**5. Decision processes: Combining arguments**

It is not surprising that human made creations in the most diversified systems are fragile and precarious and induce great complexity. They are structures influenced too much by nonpredictable events, becoming responsible for stronger and everlasting generated perceptions. A system's structure will only be compatible with a proper information amount, otherwise the structure will enter into collapse and that system will have to organize itself with some other

A system with a great amount of data to obtain less information is said to have a highly disordered structure, and induces in the observer a huge ignorance. On the contrary with an orderly and well organized structure, with a set of data with few elements, one can obtain all the necessary information. In short, the degree of knowledge we can have over a determined

To do so, a method has been developed to calculate the information amount that events generate in the observer, tested in several domains, in studies related with the loss of cohesion from a society before events related to epidemics, or the effects caused in an army before loss in combat, or still with the detection of faults related to the tannery industry, or the determi‐

Hence in this chapter's realm we are describing a method to measure information amount. The concept of measure enhances the observer's existence. Hence, the measure of information amount to Simplicity is a relativist measure, it is always dependable on who is effectively

In this sense, the choice of what messages or which messages' specter to allow measure may take the designation of those messages as relevant factors to a determined structure within a

Hence convictions and concepts into which each observer allows importance, are what we designate as a System of Beliefs. Naturally each observer will have his own, and it is single, and by the time the observer is growing through out his own existence and the world around

One of those things would be, for instance, what the Simplicity's meaning is before a deter‐ mined individual or group of individuals. Probably meaning can change from one individual to one another. Not in general, but in its specificity, which as we saw can induce to several

It all depends in the relation on how we perceive and understand the surrounding universe, which takes place in our senses, and naturally in our System of Beliefs. Already mathematician Friederich Bessel, while examining time records on stars transit in Konigsberg observatory, and facing the systematic differences present in observations made by different astronomers, concluded that perhaps he would be before the existence of a "personal equation". Being thus, one can state that an equation is also a personal experience, and it enhances the existence of a sensor that picks up information transmitted by our senses and that our brain processes.

A sensor is something like a device that receives a signal. It's associated to a specific sensation. It receives a signal – *stimuli or data* – and responds through out an electrical signal. Hence

him, he accumulates ever more beliefs and concepts in respect to serials of things.

structure.

126 Advances in Industrial Design Engineering

system.

definitions for Simplicity.

system is maximized if its uncertainty is zero.

nation of fibers distribution in paper industry.

observing, because it depends on the observer's System of Beliefs.

According to Melo-Pinto (1998), decision process results from information gathering driven to that decision. But all along, the natural appearance of new arguments (partial or not) may drove us to remake beliefs by the light of new data.

Still according to Melo-Pinto (1998), who developed a system of decision making applied to the visual recognition of images in degrading situations, he states that *due to different beliefs' functions over the same insight system, based on different bodies of evidence, he supports himself in the Dempster-Shafer rule of combination*, and as such, may help to calculate the respective functions of believe and plausibility. However, as that function is probabilistic it should be evidence resultant. But Melo-Pinto contradicts this fact, stating in turn that value associated to a given image effectively renders the beliefs we have of it, and are independent from evidence. He gives, for instance, the case of a blond woman's image (Marlene Dietrich) from whom we need no additional result to sustain how associated that image is to Marylin Monroe. Hence the capacity of combination is fundamental to a method that deals with different argument.

"Design Universal Principles" may be those "arguments" than can be embodied as Design essence. They are, no less, and according to Lidwell et al. (2010), the meanings we give to the artifacts we use, in usability terms as well as in its influence, perception and usage call in everyday life, and can assume their selves as combined data and arguments.

What will make sense is to state, that at the most, there was someone who described 225

Hence the concept of Simplicity in Design or Engineering is the one in which effectively each observer beliefs as its own, and that it naturally depends on the amount of informa‐ tion he has relatively to the data he possesses, as the result of combining different

{ } 1, *CC i m <sup>i</sup>* = = (3)

Measuring Design Simplicity http://dx.doi.org/10.5772/54753 129

{ } 1, *DD j n <sup>j</sup>* = = (4)

log 1, *H p p im i ii* =- = å (5)

( ) 1, *HC H i m <sup>i</sup>* = = å (6)

( ) 1, *HD H j n <sup>j</sup>* = = å (7)

log 1, *H p p jn j jj* =- = å (8)

in which *i = 1,m* the information amount allowed by the set of

( ) 1, *H C Bel H i m ii i i* =Ä = å (9)

arguments or weights to build or describe his own system of beliefs.

