Using Fuzzy Logic for Scheduling Multiple Chapters

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[. . .] 315). Even when executives make the effort to plan their projects carefully, they may overlook the most important ones in their attempt to organize all of the enterprise's projects in a cohesive fashion. In this regard, Dinsmore and Cabanis-Brown point out that, "Most executives are aware of the need for drastic change in multiproject management practices, but many place the emphasis in the wrong place. Unfortunately, a great deal of such investment is misdirected into multiyear efforts to implement software tools and time sheets before dealing with the highest leverage points" (2011, p. 315).

There are three discrete roles that organizations must formally define in order to develop an effective project portfolio management system as follows:

1. Governance: This executive role is one of decision making, usually conducted by top management teams. In the most effective implementations that this author has evaluated, this role includes the "C" level executives (CFO, CEO, COO, CIO) who meet monthly to make decisions about:

Which projects to approve/reject.

When to activate projects.

How many projects to activate and which projects to deactivate.

Due dates for projects.

Criteria for project proposals.


Resource allocation, including capital expenditure, people, and operating expense budget.

Project reviews, with approval for a project to proceed to the next stage or to kill the project, or approval/rejection of project improvement plans.

Investment in project management methodology and tools.

2. Management: Relative to project portfolio management, management's job is to ensure that the project management system is "in control." According to the late quality guru W. Edwards Deming, a system is in control when the goals of the system can be predictably met better than 95% of the time. Every project has three distinct goals -- to be delivered on time, on budget, and within scope, according to original commitments (not the 10th revision to a due date). This role includes providing the project management processes for planning and execution to deliver projects according to their goals. Usually, this is done by a Project Management Office or similar organization. Where such an office does not exist, this role will fall on the project portfolio management person(s).

3. Project Portfolio Management: The person(s) undertaking this role provides information and recommendations to the governance group for improved return on investment. They also monitor execution of projects. Usually, there is a close relationship between the person(s) responsible for strategic planning and the project portfolio manager. While strategic planners identify the ideas necessary to meet organization goals, the portfolio manager makes sure that there are corresponding programs and projects sufficient to accomplish those ideas. Furthermore, the portfolio manager maps and tracks the project execution against the strategies and raises the red flag when there is danger of missing a goal. Finally, the portfolio manager also lets strategic planning know when the strategy is not practical relative to project resources available (Dinsmore & Cabanis-Brown, 2011, p. 315).

Building the Fuzzy Inference System Solution

As noted in the introductory chapter, this study proposed a solution to accurately estimate completion time and cost for project tasks. The solution is based on a fuzzy inference system which is based on fuzzy logic (Guan & Zurada, 2008). According to Guan and Zurada, "Fuzzy logic has been widely studied in the relatively 'hard sciences' such as different fields of engineering with varying degrees of success" (p. 395). As an extension of Boolean logic, fuzzy logic deals the vagaries involved with partial truths that indicates the degree to which a proposition is either true or not true (Sabeghi et al., 2006). In this regard, Sabeghi and his associates report that, "Whereas classical logic holds that everything can be expressed in binary terms (0 or 1, black or white, yes or no), fuzzy logic replaces Boolean truth values with the degree of truth" (2006, p. 2). The degree of truth measure is frequently used to describe the imprecision involved in various modes of reasoning that serve as a basis for human decision-making in uncertain and imprecise environments (Sabeghi et al., 2006). As shown in Figure 1 below, a fuzzy rule-based system is comprised of the following:

A Rule Base (RB) of fuzzy rules

A Data Base (DB) of linguistic terms and their membership functions

Together the RB and DB are the knowledge base (KB)

A fuzzy inference system which maps from fuzzy inputs to a fuzzy output

Fuzzification and defuzzification processes (Kovacs, 2012).

