Project management using fuzzy logic

This document aims to show the importance and benefits offered by Fuzzy logic applied to business, in the field of administration and management, for which the theoretical-practical foundations and generalities concerning this methodology are proposed, in order to implement an algorithm to simulate strategies concerning decision-making and the art of managing projects, based on human experience and knowledge channeled through artificial intelligence systems.

Dynamic Project Management using Fuzzy Logic. This paper have for object show us the importance and benefits offered by Fuzzy Logic in business administration and management fields, so inform about theoretical and practical generalities concerning to this methodology in order to implement an algorithm for simulation of decision-making and project management strategies, based on human being experience and knowledge, channeled through artificial intelligence systems.

INTRODUCTION

Project management is the art of planning, coordinating, organizing, directing, and managing resources in such a way that an enterprise can be carried out within the defined scope, time, and cost, allowing optimal results and satisfying the fulfillment of the project's objectives..

When we talk about Dynamic Management, we are referring to the application of a methodology subject to variables that can be adapted to the environment in order to face situations that affect the initially planned development, and thus be able to achieve the expected results. Dynamic management requires the ability to make decisions in accordance with the changes and new challenges posed, in the shortest possible time and trying to minimize risk, for which it relies on the knowledge and experience of the human being, as well as on their ability reasoning.

Fuzzy Logic is one of the tools of artificial intelligence that uses human experience to generate reasoning that allows decision-making. Through this tool, a management system can be represented through a non-linear mathematical model, for which it makes use of linguistic variables and a series of previously defined conditions or rules.

This methodology tries to emulate the experience acquired by one or more human beings over time, this system will have in its memory a database with multiple solutions to the same problem, then the system will have to choose from among those solutions to the that can best be applied in order to achieve the best results. The choice of the decision structure to follow will depend on the characteristics of the work in which it will be applied, in addition the system will be able to learn over time and store its own experiences for which it can rely on neural network algorithms and genetic algorithms.

This logic can be used to explain the world in which we live, since it follows the human behavior of reasoning, drawing conclusions from observed facts. Its application in the evaluation of business management strategies allows simulating the behavior of these strategies (using software), representing a quasi-real scenario, thus being able to alter parameters and conditions without affecting the normal course of a project. Among other advantages, the development of the project can be simulated in order to direct it towards the expected social and economic optimization.

OVERVIEW OF FUZZY LOGIC

Fuzzy Logic is also known as Fuzzy Logic or Fuzzy Logic, and is based on the relative of the observed. In classical logic (binary or boolean) there are only two possible states: true and false (1 or 0), in Multivalued logic, logical systems are included that admit several possible truth values. In contrast, the Fuzzy logic assigns intermediate values within a scale in order to quantify an uncertainty. For example, according to classical logic we can only define the temperature as "cold" and as "hot", according to fuzzy logic we can assign infinite intermediate values such as "little cold", "warm", »warm", "somewhat hot", etc..

In order to understand a management process governed by a methodology based on Fuzzy systems, we must keep in mind that Logic is the science that teaches us to reason accurately, it is the art of thinking in accordance with understanding and common sense. Using the correct logic, a system can be controlled, that is, a set of actions can be established that maintain a variable within the desired operating patterns.

Every system can be represented mathematically using system identification and parameterization techniques, giving rise to a mathematical model, whose behavior can be simulated and analyzed using computer tools. Therefore we are in the capacity to evaluate the performance of said set of actions in order to establish if its application constitutes the application of the correct logic.

Fuzzy Logic uses the experience of the human being to generate a set of rules that allow to follow a logic of reasoning, it can represent the mathematical model of a system by using linguistic variables and a series of previously defined conditions or rules, its algorithms (rules) make use of IF… THEN instructions (IF… THEN), for example: IF there is a high demand for my product THEN I will increase the price.

Elements:

Linguistic Variable: They are variables evaluated in a natural language and do not correspond to an exact numerical value. Linguistic variables can be decomposed into linguistic terms. Eg temperature, behavior, position, size, earnings, time, etc.

Discourse Universe: It is the range of all the information necessary for the correct behavior of a system. For example, "temperature" in the range of 5 to 100 ° C; "Profitability" in the range of 10% to 33%, etc.

