Ioan Dzitac, Professor, Aurel Vlaicu University of Arad & Rector of Agora University of Oradea, Romania
Milan Stanojevic, Professor, Faculty of Organizational Sciences;
Bogdana Stanojevic, Researcher, Mathematical Institute of the Serbian Academy of Sciences and Arts
From Fuzzy Logic to Soft Computing: New Paradigms in Decision Making
Professor at Aurel Vlaicu University of Arad & Rector of Agora University of Oradea, Romania;
In this tutorial we will presents the influence of fuzzy logic in soft computing paradigms and decision making methods.
Humans have a remarkable capability to reason and make decisions in an environment of imprecision, uncertainty and partiality of knowledge, truth and class membership. It is this capability that is needed to achieve human-level machine intelligence. Achievement of human-level machine intelligence is beyond the reach of existing Artificial Intelligence (AI) techniques and more of these are based on fuzzy sets theory and fuzzy logic. In this paper we will present a summary of AI problems and a survey of some new trends and new directions in Soft Computing and AI research.
In many real-world situations, the problems of decision making are subjected to some constraints, objectives and consequences that are not accurately known. After Bellman and Zadeh introduced for the first time fuzzy sets within MCDM, many researchers have been preoccupied by decision making in fuzzy environments. The fusion between MCDM and fuzzy set theory has led to a new decision theory, known today as fuzzy multi-criteria decision making (FMCDM), where we have decision-maker models that can deal with incomplete and uncertain knowledge and information. The most important thing is that, when we want to assess, judge or decide we usually use a natural language in which the words do not have a clear, definite meaning. As a result, we need fuzzy numbers to express linguistic variables, to describe the subjective judgement of a decision maker in a quantitative manner. Fuzzy numbers (FN) most often used are triangular FN, trapezoidal FN and Gaussian FN. We highlight that the concept of linguistic variable introduced by Zadeh in 1975 allows computation with words instead of numbers and thus linguistic terms defined by fuzzy sets are intensely used in problems of decision theory for modelling uncertain information.
After Atanassov introduced the concept of intuitionistic fuzzy sets, where each element is characterized by a membership function, as in fuzzy sets, as well as by a non-membership function, the interest in the study of the problems of decision making theory with the help of intuitionistic fuzzy sets has increased.
Keywords: Fuzzy logic, artificial intelligence, soft computing, natural language computation, MCDM, TOPSIS.
Author’s short biographical note:
Prof. Ioan Dzitac, Ph.D., Senior Member of IEEE (since 2011), is an information sciences professor at Aurel Vlaicu University of Arad - Romania (since 2009), Adjunct Professor at University of Chinese Academy of Sciences - Beijing, China (2013-2016) and Rector of Agora University of Oradea - Romania (2012-2016) and (2016-2020). He received B.Sc.(eq.M.Sc.) in Mathematics (1977) and Ph.D. in Information Sciences (2002) from Babes-Bolyai University of Cluj - Napoca, Romania (University Place in Top Shanghai: 101-150; Academic Ranking of World Universities in Mathematics - 2013).
His current research interests include different aspects of artificial intelligence, applications of fuzzy logic in technology and economy.
He is co-founder and A. Editor-in-Chief of an ISI SCI Expanded quoted journal (2006), International Journal of Computers Communications & Control (nominee by Elsevier for Journal Excellence Award -Scopus Awards Romania2015) and member in Editorial Board of 8 scientific journals. Also he is co-founder and General Chair of International Conference on Computers Communications and Control and he was member of the Program Committee of more than 60 international conferences.
He was an invited speaker and/or invited special sessions¡¯ organizer and chair in China (2013: Beijing, Suzhou and Chengdu, 2015: Dalian), India (2014: Madurai), Russia (2014: Moscow) and Brazil (2015: Rio), Lithuania (2015: Druskininkai).
He has published 3 books, 12 courses and materials for students, 4 conference proceedings and more than 70 scientific papers in journals and conferences proceedings.
Multi-criteria optimization: applications and some limits of its achievements
Professor, Faculty of Organizational Sciences;
Researcher, Mathematical Institute of the Serbian Academy of Sciences and Arts;
Multi-criteria optimization (MCO) offers mathematical models to decision problems. A subfield of MCO is Multi-objective Combinatorial Optimization. One part of it, the Multi-criteria Decision Analysis (MCDA), achieved a great popularity in the last decades, due to a variety of applications in solving real-life problems. MCDA includes the decision problems with a finite discrete set of possible alternatives.
Solving general MCO problems is not less needed in practice but the approaches to solve them must be more sophisticated, since they have to explore continuous or countable but virtually infinite number of feasible decisions. The fundamentals of MCO are reviewed, and some limits of its achievements are discussed.
In our opinion, the main issue of MCO methods is the gap between the points of view of Decision Maker (DM) and analyst. DM understands in detail the real life problem, while the analyst knows how to solve the mathematical problem -- that is the model of the real-life system. We still do not know how to model the understanding of the reality. There are many ways to model DM's preferences but none is universal. The standard approaches to solve MCO problems -- a priori, a posteriori and interactive -- are emphasized in the literature. The last one is highly recommended in order to overcome the gap. However, a certain boost to the a posteriori approaches is the proof that the number of the non-dominated points of multi-objective combinatorial optimization problems, for constant number of criteria, increases polynomial with the problem size. The proof will be presented together with some results of practical experiments that showed that the number of the non-dominated points is even smaller than the polynomial upper bound.
The objective functions involved in the mathematical models of real-life problems originally are non-linear. In the very beginning, only linear programming problems were solved efficiently, thus the objective functions were linearized before optimization. Even when the DM faced the problem of optimizing various ratios, such as profits/costs or outputs/employee, the scientists searched for linearization approaches. When the performance of the computers increased, the researchers turned back to non-linear problems and tried to solve them efficiently. Then, the field of fractional programming problems -- that are the nearest generalization of the linear case -- became intensively studied. A method to derive efficient solutions to a MCO problem with linear fractional objective functions is presented; and possible ways to involve the method in a priori or a posteriori approaches are discussed.
Finally, a serial multi-modal biometric system based on optimized thresholds is presented as an alternative to parallel fusion based systems. We optimize the mathematical expectation of both types of errors -- the false acceptance and false rejection.
Author’s short biographical note:
Milan Stanojevic graduated at University of Belgrade, Faculty of Organizational Sciences in 1990. He obtained doctoral degree at the same faculty in 2005. Since 1993 he works at Faculty of Organizational Sciences, in the beginning as a teaching assistant and now as professor in the area of operation research. He has published more than 50 papers in national and international journals, and conference proceedings in the field of operational research. His research interest, as well as teaching subjects, includes multi-objective optimization, combinatorial optimization and software for operational research.
Bogdana Stanojevic graduated Mathematics and Computer Science specialization at "Transilvania" University of Braov in 1995, and she obtained her doctoral degree in Mathematics in 2003 from the Romanian Academy. Currently she is researcher at Mathematical Institute of the Serbian Academy of Sciences and Arts. Her research interests include different aspects of fuzzy optimization, multiple objective optimization, fractional programming and mathematical fundamentals of computers.