Figure 1. Components and information flow in a fuzzy rule-based system

Source: Kovacs, 2012

The general objective of fuzzy logic is to provide a map of an input space to an output space with the main mechanism for accomplishing this objective being a series of IF-THEN statements which are termed "rules" (Foundations of fuzzy logic, 2014, para. 2). According to Wang (1996), "The membership function of a fuzzy set corresponds to the indicator function of the classical sets. It can be expressed in the form of a curve that defines how each point in the input space is mapped to a membership value or a degree of truth between 0 and 1" (p. 37). Although the most common shape of a membership function is triangular, trapezoidal and bell curves have also been used (Wang, 1996). The input space is referred to in mot cases as "the universe of discourse" (Wang, 1996, p. 37).

According to one fuzzy logic vendor, "All rules are evaluated in parallel, and the order of the rules is unimportant. The rules themselves are useful because they refer to variables and the adjectives that describe those variables" (Foundations of fuzzy logic, 2014, para. 2). In other words, fuzzy logic rules are described in linguistic ways so that humans can understand the input space and how the output vector is generated. In this regard, MathWorks advises that, "Before a system can be built that interprets rules, practitioners must define all the terms they plan on using and the adjectives that describe them. In other words, 'To say that the water is hot, you need to define the range that the water's temperature can be expected to vary as well as what we mean by the word hot'" (Foundations of fuzzy logic, 2014, para. 2).

The fuzzy inference method interprets the values in the input vector and, following the established set of rules, assigns quantifiable values to the output vector (Foundations of fuzzy logic, 2014). According to Hamzeh, Fakhaire and Lucas (2007), "Fuzzy inference is the process of formulating the mapping from a given input set to an output using fuzzy logic. The basic elements of fuzzy logic are linguistic variables, fuzzy sets, and fuzzy rules" (p. 211). As noted above, fuzzy sets and rules employ linguistic terms to facilitate the interpretation of the generated results. In this regard, Hamzeh and his associates note that, "The linguistic variables' values are words, specifically adjectives like 'small,' 'little,' 'medium,' 'high,' and so on" (2007, p. 212).

The fuzzy logic process begins with the fuzzy set concept. According to MathWorks, "A fuzzy set is a set without a crisp, clearly defined boundary. It can contain elements with only a partial degree of membership. Any statement can be fuzzy" (Foundations of fuzzy logic, 2014, para. 3). Practitioners that have been confronted with vague and nebulous answers to straightforward questions will welcome the ability of fuzzy inference systems to provide them with answers that span a continuum. In this regard, MathWorks add that, "The major advantage that fuzzy reasoning offers is the ability to reply to a yes-no question with a not-quite-yes-or-no answer. Humans do this kind of thing all the time (think how rarely you get a straight answer to a seemingly simple question), but it is a rather new trick for computers" (Foundations of fuzzy logic, 2014).

The "new trick for computers" involved in fuzzy inference systems relies on categorization of data. According to Hahn and Ramscar (2001), this is a natural human tendency that makes fuzzy inference especially useful. For instance, Hahn and Ramscar advise that, "One of the central concerns of cognitive psychology is the process of categorization (and subsequent classification) by which humans organize and represent their knowledge of the world" (2001, p.37). In the business world, it is axiomatic that in order to improve something, it must first be measured and in order to measure something, it must first be categorized. This natural process is highly congruent with the tenets of fuzzy inference systems. For example, Hahn and Ramscar add that, "Classical category theory views the world as being comprised of natural partitions, and the purpose of categorization is to allocate objects into the appropriate partitions" (2001, p. 37). Pursuant to this perspective, all instances of a category share some type of commonality that sets them apart from other instances in ways that are adequate for defining the category (Qi & Zhu, 2008).… [END OF PREVIEW]

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Using Fuzzy Logic for Scheduling.  (2014, March 9).  Retrieved February 15, 2019, from

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"Using Fuzzy Logic for Scheduling."  9 March 2014.  Web.  15 February 2019. <>.

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"Using Fuzzy Logic for Scheduling."  March 9, 2014.  Accessed February 15, 2019.