Fuzzy Logic in Business, Management and Accounting

The aim of the paper is to show the implementation of fuzzy logic in business, administration and accounting, through the research published in Scopus. The results of the document focus on the following sections: 1) Fuzzy set theory, in business, administration and accounting. 2) Analysis of fuzzy logic bibliometrics in business, administration and accounting. 3) Identification and characterization of the documents or seminal documents most cited in applications of fuzzy logic in business, administration and accounting. The method used in this contribution is documentary research using the Scopus database and the VOSviewer science bibliometric analysis and mapping tool. In the future, this computational practice will focus on new diffuse models and the combination of these with other artificial intelligence techniques such as neural networks, genetic algorism, forage bacteria, among others.


Introduction
The fuzzy logic appears for the first time in the mid-60s of the twentieth century and since then, the theoretical contributions and the development of its applications have continued to be considered today one of the most used artificial intelligence techniques (Díaz Córdova, Coba Molina, & Navarrete, 2017;Kokles, Filanová, & Korček, 2016;Ouahli & Cherkaoui, 2019). To a certain extent, the diffuse logic is based on the observation of human behavior, where despite the knowledge of man is faced with many imperfect situations and has certain uncertainties and inaccuracies, his decisions are correct (Díaz Córdova et al., 2017;Dostál & Lin, 2018;Dostál, Rukovanský, & Králik, 2018;Kokles et al., 2016;Ouahli & Cherkaoui, 2019;Pislaru, Alexa, & Avasilcăi, 2018;Plessis, Martin, Roman, & Slabbert, 2018); that is to say: the solution of complex problems solves them with the help of approximate data which indicates that the precision is often unnecessary. In this way, any activity does not require an exact and rigorous mathematical model, as it has not been for driving a vehicle or deciding when a bank grants a loan to a client, although it is known that these are complex issues that require above all skills and knowledge. In addition to being acquired through self-effort, they are obtained through experience (Díaz Córdova et al., 2017;Dostál & Lin, 2018;Grekousis, Manetos, & Photis, 2013;Kokles et al., 2016;Morano, Locurcio, Tajani, & Guarini, 2015;Osiro, Lima-Junior, & Carpinetti, 2014;Ouahli & Cherkaoui, 2019;Pislaru et al., 2018;Plessis et al., 2018). Fuzzy logic deals with the usefulness of imprecision and the relative importance of precision (Bolloju, 1996;Chakraborty, Ravi, Shivangi, Vanshika, & Vishal, 2019;Halabi & Shaout, 2019;Levy, Mallach, & Duchessi, 1991).
From this premise, it can be inferred that the diffuse logic to provide a solution needs a human know-how. Diffuse logic can consider variables of a qualitative nature that are hardly recognized by other techniques and provides an effective approach by systematizing the empirical terrain and transcribing and giving dynamism to experts' knowledge Sharma & Saxena, 2017).
This universal aspect of fuzzy logic allows to apply it in business decision making, negotiation management and commerce processes, based mainly on the experience gained in the management of processes where classical systems have limited behavior (Almutairi, Salonitis, & Al-Ashaab, 2019;Chao & Liaw, 2019).
Fuzzy logic is currently used in a large number of processes, such as financial analysis software, control of energy management systems, validation of electoral processes, medical instruments and in many other applications (Al Nahyan, Hawas, Aljassmi, & Maraqa, 2018;Djekic, Smigic, Glavan, Miocinovic, & Tomasevic, 2018;Sivamani, Kim, Park, & Cho, 2017). The advantage of the combination of artificial intelligence techniques such as fuzzy logic, neural networks, bacteria fodder and genetic algorithms is that they provide effective solutions in a large number of applications and with a low cost of time and resources (Knight & Fayek, 2002;Kunsch & Vander Straeten, 2015;Kushwaha & Suryakant, 2014;Mujahid & Duffuaa, 2007). Artificial intelligence tools such as Fuzzy Logic have been successfully used in energy and resource management (Bravo Hidalgo, 2015;Bravo Hidalgo & León González, 2018;Hidalgo & Guerra, 2016).
The fundamental advantages of fuzzy logic are: 1) It allows to formalize and simulate the report of an expert in the conduction and normalization of a process.
2) It provides a simple answer to the difficult modeling procedures. 3) It takes into consideration several variables and its weighted merger determines the magnitude of influence. 4) It continuously considers cases or exceptions of a different nature, integrating them into the solution. 5) They allow the imple-A. B. Hernández, D. B. Hidalgo Open Journal of Business and Management mentation of multicriteria strategies incorporating the knowledge of the experts.
The objective of this contribution is to show the implementation of fuzzy logic in business, management and accounting, through the research published in Scopus. This document has among its results the following sections: 1) Theory of fuzzy sets, in Business, Management and Accounting. 2) Analysis of the bibliometric of Fuzzy Logic in Business, Management and Accounting. 3) Identification and characterization of the most cited documents or seminal papers in fuzzy logic application in business, management and accounting.