Linguistic Term: They are the sub-sets or the parts that a linguistic variable can be divided into. For example, for the variable "size" you can have the terms: high, medium, low; for the variable “profit margin” you can have the terms: expected, appropriate, fair, poor, etc.

Fuzzy Set: They are geometric shapes that represent a function generated by a linguistic term. They will create an intermediate output in the diffuse system. They can be: triangles, squares, trapezoids, Gaussian bells, among others.

Membership Function: The membership function is the grouping of fuzzy sets corresponding to a single linguistic variable, associated with its degree of membership or membership within the range 0 - 1.

Fuzzification: Fuzzification is the process carried out to convert a traditional logical, binary, decimal, and / or exact value into a fuzzy value or quantity.

Inference Process: It is the process or methodology that is carried out to evaluate the norms, given a set of rules (instructions IF… THEN) they must be allowed to determine a result. It allows to operate with sets: Union (OR), Intersection (AND), Complement (NOT).

Defuzzification: It is the reverse process of fuzzification, that is, it is the action of converting a fuzzy value into an exact value.

Fuzzy Logic and Discussion Universe

EVALUATION, DIRECTION AND PROJECT MANAGEMENT

A project is that undertaking made up of a set of actions or activities that we can divide into tasks that are not cyclical (repetitive), that can be precisely characterized, of a determined duration, formally organized and whose relationships between them are known. Projects require the use of resources (time, money, human resources, materials, energy, space, supplies, communication, quality, risk, etc.); Likewise, it responds to objectives that must be met within defined parameters, therefore a first challenge of project management is to ensure that the project is delivered within the defined parameters; A second challenge is the allocation and integration of resources to meet those predefined goals.

Every project has three different elements that need to be harmonized to achieve the desired results:

Technical dimension: Refers to the set of specific knowledge of each work area («know how») required to solve the problem in question or carry out the work entrusted to it. Human dimension: Refers to the interpersonal and negotiation relationships that inevitably arise among the human agents involved in the organization and execution of a project. Variable management: This refers to the set of actions that make up the decision-making process to direct a particular project.

The Project Evaluation consists of 3 stages, an initial one when the project is only an idea in the entrepreneur's mind, a second one when said idea is in full execution, and a third one when the project has been completed. Project evaluation is a process by which the changes generated are determined from the comparison between the current state and the state foreseen in its planning; [That is to say, an attempt is made to find out how much a project has achieved its objectives or how much capacity it would have to fulfill them. In the process of analysis and evaluation of a project, strategic information is obtained that favors decision-making, which is why it is considered as an activity aimed at optimizing project management since it promotes optimization in the allocation of resources.

Project Management consists of applying knowledge, skills, tools and techniques in the activities of a project to satisfy its requirements and achieve its objectives. Project management is a task that may fall on a work team, but many times, it is the responsibility of a single individual. This individual aims to maintain the progress and interaction of the elements, so that the risk is decreased. The project leader must be able to visualize the entire project from start to finish and have the ability to ensure that vision is realized.

Management consists of determining what should be done, how it should be done, who is responsible for doing it, and why it should be done. Project Management is the art of planning, coordinating, organizing, directing, and managing resources in such a way that an undertaking can be carried out within the defined scope, time, and cost, allowing optimal results and satisfying the fulfillment of the project objectives..

Project Management is the branch of Administration Science that deals with project planning and control.

Planning: Plan the execution of a project before its start. Control and Monitoring: Measure the progress of the project.

In the execution phase of a Project, there are always internal and external alterations because Management must be prepared to apply a methodology subject to variables that can be adapted to the environment in order to face situations that affect the initially planned development, and in this way be able to achieve the expected results. A Dynamic Management is one capable of making decisions in accordance with the changes and new challenges presented, in the shortest possible time and trying to minimize risk.