Maximum Information Amount given by set of data *C*

Maximum Information Amount given by set of data *D*

respectively.

are the sample case *Ci* ∧*Di*

Before a system of beliefs *Beli*

arguments or data:

Set of data *C*

Set of data *D*

*pi* ∧ *pj*

data *C* is:

As seen before, different arguments combining with a specific weight is what embodies our system of beliefs.

The issue we could now raise in this chapter is what is the reason why some products are most desired by some certain people over others? Which method could be used as to allow knowing which arguments each one of us gives more or less relevance?

Today we know that the supposed commercial failure of some products is due not only to problems related to an operative-functional nature, but also because they didn't made sense to the aimed target. Hence we can state that this is a consequence of something that does not fit with the positivist perception of a certain user.

In that sense, this chapter now aims to let know the "Design Universal Principles" (Lidwell et al., 2010), as a first guide to interdisciplinary reference not only to designers but also to engineers as it combines a vast set of arguments in the shape of 125 concepts related to Design and also to Psychology, Engineering and Architecture, organized through five categories, it can be used as a guide to structure the conception for Simplicity, not only for Design, but also as a reference for Engineering:


These five categories are in turn subdivided into 225 contents that raise questions as diversified as: accessibility, archetypes, linings, cognitive dissonance, color, comparison, confirmation, consistence, convergence, cost-benefice, development cycle, errors, safety factor, Fibonacci's sequence, figure-background relation, usability-flexibility, forgetting, form and function, Gutenberg's diagram, hierarchy, highlight, iconic representation, interference effects, Präg‐ nanz' law, legibility, life cycle, mental map, modularity, normal distribution, among many other, and truly it reflects a decision process, as it has the capacity to combine some of the mentioned arguments that may simplify processes while elaborating a Design or Engineering design.

But is it possible, as we call upon those 225 principals, that we became paralyzed while design acting? After all, where to start designing, which or what aspect should we allow more or less importance? Supposedly hardly anybody will be able give the answer. Even so, believing the existence of those "beliefs", there can only be, at the most, one or two… Hence, assuring the 225 (152 ) "principals" will not be in fact a statement to consider.

What will make sense is to state, that at the most, there was someone who described 225 arguments or weights to build or describe his own system of beliefs.

Hence the concept of Simplicity in Design or Engineering is the one in which effectively each observer beliefs as its own, and that it naturally depends on the amount of informa‐ tion he has relatively to the data he possesses, as the result of combining different arguments or data:

Set of data *C*

"Design Universal Principles" may be those "arguments" than can be embodied as Design essence. They are, no less, and according to Lidwell et al. (2010), the meanings we give to the artifacts we use, in usability terms as well as in its influence, perception and usage call in

As seen before, different arguments combining with a specific weight is what embodies our

The issue we could now raise in this chapter is what is the reason why some products are most desired by some certain people over others? Which method could be used as to allow knowing

Today we know that the supposed commercial failure of some products is due not only to problems related to an operative-functional nature, but also because they didn't made sense to the aimed target. Hence we can state that this is a consequence of something that does not

In that sense, this chapter now aims to let know the "Design Universal Principles" (Lidwell et al., 2010), as a first guide to interdisciplinary reference not only to designers but also to engineers as it combines a vast set of arguments in the shape of 125 concepts related to Design and also to Psychology, Engineering and Architecture, organized through five categories, it can be used as a guide to structure the conception for Simplicity, not only for Design, but also

These five categories are in turn subdivided into 225 contents that raise questions as diversified as: accessibility, archetypes, linings, cognitive dissonance, color, comparison, confirmation, consistence, convergence, cost-benefice, development cycle, errors, safety factor, Fibonacci's sequence, figure-background relation, usability-flexibility, forgetting, form and function, Gutenberg's diagram, hierarchy, highlight, iconic representation, interference effects, Präg‐ nanz' law, legibility, life cycle, mental map, modularity, normal distribution, among many other, and truly it reflects a decision process, as it has the capacity to combine some of the mentioned arguments that may simplify processes while elaborating a Design or Engineering

But is it possible, as we call upon those 225 principals, that we became paralyzed while design acting? After all, where to start designing, which or what aspect should we allow more or less importance? Supposedly hardly anybody will be able give the answer. Even so, believing the existence of those "beliefs", there can only be, at the most, one or two… Hence, assuring the

everyday life, and can assume their selves as combined data and arguments.

which arguments each one of us gives more or less relevance?

