# Design Trend Forecasting by Combining Conceptual Analysis and Semantic Projections: New Tools for Open Innovation

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Some Conceptual and Mathematical Tools

#### 2.1. Topological Generalities

- $q(a,b)=0$ and $q(b,a)=0$ if and only if $a=b,$ and
- $q(a,b)\le q(a,c)+q(c,b),$

#### 2.2. Specific Metric Tools

- (1)
- Write n for $|U|$ (the cardinal of U) and consider the $n\u2014$dimensional classical normed space ${\ell}_{n}^{p}$ for some $1\le p\le \infty $ and a weights sequence $W={\left({w}_{k}\right)}_{k=1}^{n}.$ Recall that the norm in such space is given by$$\parallel ({x}_{1},\dots ,{x}_{n}){\parallel}_{p,W}={\left(\right)}^{\sum _{1\le k\le n}}1/p$$As usual, if all the weights are equal to 1 we write ${\parallel \xb7\parallel}_{p}$ for the corresponding $p\u2014$norm; ${\parallel \xb7\parallel}_{2}$ is the Euclidean norm. We can identify each element of the class D with a vector of ${\ell}_{n}^{p}$ as $A\mapsto {\left({\mu}_{A}\left(x\right)\right)}_{x\in U},$ and so we can define a distance on D as$${d}_{p}\left(\right)open="("\; close=")">A,B{\parallel}_{p,W}$$$$={\left(\right)}^{\sum _{x\in U}}1/p$$If no reference to the weights sequence W is made, it is supposed to be ${w}_{x}=1$ for all $x\in U.$ The set D endowed with the distance ${d}_{p}$ gives a metric space $(D,{d}_{p})$.
- (2)
- Let us now define a metric in a different way, using the fuzzy version of a quasi-metric that can be defined in a canonical way using standard set theory operations. Let us motivate it in a non-fuzzy context. Given a class D of subsets of a given set $U,$ take $A,B,C\in D.$ Then we have that$$A\backslash C=\left(\right)open="["\; close="]">(A\backslash B)\backslash C\subset (A\backslash B)\cup (B\backslash C),$$$$q(A,C)\le q(A,B)+q(B,C)$$

**Lemma**

**1.**

**Proof.**

## 3. Trends as Fuzzy Sets of Concepts/Words/Tags

#### 3.1. Projection of Abstract Concepts on a Universe of Information Items

#### 3.2. What the Universe of Information Items U Is? Taxonomies, Ontologies and Machine Learning Tools

#### 3.3. Trends as Fuzzy Sets

## 4. Similarities between Trends as Distances between Fuzzy Sets: How the Algorithm Works

#### 4.1. Quasi-Metric for Fuzzy Sets

#### 4.2. Fitting Innovation Ideas and Trends

- (1)
- We formulate an innovation “idea” on any topic for which the trend system has been created, and relate to it a set of terms A in which the fundamental information is contained.
- (2)
- We compute the projection ${P}_{U}\left(A\right),$ that is a fuzzy set of elements of the universe $U.$ The subspace of all fuzzy subsets of U containing the relevant subsets have been fixed before.
- (3)
- We measure the (quasi-)distance $q(A,B)$ from ${P}_{U}\left(A\right)$ (we write A), and any fuzzy subset B that represents a trend.
- (4)
- $q(A,B)$ represents a measure of how close is our original ideal to the trend $B.$ Computing the distances with respect to any trend, we can measure “how far our idea is” from this trend.

#### 4.3. Indices as Lipschitz Functions on Metric Spaces of Trends

- Indices defined by expert supervision: we fix a set ${D}_{0}$ of trends that belong to D for which we have an evaluation given by a group of experts in the field. That is, we know the values of the index $I:{D}_{0}\to {\mathbb{R}}^{+},$ that are assumed to be right.
- Automatic computation of indices for selected items: we have an automatic procedure to estimate the index for a certain subset of trends ${D}_{0}$ using information coming from some internet-related source. For example, number of tweets detected that could be associated with hashtags that define a given trend.

