- Email: [email protected]
Modelling uncertainty
Information Sciences 180 (2010) 799–802
Contents lists available at ScienceDirect
Information Sciences journal homepage: www.elsevier.com/locate/ins
Editorial
Modelling uncertainty
a r t i c l e
i n f o
Keywords: Uncertainty Computing with words Information management Decision aid
a b s t r a c t In this note, we stress the relevance of developing tools for modelling uncertainty in information management and decision aiding, conceived as previous stages for decision making. We discuss the general framework of modelling uncertainty in decision making problems and briefly introduce the specific models we have selected to illustrate these ideas, as developed by researchers. Ó 2009 Elsevier Inc. All rights reserved.
1. The meaning of uncertainty Experimental sciences have been established on the basis of data, which become nowadays an essential prerequisite in the foundation of any scientific theory. This approach to reality contains some more or less hidden issues that deserve a careful discussion, already addressed by classical and modern Philosophy of Science (see, e.g., the classical works of Popper [31] and Feyerabend [13]). A first controversial issue is the potential identification of data and reality. A confusion that may appear meanwhile is that the scientist, as observer, understands that data represents a section of reality. Data are being seen as a subset of reality. A naïve observer can even force this identification, imposing that Science should pursue at its final objective the complete knowledge of reality, by means of certain data subsets that explain the whole reality under study. And since those data are subject to some (hopefully limited) imprecision because of the particular measurement machine, the observer may think that uncertainty is simply this lack of precision. Things are the way they are and nothing can stop us to decrease imprecision with more and more accurate machines. In this way, it is being assumed that Science starts with a direct description of certain section of reality (which has been selected by observer if obtained by means of a previously designed experiment). The observer easily becomes a deterministic scientist, as most scientists in the 19th century were. Even classical probability talks about uncertainty as a measure lack of knowledge. In fact, for Probability beginners, Probability has something to say only meanwhile complete information stage is not reached. The role of Probability decreases simultaneously with information acquisition. Hence, 19th century scientists had serious difficulties in accepting Probability as a scientific tool, based on the idea that uncertainty (understood as a lack of precision) was precisely the enemy of Science. It had no sense to model such a lack of information, only fighting against this uncertainty was a legitimate scientific objective. Probability had to wait to Quantum Mechanics in the 20th century to enter into the great Science world, proving that uncertainty was not evitable. The observer is always inside the experiment being run and probability distributions do not model just imprecision. On the other hand, it should be acknowledged that classical Probability was not properly expressing the uncertainty issue in those terms, but within a decision making problem. Probability beginners were not trying to model uncertainty itself but to evaluate real-world situations in terms of the chances associated to future possible consequences and their estimated cost. Over time, this position will be formulated in terms of uncertainty as perceived by the observer, producing what we call Subjective Probability (uncertainty is in each observer’s mind, who knows what happens in the real-world). Probability beginners were not focusing in the world’s physical uncertainty, but in the human perception, and it is within this framework where Probability appears as a modelling tool. It is not that the observer is inside the experiment, but that the observer is in some way the experiment itself. In this sense, a major revolution introduced by Probability was to move the object of study into the human perception framework. Still, any scientific theory needs to connect with reality by means of some kind of experimentation, so Probability model was finally formalized by Kolmogorov [19] in terms of a given experiment, and according to a basic consistency test: 0020-0255/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2009.11.026
800
Editorial / Information Sciences 180 (2010) 799–802
observer must be able to decide from data (the result of each experiment) if each possible event under study can be verified or not. This apparently innocuous consistency test contains, as modeled by Kolmogorov [19], a tremendous hidden assumption: the Aristotelian logic. This assumption may not be considered extremely relevant meanwhile we restrict ourselves to collect crisp information and we make crisp questions, a restriction that may be the standard within experimental Sciences. Only then we can assume that events are represented in terms of subsets of all possible results of the experiment. Therefore, assuming that observation of reality is objective is somehow misleading, since the experiment itself and the whole observation depend on the human perception, which depends on individual senses, concepts learnt in the past (consciously or not), and the logic being chosen for their manipulation, among other things. What we call data has been already processed by our brains. We