Material and Method
The material used in this contribution is the documentation and bibliometric analysis tools contained in the Scopus academic research directory and the use of the VOSviewer software; the method, a bibliographic review and critical analysis of the results of the detected contributions.
Using the phrase "Fuzzy Logic" in the title of the contributions contained in the Scopus directory; and limiting these results to the subject area "Business, Management and Accounting", 397 documents were detected between 1983 and 2019. Using the bibliometric analysis tools that Scopus provides to its subscribers, Figure 2, Figure 4 and Figure 5 were achieved; In addition, the cited index of each of the investigations referred to in Table 1 and Table 2 was determined.
The bibliometric information of the 397 documents mentioned above was exported from the Scopus directory in two different formats. First, it was exported in (.ris) format, to be processed by the EndNote bibliometric management software. Through this computational tool all the citations contained in this work were generated. This bibliographic management tool allows to make citations by the norm selected by the user, for this work the bibliographic citation norm used was the American Psychological Association (APA). The use of this tool guarantees that each citation has in its reference the organization concerning the standard used and that, based on the integrity of the exported data, the reference has the greatest number of gifted fields.
Then the bibliometric information of the 397 documents was exported from the mentioned academic directory, but this time in (.csv) format. This process allowed us to use this information in the VOSviewer science bibliometric analysis software. The use of this software is justified by its potential in the process of visualization of productivity and orientation of scientific activity. By means of this tool, the density map of terms was obtained, made of text mining on the keywords of the articles detected.

Theory of Fuzzy Sets, in Business, Management and Accounting
In classical theory an element belongs or does not belong to a set. This strict and determinant notion does not allow taking into account other frequently encoun- The notion of fuzzy set is based on the concept of partial belonging where each element belongs partially or gradually to a set. A classic and simple example; suppose that a man is considered tall when his height is greater than 1.80 m and small when he is less than 1.40 m. Where to include a man whose height is 1.78 m? Obviously, that man intuitively has a higher degree of belonging to the group of tall men than to the group of small men. If it is treated classically, the degree of belonging to the group of tall men is zero or zero because it does not reach height and therefore should be considered a short man with full membership in that group.
In general, a diffuse set Q of a universe H is defined as: which indicates that Q is a set of pairs Example of the fuzzy set Q of the numbers close to 1. For this case it is assumed that the degree of belonging to the set is given by:

Analysis of the Bibliometric of Fuzzy LOGIC in Business, Management and Accounting
Research in the application of fuzzy logic in business, management and accounting began at the beginning of the 80s. But they will be important in the scientific community at the beginning of the 21st century. This is mainly due to the increase in market dynamics and business management (Brace, Gatarek, & Musiela, 1997;Hsieh, 1991;Onnela, Chakraborti, Kaski, Kertész, & Kanto, 2003). Figure

Identification and Characterization of the Most Cited Documents or Seminal Papers in Application of Fuzzy LOGIC in Business, Management and Accounting
To date there are only 10 revision-type papers in Scopus. The last review paper related to this topic was published in 2016. Table 1 identifies each of these documents.   The researchers Chao and Skibniewski (1998)  In the paper of the authors Barclay and York (2003) Policy capturing was used to determine cue weights when a merit raise committee implemented an imprecise directive. The committee was consistent in their evaluations, but the policy was similar to that obtained by counting activities in faculty annual reports.
Evaluations by three raters of 36 faculty were regressed on actual raises. This study has implications for organizations that motivate employees through merit pay decisions in ways that are inconsistent with their mission and business objectives. Collan and Liu (2003) they expressed that: To proceed in an efficient and precise way in the dynamic management of large investments, managers must have constant access to information on the real-time situation of the investment, as well as access to up-to-date information on changes in the business environment. In other words, the economic existence of large investment processes requires a permanent dynamic management, currently. This contribution studies how emerging software technologies will help provide better support in this scenario. In addition, they will provide a support system that will make an inte-

