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The conventional, read popular, perception of mathematics assumes an abstract domain tightly governed by the interplay of integers, numbers, principles, theories, algorithms, theorems, and formulae – all cast in stone. Such perceptions fuel notions that mathematics is a very precise science that imposes a rigid matrix on all that it surveys. Large parts of such perceptions continue to hold true. However, certain aspects of modern science remain premised on elements that are external to the rigid norms and laws of math.

Consumer behavior in modern times, for instance, represents an imprecise discipline that refuses to yield to the classical constructs of mathematics. In response, the men and women of science have forged the concept of fuzzy logic – an idea that is “based on the observation that people make decisions based on imprecise and non-numerical information.” In other words, fuzzy logic models defy the limits of classical science and binary logic. Ergo, these models comprise the “mathematical means of representing vagueness and imprecise information.” The manifest forms of imprecision can extend to flowchart diagrams that may portray multiple decisions emerging from the convoluted expanses of a process depicted on a canvas.

Illustrations that seek to chart interactions between multiple elements at different levels represent prime instances that project multiple decisions in the terminal stages. The innards of such a flowchart diagram can stand on three sets of vertical stacks. The initial stack represents a series of primary stages, followed by the intermediate stack that processes data, outlines definitions, and creates the space for imprecision to take shape. Designers can distinguish the intermediate stage by applying advanced mathematical formulae, thereby leading to the generation of the third stack. This last set of stages can manifest in a series of outcomes, which might be viewed as multiple decisions. Probability plays a central role in creating value in the last set of stages. This factor is in consonance with modern interpretations, wherein more than one outcome is entirely possible and each outcome retains a high degree of validity. This analysis allows us to consider the importance of multiple decisions in modern processes.

Binary outcomes may precede the multiple decisions that appear at the end of a flowchart. This reinforces, in part, the notion that classical math continues to hold significance even as science and mathematics congregate to birth new domains (such as data analytics). To return to the premise, such a flowchart may sketch a series of operations that represent the mainstream of a system or process. However, special conditions that enter the diagram at random intervals may trigger the appearance of double outcomes; these may merit special processing and contribute to the appearance of multiple decisions at the end of said diagram. The special conditions referred to above may include, for instance, sudden surges in consumer buying prior to the holiday season. This factor, when incorporated into a diagram, helps generate multiple decisions, thereby expanding the scope of outcomes. Data science may mark said special conditions as outliers that cast a significant impact on the terminal stages of a process.

Operating conditions, more often than not, cast outsize impacts on the performance levels of a business or enterprise. Any flowchart that seeks to represent business performance must factor in said conditions, thereby leading to multiple decisions inside a flowchart. Observers may note these points of multiplicity may represent a marked contrast when compared to the performance assurances offered by businesses to the investor community. An instance of such a scenario finds representation in a potential scenario wherein quarterly revenue numbers appear disconnected from revenue forecasts issued by business leaders. To return to the premise, a number of external factors – such as regulatory requirements, changes in policy stances, geo-political risks, fluctuations in market demand, the gyrating prices of raw materials – may trigger multiple decisions in a business process flowchart. Analysts and the captains of industry may not anticipate the impact of these external factors, thereby lending a measure of validity to each outcome in the series of multiple decisions.

Subtle variations from the norm and events governed by pure chance play an important role in actions that place multiple decisions inside a flowchart. We may consider the example of an industry operator in chemicals to illustrate the premise. Said operator may devise a flowchart that details the varied lines of action, business imperatives, commercial considerations, operational requirements, decision points, etc. that attend its business operations. Once completed, the flowchart may portray a multiplicity of decisions – each of which traces intricate connections to variations in the parameters outlined earlier. Business analysts that affix timelines to said flowchart serve to complicate the depicted information by adding time to the complex interplay of aforementioned factors. The emerging visual represents the dominance of multiple decisions in flowcharts that depict modern business operations. Further to this, said industry operator may elect to craft a different response to gradations of anticipated demand for its products, for instance. Therefore, the illustration is best viewed a representation of the nuanced responses that emerge in the face of fickle variation.

Digital marketing operators can arrive at multiple decisions when they chart business strategies to locate and acquire new customers. The diagram can include multiple stages that indicate different types of customers; such as sports fans, fashionistas, information-hungry geeks, the musically inclined, auto enthusiasts, digital natives, book worms, casual surfers, online shoppers, etc. Various levels of information-dense processing can follow said stages and emerge in a horizontal stack that includes the composite answer: social media platforms, instant messaging applications, landing pages, website banners, micro sites, email campaigns, etc. Each of the components in the horizontal stack represents an instance of multiple decisions powering the success of a marketing campaign. We may view this flowchart diagram as a visual algorithm that helps to solve a given problem by offering multiple answers. In itself, the flowchart also represents a visual dialogue that illustrates the breadth of a problem, while leading to multiple instances of valid resolutions.

Corporate captains that remain interested in expanding the market share of their products and services may arrive at multiple decisions in the course of their flowcharting exertions. Such outputs may point to the validity of undertaking more than one line of action in a bid to achieve the stated objective. In line with this, the flowchart may feature a number of preparatory and middle stages that include benchmarking best practices, data analysis performed on current operations, seeking inputs from consultants, distilling the essence of discussions held inside the framework of consultative bodies, quantitative (and qualitative) analysis of operational metrics, etc. These deliberations may trigger the emergence of multiple decisions in the terminal stages of the flowchart; these may include a list of the short term benefits that follow an expansion of market share, the consequent boost to the business bottom line, de-risking advantages, and the long term desirability of such expansion vis-à-vis market competition. Intelligent readers may conclude that each decision that springs forth inside this flowchart holds special meaning for the corporate project in question.

The foregoing paragraphs have framed more than one argument in support of the concept of multiple decisions (that emanate) from a modern flowchart diagram. Readers and reviewers must consider each scenario in their quest to derive meaning from modern flowcharts.