**•** How can Design and Engineering's perception be influenced?

**•** How to improve decision taking in Design and Engineering processes?

) "principals" will not be in fact a statement to consider.

**•** How to help people learn about Design and Engineering?

**•** How to improve Design and Engineering's usability?

**•** How to raise the call for Design and Engineering?

fit with the positivist perception of a certain user.

as a reference for Engineering:

design.

225 (152

system of beliefs.

128 Advances in Industrial Design Engineering

$$\mathbf{C} = \{\mathbf{C}\_i\} \qquad \mathbf{i} = \mathbf{1}, m \tag{3}$$

Set of data *D*

$$D = \{D\_j\} \qquad \qquad j = 1, n \tag{4}$$

Maximum Information Amount given by set of data *C*

$$H\_i = \sum -p\_i \log p\_i \qquad i = 1, m \tag{5}$$

$$H(\mathbb{C}) = \sum H\_i \qquad \text{i} = 1, m \tag{6}$$

Maximum Information Amount given by set of data *D*

$$H(D) = \sum H\_j \qquad \qquad j = 1, n \tag{7}$$

$$H\_j = \sum -p\_j \log p\_j \qquad j = 1, n \tag{8}$$

*pi* ∧ *pj* are the sample case *Ci* ∧*Di* respectively.

Before a system of beliefs *Beli* in which *i = 1,m* the information amount allowed by the set of data *C* is:

$$H\_{\rm ii}(\mathbb{C}) = \sum Bel\_i \otimes H\_i \qquad \text{i} = 1, m \tag{9}$$

Before a system of beliefs *Bel <sup>k</sup>* in which *i* ∧*k* =1, *m* the information amount allowed by the set of data *C* is:

$$H\_{ki}(\mathbf{C}) = \sum Bel\_k \otimes H\_{i'}$$

$$k = 1, m \land i = 1, m \tag{10}$$

*Bel i*

*D*. *C* is simpler.

If *m*>*n* and *Bel*

we do not know.

Simplicity.

Shafer theory.

*Bel*

*<sup>i</sup>* ≠ *Bel*

amount about the unknown.

mation amount is the simpler.

*<sup>i</sup>* ≠ *Bel*

*<sup>k</sup>* when

about the incognita is the most adequate to predict.

the same information amount or even higher.

*<sup>k</sup>* when

If *m*<*n* e *Bel*

system of beliefs extracts more information amount than set *C* with fewer elements than

*C* is to system of beliefs *K* the simpler. It has less elements and allows higher information

*<sup>k</sup>* system of beliefs makes set *D* the one that gives higher information amount about what

In conclusion we can state that for the same system of beliefs the set that gives higher infor‐

For the same set of data the system of beliefs that allows a set of higher information amount

One can thus deduct that simpler is what needs less number of elements or set of data to obtain

This is the essence of Simplicity, and it can be sustained in "Design Universal Principles", in

However and as complete as it may be, the set of data that can be involved in the conception of a project of Design or Engineering there will also and always be present a System of Beliefs built over a given observer, to whom the information amount over the unknown variable will be zero, as also, there will be a system of beliefs that before a very incomplete set of data will

We can thus deduce that Design in particular and its several schools are liable to be related to mathematics. That schools are a system of beliefs, and they must be not simply a place for knowledge transmission but also a place that promotes knowledge emergence associated to

We will be, as much, before arguments or weights that each School created to give sense to its own design, in this case having as basis the combining arguments according to Dempster-

the quality of an interdisciplinary reference guide, either in Design as in Engineering.

obtain the maximum information amount over the unknown variable.

() ( ) *HC HD ki kj* ³ (16)

Measuring Design Simplicity http://dx.doi.org/10.5772/54753 131

() ( ) *HC HD ki kj* £ (17)

If *Hii* (*C*)<*Hki* (*C*), then the system of beliefs *Bel <sup>k</sup>* is better than the system of beliefs *Bel i* for the set of data *C*.

If *Hii* (*C*)>*Hki* (*C*) is the system of beliefs *Bel i* is better.

If *Hii* (*C*)=*Hki* (*C*) are *Bel i* and *Bel <sup>k</sup>* equivalent to the incognita knowledge.