actually see only those things we are ready to see. Data is not a part of reality, but something constructed by observer. The drama in Science is that the historical scientific pressure to build models from data, together with the cultural lack of an alternative logic to Aristotelian logic, has made many scientists think that they were not using any human logic and that their experiments were not conducted by a previous arbitrary personal choice. Not being deeply discussed (the first complete alternative logic had to wait till Lukasiewicz [23], early 20th century), Aristotelian binary logic has been taken in experimental Science for granted. In this context, we can understand that for an experimental scientist information is always crisp. At the same time we should all be surprised when certain common words (like much, quite, or low) are used in polls without realizing that such words cannot be properly associated to crisp concepts, and that a probabilistic approach to those words is simply an approach, subject to obvious paradoxes (everybody can agree on a yes when forced to choose between yes and no, being none of these two answers the right answer to the question). While Probability was born within a human perception framework, we should then ask ourselves if the Boolean approach imposed by set theory is the most appropriate to those problems where human perception plays a key role. In fact, last studies in neurology (see, e.g., [5,22]) point that the human brain works with sophisticated representations of concepts, where the true decision making issue takes place. Human decision making invokes several machineries located in different parts of the brain [16] and, in particular, final executive decision is mainly associated with emotion [3,4], the rational analysis playing a decision support role that produces a global picture in terms of a conceptual map. Nevertheless, words can be seen as a standard description for concepts. Much more important, the fact is that decision making processes within a conceptual framework do not adhere to the Aristotelian postulates. Our human discourse is far being binary: there are lots of intermediate different kinds of partial truths, lots of different types of assertions and negations, conjunctions, disjunctions, numerous summarizing operators, and a great deal of different kinds of representation models (natural language is indeed one of them). The recent calls from Zadeh, the founder of Fuzzy Set Theory [39], for a new perception-based rather than a measurement-based logic [42] (with the ability to model human-centric fields such as economics, law, linguistics and psychology [41]), is in this sense fully justified (see also [43,44]). Once we move outside what we call now experimental Science (Science based upon numeric experimentation and its Aristotelian logical analysis), we find that Social Sciences (partially including Economy) acutely need models that allow the management of concepts (see also [28]). Alternative models to Probability are needed to complement the management of uncertainty, whenever information is given in terms of words associated to concepts. This special issue is a testimony to this important research trend.
2. Decision making under uncertainty From the above comments, we can note that the concept of uncertainty has been mostly associated to the way human beings understand and perceive reality. It is then extremely important to distinguish between the formal (mathematical) models and reality. Every proposed model is continuously tested, comparing predictions realized by the model and observations. But whenever such a model has been built as a result of a human decision making problem, no matter how precise it becomes, the model itself and its practical consequences usually need to be translated into the natural language. As succinctly pointed out by Zadeh, it is not the mathematical theorem the one commonly considered by decision makers, but a soft version of such a result [40]. Again, comprehension of a decision making problem used to be within a conceptual framework, and it is such a comprehension the main objective we all pursue when faced to a complex decision making problem (it implies a global view of the problem, avoiding the risk of a decision maker getting lost within any apparently definitive facts that represent only partial facts). The analysis of the problem we are facing is the core we can address with a sincere rationality. In this context, for example, encountering contradictory arguments is not a blocking paradox: if contradictory arguments exist, we just need to realize its meaning and find an explanation (decision aiding focus within this aiding analysis). The non-existence of contradiction in an argument is a deduction from Aristotelian logic (which does not belong to reality but to human mind, which previously to its use imposes a serious conceptual restriction). Making a choice within a conflicting situation is another problem, and it is a problem of a nature being absolutely different from the nature of the previous analytic comprehensive stage (see also [15,21]). Such a comprehensive stage represents the natural field for decision aiding [27,29]. The development of analytical representation models plays here the main role, of course including natural language but also the fusion aggregative models needed to compress information and those image representation and graphical techniques that allow a better knowledge of the structure of information and the problem itself (see, e.g., [7]).