## 5. A Basic Example: A System for Evaluating Innovative Ideas Based on Google Search

#### 5.1. Ideas and Trends Defined by Several Words

- (1)
- We can follow the same rule given for every couple of words as above, that is$$s({u}_{j},{u}_{k}):=p\left({u}_{j}\right){{|}_{{u}_{k}}=p\left({u}_{k}\right)|}_{{u}_{j}},\phantom{\rule{1.em}{0ex}}{u}_{j},{u}_{k}\in U.$$
- (2)
- We can impose an orthogonality criterium, inspired by the definition of orthogonal basis for a finite dimensional vector space. The words in U are considered as independent, each capturing a completely different aspect of the semantic field defined by $U.$ In this case,$$s({u}_{j},{u}_{k}):=0\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{if}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}j\ne k,\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{and}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}s({u}_{j},{u}_{j}):=1,\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{1.em}{0ex}}{u}_{j},{u}_{k}\in U.$$

#### 5.2. A Basic Example: A Specific Universe Formed by Current Trends for the Analysis of Innovative Ideas in Sustainable Economy

- (1)
- We define the universe U by six (sets of) terms/expressions:${u}_{1}=$ environment, ${u}_{2}=$ clean energy, ${u}_{3}=$ low carbon footprint, ${u}_{4}=$ recycling,${u}_{5}=$ low levels of chemical waste, ${u}_{6}=$ renewable raw materials.
- (2)
- We propose an innovative idea: the creation of a specific factory to replace plastic bags with paper bags in a big vegetable distribution company. The experts in the conceptual analysis based on Deflexor code this idea by means of the items$W1=$ “paper bags”, $W2=$ “removal of plastic bags”, $W3=$ “vegetable distribution”.As a part of the process of fixing this set of terms, these experts estimate the participation of the innovative idea of each one of these words with the weights$$({w}_{1},{w}_{2},{w}_{3})=(0.4,0.2,0.4).$$
- (3)
- For this simple example, we use to measure the relevance of trends and innovative ideas the number of documents that one can find in internet using Google Search. The idea is that we can measure in a rudimentary way how the terms ${u}_{1},\dots ,{u}_{6}$ of U are involved in the semantics of the words $W1,$$W2$ and $W3$ using the projection formula given by the ratio$$p\left({W}_{i}\right){|}_{{u}_{j}}=\frac{\u201c\mathrm{words}\phantom{\rule{4.pt}{0ex}}\mathrm{defining}\phantom{\rule{4.pt}{0ex}}\mathrm{a}\phantom{\rule{4.pt}{0ex}}\mathrm{fixed}\phantom{\rule{4.pt}{0ex}}\mathrm{element}\phantom{\rule{4.pt}{0ex}}{u}_{j}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}U\u201d\mathrm{AND}\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{words}\phantom{\rule{4.pt}{0ex}}\mathrm{defining}\phantom{\rule{4.pt}{0ex}}{W}_{i}\u201d}{\u201c\mathrm{words}\phantom{\rule{4.pt}{0ex}}\mathrm{defining}\phantom{\rule{4.pt}{0ex}}{W}_{i}\u201d},$$$i=1,2,3,\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}j=1,\dots ,6.$ The results can be found in Table 1 and are represented in Figure 2. Note that for the computations below we search for exact coincidences in Google, so if the explanation of the item is too complicated we could get the empty set, as happens with ${u}_{5}.$ We get
- (4)