Project management consists of the following phases:

Conception and Planning (definition of characteristics, objectives, schedules, schemes, activities, managers, allocation of resources, etc.) Execution and Communication (keep all participants informed regarding the evolution and development of the project) Follow-up and Control (supervise the fulfillment of objectives, data collection and analysis, rethinking of strategies to follow, etc.) Final analysis (evaluation of expected results versus results obtained)

Project management must manage the following elements:

Technical-Economic Proposal, which describes the objectives of the project, the activities to be carried out and how they will be carried out. Project Planning and Schedule, which refers to the identification of activities, milestones and delivery times of the project. Cost estimation of the project. It is an activity related to the estimation of the resources required to carry out the project plan. Project supervision and review. Referred to the strategic direction of the project and those responsible for the activities. Progressive writing and reporting.

EXPERT SYSTEMS IN THE FUZZIFICATION OF VARIABLES

A Fuzzification process is one that allows converting a CRISP quantity (traditional logical, binary, decimal, exact value) into a fuzzy value or quantity, assigning it a degree of membership according to a linguistic term. This process responds to a set of pre-established standards, conceptualized from the knowledge provided by human experience channeled through an expert system implemented via software.

An Expert System is one that simulates the behavior of a group of people who are experts in a certain subject, with the aim of seeking a better quality and speed of response, thus leading to an improvement in project productivity. Expert systems consist of an extensive database fed with thousands of rules, after analyzing among these rules, select the most appropriate response to resolve a given circumstance. The systems allow great flexibility in incorporating new knowledge since new standards are simply programmed into the database.

Basic structure of the system:

Knowledge base: Contains the experience (expert knowledge) modeled using rules. Fact base (Working memory): Contains the facts about a particular problem that has arisen during the analysis. Inference engine: Models the human reasoning process, that is, the decision-making strategy. Justification modules: Explains the reasoning used by the system to reach a certain conclusion. User interface: It is the interaction between the system and the user, it is implemented via software.

The Fuzzification process assigns characteristics to the linguistic variables, giving rise to "imprecise concepts" such as: the temperature is hot, inflation is growing slowly, profits are good, the company exported little, etc. Likewise, these concepts can be associated with a degree of membership to determine how intertwined a variable is with a diffusely assigned characteristic.

For example:

We have the linguistic variable "savings" expressed in a discussion universe (range) from 0 to 100, expressed with linguistic terms "low savings", "regular savings", "high savings", and with membership functions as shown in the graphic.

Fuzzy logic

You want to perform the Fuzzification (convert to fuzzy value) of the value "55":

As shown in the graph this has a membership grade of:

0.25% of "low savings" 0.75% of "regular savings" 0% of "high savings"

DEFUZZIFICATION METHODS APPLIED TO PROJECT MANAGEMENT

After the Inference Process has been carried out (application of rules to arrive at a result), the Defuzzification process is carried out, which is the inverse process of fuzzification, that is, it is the action of converting a fuzzy value into a exact value. It makes use of mathematical functions to determine a value, thus we have:

Maximum Membership Function: It is also known as the height method, the output "crisp" is the maximum height of the final diffuse set.

Fuzzy logic

Centroid Method: Called area center, center of gravity or Sugeno method, it is the most used and most powerful method.

Fuzzy logic

Maximum Effective Average Method: Uses the effective mean value of the maximum. Used only for symmetric fuzzy output sets.

Fuzzy logic

Maximum Average Method: Same as above, but only outputs the maximum average as output.

CASE STUDY: PRACTICAL APPLICATION

A company in the process of expanding into new markets wants to better manage its advertising spending and market segmentation in order to obtain more customers. It is required to design a system based on Fuzzy methodology in order to simulate different scenarios.

Linguistic Variable	Linguistic Terms	Discussion Universe
Advertising spend	Moderate Excessive	1000 to 30000 U $ D monthly 20,000 to 50,000 U $ D monthly
Market segmentation	Light Exhaustive	1 to 6 segmentation patterns 5 to 10 segmentation patterns
Number of clients	Few Regular Many	0 to 500 end user clients 300 to 700 end user customers 500 to 1000 end user clients

Choosing the right Membership Functions has a lot to do with the experience of the programmer combined with the knowledge of the expert system, so we have:

Expert Systems and Fuzzy Logic

In short: Number of clients (CC), Market segmentation (SM), Advertising expenditure (GP).