Editorial / Information Sciences 180 (2010) 799–802
801
Due to the potential difficulties of dealing effectively with decision making in complex systems, information (or data) obtained by the above-mentioned or the reported different approaches in this special issue will be of very different nature. It may be heuristic or incomplete or data that is either of unknown origin or may be out of date or imprecise, or not fully reliable, or conflicting, and even overloaded. It is considered advantageous to have a sound and reliable mathematical framework available that provides a basis for synthesis across multidimensional information of varying quality, especially to deal with information that is not quantifiable due to its nature, and that is too complex and ill-defined, for which the traditional quantitative approach (e.g., the statistical approach) does not give an adequate answer. We have already seen some examples of such approaches as previously published in Information Sciences (pertinent to the present discussion are, e.g., [12,14,17,30,45]). 3. Contents of this special issue This special issue has its origin in the 8th International FLINS Conference on Computational Intelligence and Decision Control [34] held in Madrid (Spain), September 21–24, 2008. FLINS stands for Fuzzy Logic and Intelligent Technologies in Nuclear Science, a project launched by the Belgian Nuclear Research Centre (SCKCEN) whose initial objectives have evolved into a wide view of computational intelligence in decision and control, with the ultimate objective of fostering advances in the theory and applications of decision making and control for complex systems (see, e.g., [33,34,38]). In line with the declared objectives of the FLINS initiative to promote the multidisciplinary interchange between different scientific and industrial fields, this special issue was conceived to produce a representative sample of the ongoing research devoted to tools for dealing with uncertainty. After an open call, 24 papers were selected in a first peer review process based upon a 6-page extended abstracts. Then, the long versions of those papers were submitted to Information Sciences, where a standard peer review process produced this special issue with the current nine accepted papers. The first part of this special issue mainly addresses theoretical issues about uncertainty modelling treated from different approaches. In the first paper, Mayor and Valero [25] consider a general description of how to combine a collection of measures [6,32], reducing the dimension of the information into a simpler but informative fusion. In the second paper, Wang et al. [37] consider Shafer’s Theory of Evidence [35] showing how to efficiently combine and derive a mass function from multivariate data sets. In the third paper, Castiñeira et al. [8] address the incompatibility problem within Atanassov’s Intuitionistic Fuzzy Sets framework [2] (see also [10,11,26]) by means of geometrical methods. In the fourth paper, Torres-Blanc et al. [36] propose an axiomatic model to measure how contradictory certain information is. The second part of this special issue mainly focuses on applications. First, Martín et al. [24] offer a novel technique for the extraction of uncorrelated variant features of images and signals, a technique that can be treated as an alternative to classical statistical approaches, which is applied to shape analysis, image segmentation, tracking deformations and object motion tacking. Then, Kaya and Kahraman [18] propose a new decision making tool to determine the best supplier for building materials, based on fuzzy accuracy indices to evaluate process performance, inspired in Statistics but modified to allow fuzzy specification limits. The third paper in this applied section is devoted to knowledge discovery, where Kong et al. [20] look into an explore investment stock market decision support by searching for multi-temporal patterns. In the fourth paper, Cebi et al. [9] provide an original decision aid tool for classifying societies to redesign primary project layouts, which is then applied to the shipping industry. Finally, the paper by Alonso and Santos [1] shows how a genetic algorithm is used to optimize maneuvers involving a two-stage rocket. 