- In order to quantify how “trendy” the innovative project is that we are using as an example, we decided to use three well-known trends in the field of the environment and green economy. In particular, we used the mechanism to measure if the idea is “main stream” how the innovative idea fits the trends given in Table 2.
- (5)
- As we are using the universe $U=\{{u}_{1},{u}_{2},{u}_{3},{u}_{4},{u}_{5},{u}_{6}\},$ as a reference system, we have to also compute how the trends considered are projected on the items of $U,$ that is, we have to calculate the coefficients$${p\left(Trend\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}i\right)|}_{{u}_{j}}=\frac{\u201c\mathrm{words}\phantom{\rule{4.pt}{0ex}}\mathrm{defining}\phantom{\rule{4.pt}{0ex}}\mathrm{a}\phantom{\rule{4.pt}{0ex}}\mathrm{fixed}\phantom{\rule{4.pt}{0ex}}\mathrm{element}\phantom{\rule{4.pt}{0ex}}{u}_{j}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}U\u201d\mathrm{AND}\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{words}\phantom{\rule{4.pt}{0ex}}\mathrm{defining}\phantom{\rule{4.pt}{0ex}}Trend\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}i\u201d}{\u201c\mathrm{words}\phantom{\rule{4.pt}{0ex}}\mathrm{defining}\phantom{\rule{4.pt}{0ex}}Trend\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}i\u201d},$$$i=1,2,3,\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}j=1,\dots ,6.$ The results are given in Table 3, and their representations can be seen in Figure 3.So, the (normalized) representations of these three trends on the universe U are$${P}_{U}\left(Trend1\right)=(0.806174,0.080617,0.010396,0.586068,0.000000,0.000496),$$$${P}_{U}\left(Trend2\right)=(0.902528,0.414839,0.000203,0.115548,0.000000,0.000203),$$$${P}_{U}\left(Trend3\right)=(0.706233,0.042898,0.024926,0.706233,0.000000,0.002908).$$
- (6)
- In the next step, we compute the projections of A on the three trends. The representation of A on the universe $U,$ taking into account the values presented in Table 1 and making the convex combination with coefficients ${w}_{1}=0.4,$${w}_{2}=0.2$ and ${w}_{3}=0.4,$ is$${P}_{U}\left(A\right)=(0.939903,0.071555,0.113830,0.145120,0,0.001318),$$$${p\left(A\right)|}_{Trend1}:=\left(\right)open="\langle "\; close="\rangle ">{P}_{U}\left(A\right),{P}_{U}\left(Trend1\right)$$$${p\left(A\right)|}_{Trend2}:=\left(\right)open="\langle "\; close="\rangle ">{P}_{U}\left(A\right),{P}_{U}\left(Trend2\right)$$$${p\left(A\right)|}_{Trend3}:=\left(\right)open="\langle "\; close="\rangle ">{P}_{U}\left(A\right),{P}_{U}\left(Trend3\right)$$
- (7)
- Now, we make a change in the Euclidean space of reference. Since we assume that Trend 1, Trend 2 and Trend 3 are the independent components of the system, and taking into account that they are linearly independent, we can define the metric as the distance from the vector represented as the projections of A on each trend to each of these trends, which are considered to be the vectors Trend 1 $=(1,0,0),$ Trend 2 $=(0,1,0)$ and Trend 3 $=(0,0,1).$ That is, if $x=({x}_{1},{x}_{2},{x}_{3})$ and $y=({y}_{1},{y}_{2},{y}_{3})$ are generic vectors represented by their coordinates with respect to the basis $\mathcal{T}=\{Trend1,Trend2,Trend3\},$ we define the distance by$$d(x,y)={\left(\right)}^{{({x}_{1}-{y}_{1})}^{2}}1/2$$After normalization with respect to this distance, we get the desired representation of A over $\mathcal{T},$$${p\left(A\right)|}_{\mathcal{T}}=(0.583745,0.614684,0.530477).$$