SET OF STANDARDS and / or rules based on knowledge of human experience (expert system)

- IF GP is moderate and SM is light THEN CC is few

- IF GP is moderate and SM is exhaustive THEN CC is regular

- IF GP is excessive and SM is light THEN CC is regular

- IF GP is excessive and SM is exhaustive THEN CC is many

SIMULATION: According to the data, it is known that the monthly advertising cost is US $ 22 thousand and that there are 7 market segmentation patterns, it is desired to know the expected number of final customers.

According to the analysis, for a GP = 22 it corresponds to a degree of "moderate" membership of 0.40 and "excessive" of 0.10, in the same way for a SM = 7 it corresponds to a degree of "exhaustive" membership of 0.45.

According to the Inference Analysis (application of standards) it is observed:

For a moderate GP 0.40 and exhaustive SM 0.45, a “regular” CC is obtained with 2 degrees of membership (0.40 and 0.45), intercepting the sets the resulting fuzzy value is 0.40. For an excessive GP 0.10 and exhaustive SM 0.45, we obtain a “many” CC with 2 degrees of membership (0.10 and 0.45), intercepting the sets the resulting fuzzy value is 0.10.

Interference Analysis - Fuzzy Logic

The result of the Inference Analysis is the function delimited by the region shaded in red as shown in the graph. Then the Defuzzification process is carried out, for which we will use the Centroid method (symmetric center of a geometric figure), calculating the mathematical function results in 566 expected end customers.

(*) It should be noted that a real study needs to contemplate a greater number of linguistic variables and terms, and therefore have a much more extensive, accurate and personalized database of standards, for which the support of computer tools is required.

CONCLUSIONS

Through this document, the concepts and foundations that govern the Fuzzy Logic were raised, as well as the generalities and importance of correct project management, focusing efforts on optimizing decision-making according to changes and unforeseen events. that may arise, providing the necessary knowledge to respond positively in a short time, minimizing the risk.

In the same way, the importance of human knowledge in the development of society and more precisely in business management was determined, therefore having a method capable of storing said knowledge in a database and emulating human reasoning in order to submit strategic decisions to quasi-real scenarios, provides the possibility to generate successful businesses. The use of artificial intelligence algorithms implemented using computer tools brings enormous advantages over traditional decision-making methods, since it minimizes the risk of experimenting in the real field and increases the skills of people in charge of managing and directing projects.

By means of the present, it was possible to show the advantages and applications of fuzzy logic in the field of administration, direction, and business and project management in general, using a set of standards stored in expert systems, providing a methodology of easy implementation, robust over time, flexible to changes and shocks, scalable to new implementations, capable of offering accurate results, and agile performance, among others.

BIBLIOGRAPHY

Bojadziev, G.; Bojadziev, M. (1997). "Fuzzy Logic for Business, Finance and Management". World Scientific. De Cós, M. (1997). "General Theory of the Project, Vol. I Project Management". Editorial Síntesis.Harvey, Robert L. (1994). "Neural network principles". Prentice-Hall. Englewood Cliffs.Heredia, R. (1999). «Integrated Project Management». UPM Editorial - ETSII.Herrera, F.; Herrera-Viedma, E. (2000). "Linguistic decision analysis: steps for solving decision problems under linguistic information". Fuzzy Sets and Systems, vol. 115, pp. 67-82.Kaufmann A.; Gil Aluja J. (1987). "Operational management techniques for dealing with uncertainty". Editorial Hispano Europea.Cordón, F. Herrera, F. Hoffmann, L. Magdalena. (2001). Genetic fuzzy systems. Evolutionary tuning and learning of fuzzy knowledge bases ”. World ScientificShtub, A. and others.(2001). "Project Management, Engineering, Technology and Implementation". Prentice Hall, Terceiro, JB (1996). "Digital Society: from Homo Sapiens to Homo Digitalis". Alliance Editorial

_____________

Executive Director, Kaynum (Smart Solutions for Business) Corp.

Kaynum is an integrator of solutions for business and project management. Carry out consulting studies and analysis of business strategies. It also provides the provision of human resources necessary for the management and development of investment projects.

Download the original file