4. Final notes In this special issue, we have illustrated some recent advances in the search for uncertainty management, allowing an interesting view to some specific perspectives, addressing not only some formal developments but also bringing some interesting applications. We hope the readers will find this special issue both informative and inspiring. Acknowledgments The work presented in this paper was in part supported by the Government of Spain under the Project Grant TIN200907901. We thank Prof. Witold Pedrycz for his continuous support towards this project, kindly encouraging the authors to improve the quality of their final research papers. References [1] [2] [3] [4] [5] [6] [7] [8]
F. Alonso, M. Santos, Multi-criteria genetic optimization of the manoeuvres of a two-stage launcher, Information Sciences, this issue. K. Atanassov, Intuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, 1999. A. Bechara, H. Damasio, A.R. Damasio, Role of the amygdala in decision making, Annals of the New York Academy of Sciences 985 (2003) 356–369. A. Bechara, D. Tranel, H. Damasio, Characterization of the decision-making deficit of patients with ventromedial prefrontal cortex lesions, Brain 123 (2000) 189–2202. E.D. Booman, M.F.S. Rushworth, Conceptual representation and the making of new decisions, Neuron 63 (2009) 721–723. J. Borsik, J. Dobos, On a product of metric spaces, Mathematica Slovaka 31 (1981) 193–205. H. Bustince, F. Herrera, J. Montero, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, Springer, Berlin, 2008. E.E. Castiñeira, S. Cubillo, W. Montilla, Measuring incompatibility between Atanassov’s Intuitionistic fuzzy sets, Information Sciences, this issue.
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[9] S. Cebi, M. Celik, M. Kahraman, Structuring ship design project approval mechanism towards installation of operator-system interfaces via fuzzy axiomatic design principles, Information Sciences, this issue. [10] G. Deschirijver, E.E. Kerre, On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision, Information Sciences 177 (2007) 1860–1866. [11] D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, H. Prade, Terminological difficulties in fuzzy set theory – the case of intuitionistic fuzzy sets, Fuzzy Sets and Systems 156 (2005) 485–491. [12] T. Ertay, D. Ruan, U.R. Tuzkaya, Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems, Information Sciences 176 (2006) 237–262. [13] P.K. Feyerabend, Against Method, Verso, London, 1993. [14] D. Gómez, J. Montero, J. Yánez, A coloring algorithm for image classification, Information Sciences 176 (2006) 3645–3657. [15] M. Hsu, M. Bahtt, R. Adolfs, D. Tranel, C.F. Camarer, Neural systems responding to degrees of uncertainty in human decision-making, Science 310 (2005) 1680–1683. [16] J.W. Kable, P.W. Glimcher, The neurobiology of decision: consensus and controversy, Neuron 63 (2009) 733–745. [17] C. Kahraman, D. Ruan, E. Tolga, Capital budgeting techniques using discounted fuzzy versus probabilistic cash flows, Information Sciences 142 (2002) 57–76. [18] I. Kaya, C. Kahraman, Development of fuzzy process accuracy index for decision making problems, Information Sciences, this issue. [19] A.N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, New York, 1956. [20] X. Kong, Q. Wei, G. Chen, An approach to discovering mutli-temporal patterns and its application to financial databases, Information Sciences, this issue. [21] J. Kounios, J.L. Frymiare, E.M. Bowden, J.I. Fleck, K. Subramaniam, T.B. Parrish, M. Jung-Beeman, The prepared mind neural activity prior to problem presentation predicts subsequent solution by sudden insight, Psychological Science 17 (2006) 