**Remark**

**1.**

- (8)
- Now we compute the Lipschitz extension of the Trend Index $=TI.$ A direct computation using the distances among the three trends given by the metric matrix$$d=\left[\begin{array}{ccc}0& \sqrt{2}& \sqrt{2}\\ \sqrt{2}& 0& \sqrt{2}\\ \sqrt{2}& \sqrt{2}& 0\end{array}\right],$$$$TI\left(Trend1\right)=298.000.000,\phantom{\rule{1.em}{0ex}}TI\left(Trend2\right)=7.960,TI\left(Trend3\right)=7.820.000.$$The distances from A to each of the trends are$$d(A,Trend1)=0.912420,\phantom{\rule{1.em}{0ex}}d(A,Trend2)=0.877857,\phantom{\rule{1.em}{0ex}}d(A,Trend3)=0.969043.$$Thus, we can estimate the Trend Index for the innovation idea A using the mean of the McShane and Whitney extension, obtaining$$T{I}^{M}\left(A\right)=105,741,949,\phantom{\rule{1.em}{0ex}}T{I}^{W}\left(A\right)=184,983,129.$$Thus, taking as extension the mean of these values (interpolation for $\alpha =1/2$), we get the final result$$TrendIndex\left(A\right)=TI\left(A\right)=145,362,539.$$If we normalize to the maximum value of $TI$ for all the trends, ($max=298,000,000,$) we get (approximately) the value $0.4878,$ that is, the “Relative Trend Index” is$$48.78\%\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathit{trend\; of\; the\; innovative\; idea\; A}$$

#### 5.3. A Shiny App for Trend Analysis Based on Deflexor

## 6. An Advanced Example

#### 6.1. The General Setting

- (1)
- We fix the proposed “idea” with a set of terms as simple as possible. An example would be $A=\left\{\u201c\mathrm{plastic}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{chair}\u201d\right\}$ in case we want to analyze the trends about the acceptance of a plastic chair with respect to the trends of the universe $U.$
- (2)
- We compute the projection ${P}_{U}\left(A\right),$ that gives for the term “plastic”$${P}_{U}\left({A}_{1}\right)=(0.2205327,0.2407994,0.4085899,0.3055694,0.4510627),$$(Figure 5a), and for the word “chair”$${P}_{U}\left({A}_{2}\right)=(0.1722883,0.2825582,0.2441297,0.2628509,0.4357773),$$(Figure 5b).
- (3)
- We measure the (quasi-)distance $q(A,B)$ from ${P}_{U}\left(A\right)$ and any fuzzy subset B that represents a trend.
- (4)
- $q(A,B)$ represents a measure of how close is our original idea to the trend $B.$ Computing the distances with respect to any trend, we can measure “how far our idea is” from this trend.