The same is applied to the set of data *D*.

$$H\_{jj}(D) = \sum Bel\_j \otimes H\_{j'} / j = 1 \,\text{n} \tag{11}$$

$$H\_{k\circ}(D) = \sum Bel\_k \otimes H\_j \quad k \wedge j = 1, n \tag{12}$$

If *m*<*n* and *Bel <sup>i</sup>* = *Bel <sup>k</sup>* when

$$H(\mathbb{C}) \ge H(\mathbb{D})\tag{13}$$

It indicates that for the system of beliefs *Bel <sup>i</sup> C* we need less number of elements than the set *D* to give higher information amount about the unknown variable. Hence, *C* is simpler.

If *m*<*n* and *Bel <sup>i</sup>* ≠ *Bel <sup>k</sup>* when

*Hii* (*C*)≥*H jj* (*D*)⇒ *C* is simpler.

If *m*<*n* and *Bel <sup>i</sup>* ≠ *Bel <sup>k</sup>* when

$$H\_{\vec{\mu}}(\mathbf{C}) \le H\_{\vec{\mu}}(\mathbf{D})\tag{14}$$

*Bel <sup>k</sup>* system of beliefs makes set *D* the simpler set though with more elements than set *C*. If *m*<*n* and *Bel <sup>i</sup>* ≠ *Bel <sup>k</sup>* when

$$H\_{\vec{\text{il}}}(\mathbf{C}) \ge H\_{\vec{\text{jj}}}(\mathbf{D}) \tag{15}$$

*Bel i* system of beliefs extracts more information amount than set *C* with fewer elements than *D*. *C* is simpler.

If *m*<*n* e *Bel <sup>i</sup>* ≠ *Bel <sup>k</sup>* when

Before a system of beliefs *Bel*

130 Advances in Industrial Design Engineering

*<sup>k</sup>* ⊗ *Hi* ,

(*C*) are *Bel*

*<sup>i</sup>* = *Bel*

*<sup>i</sup>* ≠ *Bel*

*<sup>i</sup>* ≠ *Bel*

*<sup>i</sup>* ≠ *Bel*

(*D*)⇒ *C* is simpler.

The same is applied to the set of data *D*.

(*C*), then the system of beliefs *Bel*

(*C*) is the system of beliefs *Bel*

*i* and *Bel*

*<sup>k</sup>* when

It indicates that for the system of beliefs *Bel*

*<sup>k</sup>* when

*<sup>k</sup>* when

*<sup>k</sup>* when

*i*

*D* to give higher information amount about the unknown variable. Hence, *C* is simpler.

*<sup>k</sup>* system of beliefs makes set *D* the simpler set though with more elements than set *C*.

is better.

*<sup>k</sup>* equivalent to the incognita knowledge.

of data *C* is:

(*C*)=∑ *Bel*

(*C*)<*Hki*

(*C*)>*Hki*

(*C*)=*Hki*

If *m*<*n* and *Bel*

If *m*<*n* and *Bel*

(*C*)≥*H jj*

If *m*<*n* and *Bel*

If *m*<*n* and *Bel*

*Hii*

*Bel*

set of data *C*.

*Hki*

If *Hii*

If *Hii*

If *Hii*

*<sup>k</sup>* in which *i* ∧*k* =1, *m* the information amount allowed by the set

*k mi m* = Ù= 1, 1, (10)

( ) , 1, *H D Bel H j n jj j j* = Ä= å (11)

( ) 1, *H D Bel H k j n kj k j* = Ä Ù= å (12)

*HC HD* () ( ) ³ (13)

() ( ) *HC HD ii jj* £ (14)

() ( ) *HC HD ii jj* ³ (15)

*<sup>i</sup> C* we need less number of elements than the set

*<sup>k</sup>* is better than the system of beliefs *Bel*

*i* for the

$$H\_{ki}(\mathbb{C}) \cong H\_{kj}(\mathbb{D})\tag{16}$$

*C* is to system of beliefs *K* the simpler. It has less elements and allows higher information amount about the unknown.

If *m*>*n* and *Bel <sup>i</sup>* ≠ *Bel <sup>k</sup>* when

$$H\_{ki}(\mathbb{C}) \le H\_{kj}(\mathcal{D}) \tag{17}$$

*Bel <sup>k</sup>* system of beliefs makes set *D* the one that gives higher information amount about what we do not know.

In conclusion we can state that for the same system of beliefs the set that gives higher infor‐ mation amount is the simpler.

For the same set of data the system of beliefs that allows a set of higher information amount about the incognita is the most adequate to predict.

One can thus deduct that simpler is what needs less number of elements or set of data to obtain the same information amount or even higher.

This is the essence of Simplicity, and it can be sustained in "Design Universal Principles", in the quality of an interdisciplinary reference guide, either in Design as in Engineering.