Discussion
Regularly, various methods are used for decision making in business, administration and accounting processes: classics and methods that use soft computing non-linearity. Fuzzy logic differs from conventional computing in that it tolerates inaccuracy, uncertainty and approximation (Sivamani et al., 2017). In effect, the model to follow for fuzzy logic is the human mind (Somasundaram & Genish, 2014). The guiding principle of fuzzy logic is to exploit this tolerance to achieve management capacity, robustness and low cost of solution. Table 2  Flexible computing symbolizes a paradigm shift in computing design, a change that reflects the fact that the human mind, unlike today's computers, possesses an important capacity to store and process information that is inaccurate and approximate (Sheeba & Vivekanandan, 2016;Yager & Zadeh, 2012).
Fuzzy logic in business, management and accounting applications have specific characteristics. They can help in the decentralization of decision-making processes so that they are standardized, reproducible and documented. These methods play very important roles in companies because they help reduce costs, and that can generate higher profits; they can also help companies compete successfully and decrease expenses.   Purpose: This paper aims to provide a tool for decision makers to help them with selection of the appropriate supplier. Design/methodology/approach: Companies often depend on their suppliers to meet customers' demands. Thus, the key to the success of these companies is selection of the appropriate supplier. A methodology is proposed to address this issue by first identifying the appropriate selection criteria and then developing a mechanism for their inclusion and measurement in the evaluation process. Such an evaluation process requires decision maker's preferences on the importance of these criteria as inputs. Findings: Human assessments contain some degree of subjectivity that often cannot be expressed in pure numeric scales and requires linguistic expressions. To capture this subjectivity the authors have applied fuzzy logic that allows the decision makers to express their preferences/opinions in linguistic terms. Decision maker's preferences on appropriate criteria as well as his/her perception of the supplier performance with respect to these criteria are elicited. Fuzzy membership functions are used to convert these preferences expressed in linguistic terms into fuzzy numbers. Fuzzy mathematical operators are then applied to determine a fuzzy score for each supplier. These fuzzy scores are in turn translated into crisp scores to allow the ranking of the suppliers. The proposed methodology is multidisciplinary across several diverse disciplines like mathematics, psychology, and operations management. Practical implications: The procedure proposed here can help companies to identify the best supplier. Originality/value: The paper describes a decision model that incorporates decision maker's subjective assessments and applies fuzzy arithmetic operators to manipulate and quantify these assessments. (Ordoobadi, 2009)  Competitive advantage is often determined by the effectiveness of an organization's supply chain, and as a result, the evaluation and selection of suppliers has become an increasingly important management activity. But the evaluation process is complex. The data that must be considered are both technical and social/organizational. Much of the data are difficult to obtain and ambiguous or vague to interpret. In addition, the dynamic global environment of changing exchange rates, economic conditions, and technical infrastructure, demand that the pool of potential suppliers be re-evaluated periodically. Nonetheless, a rational process of evaluation must exist to select the most appropriate suppliers. This paper addresses one dimension of the evaluation process, the information sharing capability of potential supply chain partners. It is an especially important dimension since information technology is necessary to horizontally integrate geographically dispersed operations. Fuzzy logic, a subset of artificial intelligence, together with analytical hierarchy process is used to model this process and rank potential suppliers. It is an appropriate methodology to use for this application and has the potential to be used with other supply chain design decisions since it explicitly handles vague, ambiguous, and imprecise data. (Shore & Venkatachalam, 2003)  Manufacturing decisions inherently face uncertainties and imprecision. Fuzzy logic, and tools based on fuzzy logic, allow for the inclusion of uncertainties and imperfect information in decision making models, making them well suited for manufacturing decisions.
In this study, we first review the progression in the use of fuzzy tools in tackling different manufacturing issues during the past two decades. We then apply fuzzy linear programming to a less emphasized, but important issue in manufacturing, namely that of product mix prioritization. The proposed algorithm, based on linear programming with fuzzy constraints and integer variables, provides several advantages to existing algorithm as it carries increased ease in understanding, in use, and provides flexibility in its application. We present an interactive user-friendly microcomputer-based decision support system for consensus reaching processes. The point of departure is a group of individuals (experts, decision makers …) who present their testimonies (opinions) in the form of individual fuzzy preference relations. Initially, these opinions are usually quite different, i.e., the group is far from consensus. Then, in a multistage session a moderator, who is supervising the session, tries to make the individuals change their testimonies by, e.g., rational argument, bargaining, etc. to eventually get closer to consensus. For gauging and monitoring the process a new "soft" degree (measure) of consensus is used whose essence is the determination to what degree, e.g., "most of the individuals agree as to almost all of the relevant options". A fuzzy-logic-based calculus of linguistically quantified propositions is employed. (Fedrizzi, Kacprzyk, & Zadrozny, 1988) Open Journal of Business and Management When making decisions we need to consider the possible alternatives and then choose the optimal alternative. The uncertainty of subjective judgment is present during this selection process. Also, decision making becomes difficult when the available information is incomplete or imprecise. This kind of problem exists while selecting a project. There are also several critical factors that are involved in the selection process, including market conditions, availability of raw materials, etc. The decision mechanism is constrained by the uncertainty inherent in the determination of the relative importance of each attribute element. In this paper, we develop a system for the project selection using fuzzy logic. Fuzzy logic enables us to emulate the human reasoning process and make decisions based on vague or imprecise data. Our approach is based on uncertainty reduction. The optimal alternative is formed by the relative weights of each attribute's elements combined over all the attribute membership functions. We also do a case study for the selection of software packages. Our system could be easily applied to other project selection problems under uncertainty. (Machacha & Bhattacharya, 2000) 10 Fuzzy logic-based leanness assessment and its decision support system Vinodh, S. Balaji, S. R. 2011 70 International