#### 6.2. How to Choose the Best Design Project According to Our Trend Analysis

## 7. Discussion: Using Deflexor to Motivate Open Innovation

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Fallis, D. A Conceptual Analysis of Disinformation; iConference: Chapel Hill, NC, USA, 2009; pp. 1–8. [Google Scholar]
- Margolis, E.; Laurence, S. Concepts; Stanford Encyclopedia of Philosophy: Stanford, CA, USA, 2006. [Google Scholar]
- Jackson, F. From Metaphysics to Ethics: A Defense of Conceptual Analysis; Oxford University Press: Oxford, UK, 1998. [Google Scholar]
- Guarino, N. Formal ontology, conceptual analysis and knowledge representation. Int. J. Hum. Comput. Stud.
**1995**, 43, 625–640. [Google Scholar] [CrossRef] [Green Version] - Deflexor 2033: Future Macrotrends Maps. Available online: https://deflexor.com/ (accessed on 19 January 2021).
- Lara-Navarra, P.; Falciani, H.; Sánchez-Pérez, E.A.; Ferrer-Sapena, A. Information management in healthcare and environment: Towards an automatic system for fake news detection. Int. J. Environ. Res. Public Health
**2020**, 17, 1066. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lara-Navarra, P.; López-Borrull, A.; Sánchez-Navarro, J.; Yànez, P. Medición de la influencia de usuarios en redes sociales: Propuesta SocialEngagement. Prof. Inf.
**2018**, 27, 899–908. [Google Scholar] [CrossRef] - Martínez-Martínez, S.; Lara-Navarra, P. El big data transforma la interpretación de los medios sociales. Prof. Inf.
**2015**, 23, 575–581. [Google Scholar] [CrossRef] [Green Version] - Cobzaş, Ş.; Miculescu, R.; Nicolae, A. Lipschitz Functions; Springer: Berlin/Heidelberg, Germany, 2019. [Google Scholar]
- Schwartz, J.T. Nonlinear Functional Analysis; Gordon and Breach Science: New York, NY, USA, 1969. [Google Scholar]
- Juutinen, P. Absolutely minimizing Lipschitz extensions on a metric space. Ann. Acad. Sci. Fenn.
**2002**, 27, 57–67. [Google Scholar] - Mustăţa, C. Extensions of semi-Lipschitz functions on quasi-metric spaces. Rev. Anal. Numer. Theor. Approx.
**2001**, 30, 61–67. [Google Scholar] - Mustăţa, C. On the extremal semi-Lipschitz functions. Rev. Anal. Numer. Theor. Approx.
**2002**, 31, 103–108. [Google Scholar] - Romaguera, S.; Sanchis, M. Semi-Lipschitz functions and best approximation in quasi-metric spaces. J. Approx. Theory
**2000**, 103, 292–301. [Google Scholar] [CrossRef] - Dugundji, J. Topology; Allyn and Bacon Inc.: Boston, MA, USA, 1966. [Google Scholar]
- Kelley, J.L. General Topology; Dover Publications, Inc.: Mineola, NY, USA, 2017. [Google Scholar]
- Willard, S. General Topology; Addison-Wesley: Reading, MA, USA, 1970. [Google Scholar]
- McShane, E.J. Extension of range of functions. Bull. Am. Math. Soc.
**1934**, 40, 837–842. [Google Scholar] [CrossRef] [Green Version] - Whitney, H. Analytic extensions of functions defined in closed sets. Trans. Am. Math. Soc.
**1934**, 36, 63–89. [Google Scholar] [CrossRef] - Barsalou, L.W.; Simmons, W.K.; Barbey, A.K.; Wilson, C.D. Grounding conceptual knowledge in modality-specific systems. Trends Cogn. Sci.
**2003**, 7, 84–91. [Google Scholar] [CrossRef] - El-Diraby, T.E. Domain ontology for construction knowledge. J. Constr. Eng. Manag.
**2013**, 139, 768–784. [Google Scholar] [CrossRef] - Annesi, P.; Storch, V.; Basili, R. Space projections as distributional models for semantic composition. In Proceedings of the International Conference on Intelligent Text Processing and Computational Linguistics, New Delhi, India, 11–17 March 2012; Springer: Berlin/Heidelberg, Germany, 2012; pp. 323–335. [Google Scholar]
- Grand, G.; Blank, I.A.; Pereira, F.; Fedorenko, E. Semantic projection: Recovering human knowledge of multiple, distinct object features from word embeddings. arXiv