882–890. [22] D. Kumaran, J.J. Summerfield, D. Hassabais, E.A. Maguire, Tracking the emergence of conceptual knowledge during human decision making, Neuron 63 (2009) 889–901. [23] J. Lukasiewicz, On 3-valued logic, in: S. McCall (Ed.), Polish Logic, Oxford U.P., Oxford, 1967. [24] J.M. Martín, M. Santos, J. De Lope, Orthogonal variant moments features in image analysis, Information Sciences, this issue. [25] G. Mayor, O. Valero, Aggregation of asymmetric distances in computer science, Information Sciences, this issue. [26] J. Montero, D. Gómez, H. Bustince, On the relevance of some families of fuzzy sets, Fuzzy Sets and Systems 158 (2007) 2439–2442. [27] J. Montero, Classifiers and decision makers, in: D. Ruan et al. (Eds.), Applied Computational Intelligence, World Scientific, Singapore, 2003, pp. 19–24. [28] J. Montero, Fuzzy logic and science, Studies in Fuzziness and Soft Computing 243 (2009) 67–78. [29] J. Montero, V. López, D. Gómez, The role of fuzziness in decision making, in: D. Ruan et al. (Eds.), Fuzzy Logic: A Spectrum of Applied and Theoretical Issues, Springer, Berlin, 2006, pp. 337–349. [30] Z. Pei, Y. Xu, D. Ruan, K. Qin, Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations, Information Sciences 179 (2009) 2325–2332. [31] K.R. Popper, The Logic of Scientific Discovery, Routledge, London, 2002. [32] S. Romaguera, M. Schellekens, Topology and its Applications 98 (1999) 311–322. [33] D. Ruan, F. Hardeman, K. van der Meer (Eds.), Intelligent Decision and Policy Making Support Systems, Springer, Heidelberg, 2008. [34] D. Ruan, J. Montero, J. Lu, L. Martinez, P. D’hondt, E.E. Kerre (Eds.), Computational Intelligence in Decision and Control, The Proceedings of FLINS2008, World Scientific, Singapore, 2008. [35] G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, 1976. [36] C. Torres-Blanc, S. Cubillo, E.E. Castiñeira, An axiomatic model for measuring contradiction and N-contradiction between two AIFSs, Information Sciences, this issue. [37] H. Wang, J. Liu, J.C. Augusto, Mass function derivation and combination in multivariate data spaces, Information Sciences, this issue. [38] X. Wang, D. Ruan, E.E. Kerre, Mathematics of Fuzziness – Basic Issues, Springer, Heidelberg, 2009. [39] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353. [40] L.A. Zadeh, The concept of linguistic variable and its application to approximate reasoning, part 3, Information Sciences 9 (1975) 43–80. [41] L.A. Zadeh, Is there a need for fuzzy logic?, Information Sciences 178 (2008) 2751–2779 [42] L.A. Zadeh, Toward extended fuzzy logic – a first step, Fuzzy Sets and Systems 160 (2009) 3175–3181. [43] L.A. Zadeh, J. Kacprzyk (Eds.), Computing with Words in Information-intelligent Systems, vol. 1, Physica-Verlag, Heidelberg, 1999. [44] L.A. Zadeh, J. Kacprzyk (Eds.), Computing with Words in Information-intelligent Systems, vol. 2, Physica-Verlag, Heidelberg, 1999. [45] C. Zhou, D. Ruan, Fuzzy control rules extraction from perception-based information using computing with words, Information Sciences 142 (2002) 275–290.
Javier Montero Faculty of Mathematics, Complutense University of Madrid, Spain Tel.: +34 91 394 4522; fax: +34 91 394 4607 E-mail address: [email protected] Da Ruan Belgian Nuclear Research Centre (SCKCEN) and Ghent University, Belgium E-mail address: [email protected]
Contents lists available at ScienceDirect
Information Sciences journal homepage: www.elsevier.com/locate/ins
Editorial
Modelling uncertainty
a r t i c l e
i n f o
Keywords: Uncertainty Computing with words Information management Decision aid
a b s t r a c t In this note, we stress the relevance of developing tools for modelling uncertainty in information management and decision aiding, conceived as previous stages for decision making. We discuss the general framework of modelling uncertainty in decision making problems and briefly introduce the specific models we have selected to illustrate these ideas, as developed by researchers. Ó 2009 Elsevier Inc. All rights reserved.