Journal of Production Research
Manufacturing organizations have been witnessing a transition from mass manufacturing to lean manufacturing. Lean manufacturing is focused on the elimination of obvious wastes occurring in the manufacturing process, thereby enabling cost reduction. The quantification of leanness is one of the contemporary research agendas of lean manufacturing. This paper reports a study which is carried out to assess the leanness level of a manufacturing organization. During this research study, a leanness measurement model has been designed. Then the leanness index has been computed. Since the manual computation is time consuming and error-prone, a computerized decision support system has been developed. This decision support system has been designated as FLBLA-DSS (decision support system for fuzzy logic-based leanness assessment). FLBLA-DSS computes the fuzzy leanness index, Euclidean distance and identifies the weaker areas which need improvement. The developed DSS has been test implemented in an Indian modular switch manufacturing organization. (Vinodh & Balaji, 2011) Fuzzy logic models are not a black box; because the rules are defined. The advantages of fuzzy logic can be found in the configuration of rules of phenomena and processes of great complexity and their ability to adjust and simulate before implementation. Neuro-fuzzy models could be an advantage in the configuration of rules (Lin & Lee, 1991;Zadeh, 1994).
In the future it is expected that this computational practice will focus fundamentally on new diffuse models and the combination of these with other artifi-A. B. Hernández, D. B. Hidalgo Open Journal of Business and Management cial intelligence techniques such as neural networks, genetic algorism, forage bacteria, among others. Future scientific contributions will focus on various applications to allow business decision making to be faster and more precise, this will be the main research focus because the amount of data to be processed increases exponentially in business, management and accounting. More and more decisions will be made by automatic systems without the timely influence of the analyst (Nasiri & Darestani, 2016;Singhal, Ranganth, Batra, & Nanda, 2016).
The evolution of rapid, more precise, partially or fully automated decision-making systems is where flexible computing methods will be used. They will save time, reduce errors, prevent human failures and reduce costs, thus, favoring the competitiveness of companies (Dostál & Kruljacová, 2019;Geramian et al., 2019;Plessis et al., 2018).
The contributions of fuzzy logic in business, management and accounting have advantageous consequences: in many cases, a problem can be solved effectively and agile using this mathematical method Zohuri & Moghaddam, 2017). The rapid growth in the number and variety of applications of fuzzy logic methods, together with the growing interest of the international scientific community, demonstrates the value of this practice, and suggest that its impact will increasingly be felt in the coming years in the world of business, management and accounting.

Limitations of the Study
• This research is limited to the analysis of documents published in the academic directory Scopus.
• Only paper written in English is studied.
• Only analyze the scientific publications between the years 1983 and 2019. • The number of citations per investigation, shown in Table 1 only refers to citations made by research published in Scopus.
• The analysis of text mining to make the map of terms of Figure 3 is only done in the keywords of the articles detected.

Conclusion
Fuzzy logic is a theory that uses fuzzy sets and very precise rules. This mathematical method uses linguistic variables, the base of rules or fuzzy sets are easily modified, the input and output are related in linguistic terms, they are easily understood and some rules cover a great complexity. The applications of fuzzy logic for the solution of problems in the field of denial, administration and accounting activity have had a notable increase in the international scientific community, in recent decades. This condition will continue in the future given the dynamism and the large amount of information that is currently handled in the areas of economic and business sciences. On the other hand, the application of fuzzy logic in this field finds its greatest utility, in models or algorithms for decision making. In the future, it is expected that this computational practice will focus fundamentally on new diffuse models and the combination of these with other artificial intelligence techniques such as neural networks, genetic algorism, forage bacteria, among others. Future scientific contributions will focus on various applications to allow business decision making to be faster and more precise. This will be the main research focus, because the amount of data to be processed increases exponentially in the subject area: business, management and accounting.