue studies in this area, and practical advances in fuzzy logic were theoretically substantiated. The fuzzy set theory approach has three main features: 1) instead of or in addition to numerical variables, fuzzy quantities and so-called 'linguistic' variables are used; 2) simple relations between variables are described by vague statements; 3) complex relations are described by fuzzy algorithms.
This study uses the fuzzy set theory tools, including fuzzy multicriteria analysis methods (Fuzzy SAW-method (FSAW), Fuzzy TOPSIS-method (FTOPSIS) (Chen, 2000), and systems of fuzzy inference (Mamdani, 1977) to solve the set tasks of assessing the level of the commercial potential of creative ideas of a new product. The process of fuzzy inference is an algorithm for obtaining fuzzy inferences based on fuzzy conditions using the concepts of fuzzy logic. This process combines all the basic concepts of fuzzy set theory: belonging functions, logical, linguistic operations, methods of fuzzy implication, and fuzzy composition.
The need to consider a large number of factors influencing the level of risk and uncertainty of the outcome, the multidimensionality of the process, the presence of complex indirect links between evaluation criteria, vagueness and ambiguity of expert assessments call for the search for unconventional tools for formalizing cognitive processes to analyze parameters and content of creative ideas.

AIMS
This study aims to develop a methodological approach to measuring the commercial potential of creative product ideas and their selection using multi-criteria analysis, fuzzy set theory, and fuzzy logic.

RESULTS
To measure the level of the commercial potential of new ideas for a new product, a methodological Source: Authors' elaboration. approach was developed. Figure 1 demonstrates the main stages of this approach.
The stages of the suggested methodological approach aimed at measuring the commercial potential of creative ideas are as follows.

Stage 1.
Setting up a working group of experts with relevant professional competencies and responsibilities. According to Soukhoroukova et al. (2010), "the inclusion of multiple, various evaluators appears beneficial for the idea selection process. Within a company, these evaluators may represent different organizational functions, such as marketing, research and development (R&D), and production". It is advised to include external experts who have qualifications and relevant competencies in the area.

Stage 2.
It involves drawing up a general list of creative ideas for a new product based on various ideation procedures (using synectic methods, brainstorming, morphological analysis, etc.). According to Rometty (2006), the most important sources of ideas are employees (41%), business partners and customers (over 35%), consultants and competitors (over 20% each), internal sales and service departments, and internal R&D (slightly less than 20%). Based on the results of a broad and detailed analysis of existing literature and empirical studies, the generalization method was used and the following list of criteria for evaluating ideas was suggested, which is quite general and may be adjusted depending on the industry and specific tasks: • creative: originality; unexpectedness; attractiveness; provocativeness; relevance; effectiveness; novelty; elegance; genesis; pleasingness; • technical and technological: reliability; compatibility/trialability; relative advantage; acceptability; development of enabling technologies; aesthetics; R&D intensity; functionality; safety; environmental friendliness; prototype; gracefulness; cost of development and production cost; after-sales service; • financial: ROI; stock index; sales volume; perceived risk; stakeholder support; the magnitude of the percentage growth of the market for this idea; the amount of expected income in 5 years; cost amortization period; • market: market size; advertising intensity; competition; usability; exiting market stimulation/satisfaction; market acceptance; intellectual property; potential market share; • organizational: team; incentives/disincentives/regulations; managerial capacity; ability to evaluate risk; management leadership abilities; social significance; affordability.

Stage 4.
To determine the importance of the criteria and their evaluation sub-criteria, the following steps must be performed.
Step 1. Linguistic evaluation by each of the K experts of the importance of evaluation criteria, and their sub-criteria. To do this, one can use a seven-level term set (Table 1). For example, analytical representation of the membership function for a term with a triangular representation (;;) u abc =  will look as follows: Thus, linguistic evaluation leads to the following important valuations: 1) evaluation criteria: Step 2. Transformation of experts' linguistic evaluations, obtained in step 1, into fuzzy triangular numbers:

( )
;; , Step 4. Defuzzification of the obtained wights according to the formula (2). As a result, the following 'crisp' values are obtained: 1) for evaluation criteria: 2) for their sub-criteria: Step 5. The normalization of weights: 1) for evaluation criteria: 1) for their sub-criteria: To measure the commercial potential of creative ideas according to the sub-criteria defined at the previous stage, each of these sub-criteria is considered as a linguistic variable, for which one can use the same term set as for evaluating criteria, followed by transformation of obtained values into triangular fuzzy numbers. If, according to some subcriteria, the measurement is based on fuzzy data in Suppose that as a result of this procedure, the fuzzy normalized triangular estimate of the i-creative    3) using the defuzzification procedure by formu- can calculate the crisp-value of the commercial potential of each analyzed idea according to certain criteria and its (commercial potential) integral value, respectively. Scheme 2 involves using the fuzzy TOPSIS method (Chen, 2000). Next, one determines the weights of the sub-criteria, taking into account the importance of the main criteria, and labels them as follows ( Table 2).
It is also necessary to re-label the aggregate fuzzy estimates obtained according to formulae (18) -(22) by subcriteria (Table 3).
Thus, fuzzy matrix obtained is   As a result of applying these relations, crisp estimates are obtained, which can be used to rank creative ideas by calculating the relative distance from each of the given alternatives to FPIS and FNIS according to the formula: Scheme 3 is based on the Mamdani fuzzy inference system algorithm (Mamdani, 1977) and can be used to account for fuzzy expert estimates without using fuzzy additive weighing procedures as in the FSAW method and finding the distance to ideal positive and negative alternatives as in the FTOPSIS method. In this case, fuzzy inference is performed on FKBs (Fuzzy Knowledge Bases), which are developed on the basis of professional expert judgment. This scheme can be implemented according to the following algorithm ( Figure 3).
Step 1. Here, if there are accurate expert evaluations and interval data of creative ideas according to certain sub-criteria, then they should be transformed into linguistic estimates. Then fuzzification of all linguistic estimates is carried out, i.e. their translation into triangular fuzzy numbers with the corresponding triangular membership functions.
Step 2. Development of fuzzy knowledge bases based on the production rules of fuzzy logic, which allow summarizing and integrating information about each creative idea according to certain sub-criteria of each evaluation criterion. The weights of the sub-criteria need to be considered when constructing fuzzy rule databases, as this affects the combinations of terms of the input variables in the conjunction. Table 4 shows a section of the fuzzy knowledge base FKB (C) to determine the level of the commercial potential of ideas according to the sub-criteria of criterion C -'creativity'.
A fuzzy knowledge base, for example, to determine the overall level of the commercial potential of a creative idea by the criterion of 'creativity' in mathematical form is written using the production rules of fuzzy logic as follows: 11 with .     Table 4. Section of the FKB (C) -fuzzy knowledge base to determine the level of ideas' commercial potential according to the sub-criteria of criterion C -'creativity' Source: Authors' elaboration.

Linguistic values of original variables Weights
Original variable value d  (25) where ∧ -the sign of fuzzy conjunction, ∨ -the sign of fuzzy disjunction, ( ) 12 , , ..., Step 3. Aggregation of fuzzy estimates according to the criteria obtained in the previous step into an integrated measurement of the commercial potential is performed for each analyzed idea. To do this, as in the previous step, one needs to build a fuzzy knowledge base FKB(C).
Step 4. It involves defuzzification according to formula (2) of the obtained fuzzy values of the commercial potential of the analyzed ideas according to individual criteria and their integrated level.

Stage 7.
To check the consistency of the results obtained by different schemes, one can calculate, for example, the concordance coefficient. After that, a generalized ranking of creative ideas according to their commercial potential must be built.

Stage 8.
The obtained ranking data for creative ideas can be used to develop appropriate managerial decisions, in particular, to stratify ideas or identify the most promising one(s) for further implementation.
To facilitate the practical application of the developed methodological approach, the model is developed as an Excel framework, containing the following main blocks:

DISCUSSION
Although the developed methodology has several advantages over existing approaches, the complexity of the research problem may require further discussion of the following aspects: 1) building the original set of creative ideas from a general list for their evaluation according to certain criteria; 2) organizational and methodological aspects of determining criteria and singling out sub-criteria for evaluating creative ideas; 3) solving the problem of compensatory effects when using the FSAW method; 4) using Excel software for the development of the framework where the possibilities and potential of logical-linguistic modeling and "soft" computations of fuzzy set theory are somewhat limited.
As follows from the above-mentioned issues, as well as any other aspects for discussion, further research on the topic of this study may aim at improving the following components of the suggested methodological approach: • selecting expert group members based on the level of their competence and experience in the subject area; • establishing and applying simple heuristic procedures of reduction for the initial set of ideas to reject unpromising or irrelevant ones; for example, using the method of criterion constraints to set minimum requirements for the criteria; • improving the procedure for forming evaluation criteria using fuzzy tools; for example, Fuzzy DEMATEL-method; • developing and including procedures for harmonization of experts' opinions at all stages of the evaluation process; • developing a framework for evaluation and selecting creative ideas for a new product using specialized applications that encompass the possibilities of fuzzy modeling, for example, Fuzzy Logic Toolbox of the Matlab computer system, Fuzzy Control Design Toolbox, fuzz-yTECH, etc.
A further task of an applied nature can be the approbation of this methodological approach by adapting the evaluation criteria and their sub-criteria following the needs of the analysis, taking into account various aspects of the situation.

CONCLUSION
This study aims to develop an improved solution for one of the most critical and complex tasks in innovation management, namely the problem of measuring the commercial potential of creative ideas. This problem should be considered through the prism of subjective perception of each member of the expert group as they see their promise for new goods, products, or services. The suggested methodology for the analysis and evaluation of creative ideas uses the tools of fuzzy set theory. In particular, fuzzy multicriteria methods FSAW, FTOPSIS, and logical-linguistic modeling based on Mamdani fuzzy inference algorithm are used. They provide for a more comprehensive and flexible approach to the process due to fuller consideration of various factors, as well as subjective, informal, fuzzy input data, opinions, and judgments of experts. The Excel-based framework developed for the suggested methodology helps to reduce the complexity of analytical calculations by suggested schemes, allows assessing the reliability of the results, and can be used as the basis for creating appropriate management decision support systems. The suggested methodology will be most effective when all the three calculation schemes are used together; yet, in case of limited resources, lack of time, etc., only one of the calculation schemes or a combination thereof may be applied.