**2018**, arXiv:1802.01241. [Google Scholar] - Xiao, H.; Huang, M.; Meng, L.; Zhu, X. SSP: Semantic space projection for knowledge graph embedding with text descriptions. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, CA, USA, 4–9 February 2017. [Google Scholar]
- Fanizzi, N.; d’Amato, C.; Esposito, F. Metric-based stochastic conceptual clustering for ontologies. Inf. Syst.
**2009**, 34, 792–806. [Google Scholar] [CrossRef] - Yang, H.; Callan, J. Metric-based ontology learning. In Proceedings of the 2nd International Workshop on Ontologies and Information Systems for the Semantic Web, Napa Valley, CA, USA, 30 October 2008; pp. 1–8. [Google Scholar]
- Gangemi, A.; Catenacci, C.; Ciaramita, M.; Lehmann, J. Modelling ontology evaluation and validation. In The Semantic Web: Research and Applications, Proceedings of the European Semantic Web Conference (ESWC), Budva, Montenegro, 11–14 June 2006; York, S., Domingue, J., York, S., Domingue, J., Eds.; Springer: Berlin/Heidelberg, Germany, 2006; pp. 140–154. [Google Scholar]
- Sure, Y.; Domingue, J. (Eds.) The Semantic Web: Research and Applications; Springer: Berlin/Heidelberg, Germany, 2006. [Google Scholar]
- Lau, R.Y.; Li, C.; Liao, S.S. Social analytics: Learning fuzzy product ontologies for aspect-oriented sentiment analysis. Decis. Support Syst.
**2014**, 65, 80–94. [Google Scholar] [CrossRef] - Arguello Casteleiro, M.; Demetriou, G.; Read, W.; Fernández Prieto, M.J.; Maroto, M.; Maseda Fernández, D.; Nenadic, G.; Klein, J.; Keane, J.; Stevens, R. Deep learning meets ontologies: Experiments to anchor the cardiovascular disease ontology in the biomedical literature. J. Biomed. Semant.
**2018**, 9, 1–24. [Google Scholar] [CrossRef] [Green Version] - Nezhadi, A.H.; Shadgar, B.; Osareh, A. Ontology alignment using machine learning techniques. Int. J. Comput. Sci. Inf. Technol.
**2011**, 3, 139–149. [Google Scholar] - Albagli, S.; Ben-Eliyahu-Zohary, R.; Shimony, S.E. Markov network based ontology matching. J. Comput. Syst. Sci.
**2012**, 78, 105–118. [Google Scholar] [CrossRef] [Green Version] - Cerón-Figueroa, S.; López-Yánez, I.; Alhalabi, W.; Camacho-Nieto, O.; Villuendas-Rey, Y.; Aldape-Pérez, M.; Yánez-Márquez, C. Instance-based ontology matching for e-learning material using an associative pattern classifier. Comput. Hum. Behav.
**2017**, 69, 218–225. [Google Scholar] [CrossRef] - Laadhar, A.; Ghozzi, F.; Bousarsar, I.M.; Ravat, F.; Teste, O.; Gargouri, F. The Impact of Imbalanced training Data on Local matching learning of ontologies. In Proceedings of the 22nd International Conference Business Information Systems BIS 2019, Seville, Spain, 26–28 June 2019; Abramowicz, W., Corchuelo, R., Eds.; Springer: Cham, Switzerland, 2019. [Google Scholar]
- Otero-Cerdeira, L.; Rodríguez-Martínez, F.J.; Gómez-Rodríguez, A. Ontology matching: A literature review. Expert Syst. Appl.