However and as complete as it may be, the set of data that can be involved in the conception of a project of Design or Engineering there will also and always be present a System of Beliefs built over a given observer, to whom the information amount over the unknown variable will be zero, as also, there will be a system of beliefs that before a very incomplete set of data will obtain the maximum information amount over the unknown variable.

We can thus deduce that Design in particular and its several schools are liable to be related to mathematics. That schools are a system of beliefs, and they must be not simply a place for knowledge transmission but also a place that promotes knowledge emergence associated to Simplicity.

We will be, as much, before arguments or weights that each School created to give sense to its own design, in this case having as basis the combining arguments according to Dempster-Shafer theory.

Truly a designer can assign determined values to the arguments or weights in cause and another designer can assign to the same arguments or weights another set of values.

Hence Design is no longer a derivation from art, not even from object engineering (MOURA, 2012). Design can be what informs about human creativity, that emerges from the combination and interaction between the several fields of creativity itself, to what we would like to add that it depends on the combining of different arguments and weights of the system of beliefs to what that designer pertains and that will always be the one he received in its School as a student.

We here designate as pertaining to a same school all those who share the same arguments with the same weight.

Hence we can state that we can have as much Schools or Systems of Beliefs as the nature of arguments (*Ma*) or weights (*P*):

$$\left\{\mathbf{M}a\_{i\prime}P\_i\right\} = E\_i \tag{18}$$

**6. Conclusion**

intuitive.

restricted data;

part of itself.

need further increase.

surrounds us.

Maeda's System of Beliefs;

measures and, as such, to quantify.

being measurable, is also an Engineering parameter.

In conclusion, some aspects can be evidenced:

**a.** The essence of the meaning of "Simplicity" is not one of easy understanding in the way it has been, so far, described. The common knowledge is that there are undetermined

Measuring Design Simplicity http://dx.doi.org/10.5772/54753 133

**b.** That "Simplicity is relativist", as an example of "easiness", of "difficultness", of "infor‐ mation", or "complexity", among others, are issues of each one measurements. As a

**c.** That like "Simplicity", until now the concept or notion of "Information" is vague and

**d.** That before a huge Simplicity, we will be before a major amount of information, with

**e.** That Design in particular and its several schools are also passable of "mathematization";

**f.** That Maeda's laws to describe "Simplicity" are a set of arguments and weights built in

**g.** At last that a school is always committed to its shared System of Beliefs, and as such it is responsible for values, ideals, feelings and actions transmitted to those who are or were,

In conclusion we can also state that Maeda's laws are not effectively laws, but methods or suggestions to define simplicity, because as we saw the simplicity measure explained does not

Hence, if we use this relativist measure for simplicity coupled with the complexity measure, we then have the quantitative parameters that release us of qualitative laws for engineering or for design. They allow us the necessary amount to assess design, or engineering, or both.

Therefore the encounter between complexity and simplicity is an art, once we are capable of measuring it and, as such, to quantify it, we acquired the necessary tools for either an engineer or a designer, to achieve the objective of conceiving and build concepts, methods, processes or products, either organic or functional, and hence, at the very end this is what an engineer or a designer aims to. Complexity and simplicity is an art over which we are capable to put

In conclusion we dare state that if we were in the presence of a philosopher; he would say that the true definition for simplicity would be: it exists as to make sense within the world that

It will be then demonstrated that "Simplicity" (its measurement) in particular that of Design,

number of definitions to explain what effectively is Simplicity;

system of beliefs it will always be associated with the observer.

$$\left\{\mathbf{M}\mathbf{a}\_{j\prime}P\_{j}\right\} = E\_{j} \tag{19}$$

$$\left\{\mathbf{M}a\_{k\prime}P\_k\right\} = E\_k \tag{20}$$

So that a School can be shaped:

$$\text{Bel}\_{i,k} \bigcup \text{Bel}\_{i,l} \bigcup \text{Bel}\_{i,m} \implies \text{Bel}\_{i,k} = \text{Bel}\_{i,l} = \text{Bel}\_{i,m} \tag{21}$$

when:

$$\frac{m}{n} \equiv 1\tag{22}$$

The result is that a System of Beliefs is a School, a cluster, and it shares the same arguments with the same weight allowed to the same arguments:

$$Bel\_{i,k} = E\_i \ \ k = 1, \ldots, m \tag{23}$$

Hence we can deduce that Schools have the gift to simplify things. And that the set of data or arguments is equal to *1*. Naturally the better the School the less data it will need to explain or transmit its knowledge.