1. The meaning of uncertainty Experimental sciences have been established on the basis of data, which become nowadays an essential prerequisite in the foundation of any scientific theory. This approach to reality contains some more or less hidden issues that deserve a careful discussion, already addressed by classical and modern Philosophy of Science (see, e.g., the classical works of Popper [31] and Feyerabend [13]). A first controversial issue is the potential identification of data and reality. A confusion that may appear meanwhile is that the scientist, as observer, understands that data represents a section of reality. Data are being seen as a subset of reality. A naïve observer can even force this identification, imposing that Science should pursue at its final objective the complete knowledge of reality, by means of certain data subsets that explain the whole reality under study. And since those data are subject to some (hopefully limited) imprecision because of the particular measurement machine, the observer may think that uncertainty is simply this lack of precision. Things are the way they are and nothing can stop us to decrease imprecision with more and more accurate machines. In this way, it is being assumed that Science starts with a direct description of certain section of reality (which has been selected by observer if obtained by means of a previously designed experiment). The observer easily becomes a deterministic scientist, as most scientists in the 19th century were. Even classical probability talks about uncertainty as a measure lack of knowledge. In fact, for Probability beginners, Probability has something to say only meanwhile complete information stage is not reached. The role of Probability decreases simultaneously with information acquisition. Hence, 19th century scientists had serious difficulties in accepting Probability as a scientific tool, based on the idea that uncertainty (understood as a lack of precision) was precisely the enemy of Science. It had no sense to model such a lack of information, only fighting against this uncertainty was a legitimate scientific objective. Probability had to wait to Quantum Mechanics in the 20th century to enter into the great Science world, proving that uncertainty was not evitable. The observer is always inside the experiment being run and probability distributions do not model just imprecision. On the other hand, it should be acknowledged that classical Probability was not properly expressing the uncertainty issue in those terms, but within a decision making problem. Probability beginners were not trying to model uncertainty itself but to evaluate real-world situations in terms of the chances associated to future possible consequences and their estimated cost. Over time, this position will be formulated in terms of uncertainty as perceived by the observer, producing what we call Subjective Probability (uncertainty is in each observer’s mind, who knows what happens in the real-world). Probability beginners were not focusing in the world’s physical uncertainty, but in the human perception, and it is within this framework where Probability appears as a modelling tool. It is not that the observer is inside the experiment, but that the observer is in some way the experiment itself. In this sense, a major revolution introduced by Probability was to move the object of study into the human perception framework. Still, any scientific theory needs to connect with reality by means of some kind of experimentation, so Probability model was finally formalized by Kolmogorov [19] in terms of a given experiment, and according to a basic consistency test: 0020-0255/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2009.11.026
800
Editorial / Information Sciences 180 (2010) 799–802
observer must be able to decide from data (the result of each experiment) if each possible event under study can be verified or not. This apparently innocuous consistency test contains, as modeled by Kolmogorov [19], a tremendous hidden assumption: the Aristotelian logic. This assumption may not be considered extremely relevant meanwhile we restrict ourselves to collect crisp information and we make crisp questions, a restriction that may be the standard within experimental Sciences. Only then we can assume that events are represented in terms of subsets of all possible results of the experiment. Therefore, assuming that observation of reality is objective is somehow misleading, since the experiment itself and the whole observation depend on the human perception, which depends on individual senses, concepts learnt in the past (consciously or not), and the logic being chosen for their manipulation, among other things. What we call data has been already processed by our brains. We actually see only those things we are ready to see. Data is not a part of reality, but something constructed by observer. The drama in Science is that the historical scientific pressure to build models from data, together with the cultural lack of an alternative logic to Aristotelian logic, has made many scientists think that they were not using any human logic and that their experiments