**2015**, 42, 949–971. [Google Scholar] [CrossRef] - Rubiolo, M.; Caliusco, M.L.; Stegmayer, G.; Coronel, M.; Fabrizi, M.G. Knowledge discovery through ontology matching: An approach based on an Artificial Neural Network model. Inf. Sci.
**2012**, 194, 107–119. [Google Scholar] [CrossRef] - Nkisi-Orji, I.; Wiratunga, N.; Massie, S.; Hui, K.-Y.; Heaven, R. Ontology alignment based on word embedding and random forest classification. In Machine Learning and Knowledge Discovery in Databases, Proceedings of the Conference ECML PKDD 2018. LNCS (LNAI), Dublin, Ireland, 10–14 September 2018; Berlingerio, M., Bonchi, F., Gärtner, T., Hurley, N., Ifrim, G., Eds.; Springer: Berlin/Heidelberg, Germany, 2019; pp. 557–572. [Google Scholar]
- Abramowicz, W.; Corchuelo, R. Business Information Systems. In Proceedings of the 22nd International Conference, BIS 2019, Seville, Spain, 26–28 June 2019; Springer Nature: Cham, Switzerland, 2019. [Google Scholar]
- Cross, V. Fuzzy semantic distance measures between ontological concepts. In Proceedings of the IEEE Annual Meeting of the Fuzzy Information, NAFIPS’04, Banff, AB, Canada, 27–30 June 2004; Volume 2, pp. 635–640. [Google Scholar]
- Cross, V.; Yu, X. Investigating ontological similarity theoretically with fuzzy set theory, information content, and Tversky similarity and empirically with the gene ontology. In Proceedings of the International Conference on Scalable Uncertainty Management, Dayton, OH, USA, 10–13 October 2011; Springer: Berlin/Heidelberg, Germany, 2011; pp. 387–400. [Google Scholar]
- Jiang, Y.; Liu, H.; Tang, Y.; Chen, Q. Semantic decision making using ontology-based soft sets. Math. Comput. Model.
**2011**, 53, 1140–1149. [Google Scholar] [CrossRef] - Martínez-Cruz, C.; Noguera, J.M.; Vila, M.A. Flexible queries on relational databases using fuzzy logic and ontologies. Inf. Sci.
**2016**, 366, 150–164. [Google Scholar] [CrossRef] - Zhai, J.; Chen, Y.; Wang, Q.; Lv, M. Fuzzy ontology models using intuitionistic fuzzy set for knowledge sharing on the semantic web. In Proceedings of the 12th International Conference on Computer Supported Cooperative Work in Design, Xi’an, China, 16–18 April 2008; pp. 465–469. [Google Scholar]
- Furniture. Available online: https://en.wikipedia.org/wiki/List-of-furniture-types (accessed on 9 February 2021).
- Yun, J.J.; Kim, D.; Yan, M. Open innovation engineering—Preliminary study on new entrance of technology to market. Electronics
**2020**, 9, 791. [Google Scholar] [CrossRef] - Munir, H.; Wnuk, K.; Runeson, P. Open innovation in software engineering: A systematic mapping study. Empir. Softw. Eng.
**2016**, 21, 684–723. [Google Scholar] [CrossRef] - Petersen, K.; Vakkalanka, S.; Kuzniarz, L. Guidelines for conducting systematic mapping studies in software engineering: An update. Inf. Softw. Technol.
**2015**, 64, 1–18. [Google Scholar] [CrossRef] - Yun, J.J.; Liu, Z. Micro-and macro-dynamics of open innovation with a quadruple-helix model. Sustainability
**2019**, 11, 3301. [Google Scholar] [CrossRef] [Green Version] - Noble, C.H.; Durmusoglu, S.S.; Griffin, A. (Eds.) Open Innovation New Product Development Essentials from the PDMA; John Wiley and Sons Inc.: Hoboken, NJ, USA, 2014. [Google Scholar]
- Saguy, I.S. Challenges and opportunities in food engineering: Modeling, virtualization, open innovation and social responsibility. J. Food Eng.
**2016**, 176, 2–8. [Google Scholar] [CrossRef] - Calabuig, J.M.; Falciani, H.; Sánchez-Pérez, E.A. Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial markets. Neurocomputing
**2020**, 398, 172–184. [Google Scholar] [CrossRef] [Green Version] - Ferrer-Sapena, A.; Erdogan, E.; Jiménez-Fernández, E.; Sánchez-Pérez, E.A.; Peset, F. Self-defined information indices: Application to the case of university rankings. Scientometrics
**2020**, 124, 2443–2456. [Google Scholar] [CrossRef]

**Figure 1.**General scheme of the universe created for Deflexor. Although the words written in the nodes cannot be read, the picture gives an idea of the complexity of categories (big fields), concepts (words) and relations (arrows) of the model. More information can be found in [5].

**Figure 4.**Representation of the projection of the object “wood house” on a restricted universe based on Deflexor.

**Figure 5.**(

**a**) Representation of the projection of the object “plastic” on the universe U. (

**b**) Representation of the projection of the object “chair” on the universe U.

**Figure 6.**Representation of the projection of the object “desk” on the universe $U=\left\{\u201c\mathrm{sustainable}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{environment}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{wood}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{waste}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{furniture}\u201d\right\}$.

**Figure 7.**Representation of the projection of the object “cabinet” on the universe $U=\left\{\u201c\mathrm{sustainable}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{environment}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{wood}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{waste}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{furniture}\u201d\right\}$.

**Figure 8.**Representation of the projection of the object “carpet” on the universe $U=\left\{\u201c\mathrm{sustainable}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{environment}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{wood}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{waste}\u201d,\phantom{\rule{4.pt}{0ex}}\u201c\mathrm{furniture}\u201d\right\}$.

${\mathit{u}}_{1}$ | ${\mathit{u}}_{2}$ | ${\mathit{u}}_{3}$ | ${\mathit{u}}_{4}$ | ${\mathit{u}}_{5}$ | ${\mathit{u}}_{6}$ | |
---|---|---|---|---|---|---|

W1 | 0.212143 | 0.016 | 0.00135 | 0.000003 | 0 | 0.000693 |

W2 | 0.887805 | 0.08 | 0.629268 | 0.531707 | 0 | 0.000010 |

W3 | 0.737101 | 0.052826 | 0.014201 | 0.107371 | 0 | 0.000025 |

Trend 1 | Trend 2 | Trend 3 | |
---|---|---|---|

Definition: | “sustainability” | “proximity trade” | “circular economy” |

Items in Google: | 298.000.000 | 7.960 | 7.820.000 |

${\mathit{u}}_{1}$ | ${\mathit{u}}_{2}$ | ${\mathit{u}}_{3}$ | ${\mathit{u}}_{4}$ | ${\mathit{u}}_{5}$ | ${\mathit{u}}_{6}$ | |
---|---|---|---|---|---|---|

Trend 1 | 1 | 0.1 | 0.012895 | 0.726974 | 0 | 0.000615 |

Trend 2 | 0.560302 | 0.257538 | 0.000126 | 0.071734 | 0 | 0.000126 |

Trend 3 | 1 | 0.060742 | 0.035294 | 1 | 0 | 0.004118 |

**Table 4.**Projections for the terms considered, together with the corresponding values of the (extended) index ${I}_{F}/Ext$.

Terms | Sustain. | Environ. | Wood | Waste | Furniture | ${\mathit{I}}_{\mathit{F}}$/Ext |
---|---|---|---|---|---|---|

chair | 0.1722 | 0.2825 | 0.2441 | 0.2628 | 0.4357 | 0.4867 |

table | 0.1562 | 0.1762 | 0.4399 | 0.1623 | 0.25 | 0.7421 |

mirror | 0.1645 | 0.2096 | 0.4170 | 0.1805 | 0.3017 | 0.7069 |

bed | 0.1807 | 0.2511 | 0.3723 | 0.2779 | 0.3748 | 0.5948 |

sofa | 0.0799 | 0.1069 | 0.312 | 0.1004 | 0.1544 | 0.7416 |

desk | 0.1317 | 0.2356 | 0.1891 | 0.2417 | 0.1756 | 0.632 |

cabinet | 0 | 0 | 0.0693 | 0 | 0.163 | 0.721 |

carpet | 0 | 0.1337 | 0 | 0 | 0.2168 | 0.6743 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Manetti, A.; Ferrer-Sapena, A.; Sánchez-Pérez, E.A.; Lara-Navarra, P.
Design Trend Forecasting by Combining Conceptual Analysis and Semantic Projections: New Tools for Open Innovation. *J. Open Innov. Technol. Mark. Complex.* **2021**, *7*, 92.
https://doi.org/10.3390/joitmc7010092

**AMA Style**

Manetti A, Ferrer-Sapena A, Sánchez-Pérez EA, Lara-Navarra P.
Design Trend Forecasting by Combining Conceptual Analysis and Semantic Projections: New Tools for Open Innovation. *Journal of Open Innovation: Technology, Market, and Complexity*. 2021; 7(1):92.
https://doi.org/10.3390/joitmc7010092

**Chicago/Turabian Style**

Manetti, Alessandro, Antonia Ferrer-Sapena, Enrique A. Sánchez-Pérez, and Pablo Lara-Navarra.
2021. "Design Trend Forecasting by Combining Conceptual Analysis and Semantic Projections: New Tools for Open Innovation" *Journal of Open Innovation: Technology, Market, and Complexity* 7, no. 1: 92.
https://doi.org/10.3390/joitmc7010092