were not conducted by a previous arbitrary personal choice. Not being deeply discussed (the first complete alternative logic had to wait till Lukasiewicz [23], early 20th century), Aristotelian binary logic has been taken in experimental Science for granted. In this context, we can understand that for an experimental scientist information is always crisp. At the same time we should all be surprised when certain common words (like much, quite, or low) are used in polls without realizing that such words cannot be properly associated to crisp concepts, and that a probabilistic approach to those words is simply an approach, subject to obvious paradoxes (everybody can agree on a yes when forced to choose between yes and no, being none of these two answers the right answer to the question). While Probability was born within a human perception framework, we should then ask ourselves if the Boolean approach imposed by set theory is the most appropriate to those problems where human perception plays a key role. In fact, last studies in neurology (see, e.g., [5,22]) point that the human brain works with sophisticated representations of concepts, where the true decision making issue takes place. Human decision making invokes several machineries located in different parts of the brain [16] and, in particular, final executive decision is mainly associated with emotion [3,4], the rational analysis playing a decision support role that produces a global picture in terms of a conceptual map. Nevertheless, words can be seen as a standard description for concepts. Much more important, the fact is that decision making processes within a conceptual framework do not adhere to the Aristotelian postulates. Our human discourse is far being binary: there are lots of intermediate different kinds of partial truths, lots of different types of assertions and negations, conjunctions, disjunctions, numerous summarizing operators, and a great deal of different kinds of representation models (natural language is indeed one of them). The recent calls from Zadeh, the founder of Fuzzy Set Theory [39], for a new perception-based rather than a measurement-based logic [42] (with the ability to model human-centric fields such as economics, law, linguistics and psychology [41]), is in this sense fully justified (see also [43,44]). Once we move outside what we call now experimental Science (Science based upon numeric experimentation and its Aristotelian logical analysis), we find that Social Sciences (partially including Economy) acutely need models that allow the management of concepts (see also [28]). Alternative models to Probability are needed to complement the management of uncertainty, whenever information is given in terms of words associated to concepts. This special issue is a testimony to this important research trend.
2. Decision making under uncertainty From the above comments, we can note that the concept of uncertainty has been mostly associated to the way human beings understand and perceive reality. It is then extremely important to distinguish between the formal (mathematical) models and reality. Every proposed model is continuously tested, comparing predictions realized by the model and observations. But whenever such a model has been built as a result of a human decision making problem, no matter how precise it becomes, the model itself and its practical consequences usually need to be translated into the natural language. As succinctly pointed out by Zadeh, it is not the mathematical theorem the one commonly considered by decision makers, but a soft version of such a result [40]. Again, comprehension of a decision making problem used to be within a conceptual framework, and it is such a comprehension the main objective we all pursue when faced to a complex decision making problem (it implies a global view of the problem, avoiding the risk of a decision maker getting lost within any apparently definitive facts that represent only partial facts). The analysis of the problem we are facing is the core we can address with a sincere rationality. In this context, for example, encountering contradictory arguments is not a blocking paradox: if contradictory arguments exist, we just need to realize its meaning and find an explanation (decision aiding focus within this aiding analysis). The non-existence of contradiction in an argument is a deduction from Aristotelian logic (which does not belong to reality but to human mind, which previously to its use imposes a serious conceptual restriction). Making a choice within a conflicting situation is another problem, and it is a problem of a nature being absolutely different from the nature of the previous analytic comprehensive stage (see also [15,21]). Such a comprehensive stage represents the natural field for decision aiding [27,29]. The development of analytical representation models plays here the main role, of course including natural language but also the fusion aggregative models needed to compress information and those image representation and graphical techniques that allow a better knowledge of the structure of information and the problem itself (see, e.g., [7]).
Editorial / Information Sciences 180 (2010) 799–802
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Due to the potential difficulties of dealing effectively with decision making in complex systems, information (or data) obtained by the above-mentioned or the reported different approaches in this special issue will be of very different nature. It may be heuristic or incomplete or data that is either of unknown origin or may be out of date or imprecise, or not fully reliable, or conflicting, and even overloaded. It is considered advantageous to have a sound and reliable mathematical framework available that provides a basis for synthesis across multidimensional information of varying quality, especially to deal with information that is not quantifiable due to its nature, and that is too complex and ill-defined, for which the traditional quantitative approach (e.g., the statistical approach) does not give an adequate answer. We have already seen some examples of such approaches as previously published in Information Sciences (pertinent to the present discussion are, e.g., [12,14,17,30,45]). 3. Contents of this special issue This special issue has its origin in the 8th International FLINS Conference on Computational Intelligence and Decision Control [34] held in Madrid (Spain), September 21–24, 2008. FLINS stands for Fuzzy Logic and Intelligent Technologies in Nuclear Science, a project launched by the Belgian Nuclear Research Centre (SCKCEN) whose initial objectives have evolved into a wide view of computational intelligence in decision and control, with the ultimate objective of fostering advances in the theory and applications of decision making and control for complex systems (see, e.g., [33,34,38]). In line with the declared objectives of the FLINS initiative to promote the multidisciplinary interchange between different scientific and industrial fields, this special issue was conceived to produce a representative sample of the ongoing research devoted to tools for dealing with uncertainty. After an open call, 24 papers were selected in a first peer review process based upon a 6-page extended abstracts. Then, the long versions of those papers were submitted to Information Sciences, where a standard peer review process produced this special issue with the current nine accepted papers. The first part of this special issue mainly addresses theoretical issues about uncertainty modelling treated from different approaches. In the first paper, Mayor and Valero [25] consider a general description of how to combine a collection of measures [6,32], reducing the dimension of the information into a simpler but informative fusion. In the second paper, Wang et al. [37] consider Shafer’s Theory of Evidence [35] showing how to efficiently combine and derive a mass function from multivariate data sets. In the third paper, Castiñeira et al. [8] address the incompatibility problem within Atanassov’s Intuitionistic Fuzzy Sets framework [2] (see also [10,11,26]) by means of geometrical methods. In the fourth paper, Torres-Blanc et al. [36] propose an axiomatic model to measure how contradictory certain information is. The second part of this special issue mainly focuses on applications. First, Martín et al. [24] offer a novel technique for the extraction of uncorrelated variant features of images and signals, a technique that can be treated as an alternative to classical statistical approaches, which is applied to shape analysis, image segmentation, tracking deformations and object motion tacking. Then, Kaya and Kahraman [18] propose a new decision making tool to determine the best supplier for building materials, based on fuzzy accuracy indices to evaluate process performance, inspired in Statistics but modified to allow fuzzy specification limits. The third paper in this applied section is devoted to knowledge discovery, where Kong et al. [20] look into an explore investment stock market decision support by searching for multi-temporal patterns. In the fourth paper, Cebi et al. [9] provide an original decision aid tool for classifying societies to redesign primary project layouts, which is then applied to the shipping industry. Finally, the paper by Alonso and Santos [1] shows how a genetic algorithm is used to optimize maneuvers involving a two-stage rocket. 4. Final notes In this special issue, we have illustrated some recent advances in the search for uncertainty management, allowing an interesting view to some specific perspectives, addressing not only some formal developments but also bringing some interesting applications. We hope the readers will find this special issue both informative and inspiring. Acknowledgments The work presented in this paper was in part supported by the Government of Spain under the Project Grant TIN200907901. We thank Prof. Witold Pedrycz for his continuous support towards this project, kindly encouraging the authors to improve the quality of their final research papers. References [1] [2] [3] [4] [5] [6] [7] [8]
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Javier Montero Faculty of Mathematics, Complutense University of Madrid, Spain Tel.: +34 91 394 4522; fax: +34 91 394 4607 E-mail address: [email protected] Da Ruan Belgian Nuclear Research Centre (SCKCEN) and Ghent University, Belgium E-mail address: [email protected]