5

A Retrospective Glance from Russiaat Wonderland of Fuzziness

Ildar Batyrshin

I have received my engineering diploma in Systems of Automated Control from theMoscow Institute of Physics and Technology (MIPT, sometimes referred to as “theRussian MIT”) in 1975. This institute prepared specialists for high-tech govern-mental research institutes mainly located around the Moscow city. But I preferredto be free from duties of researcher working on prescribed tasks and returned tomy city Kazan where I held assistant professor position in Department of AppliedMathematics of Kazan Institute of Chemical Technology (now it is Kazan NationalResearch Technological University). I looked for some interesting areas of researchand thanks to the department head Prof. Vladimir Skvortsov that drew my attentionon the paper of Zadeh [39]. This paper was translated in Russian and published in1974 in periodical collection of papers “Mathematics Today” in series “Mathematicsand Cybernetics. News in Life, Science, and Engineering”. The mathematics thatwas presented in this paper and the style of presentation of results were so unusualand different from the mathematics that I have studied in university so I read this pa-per as a truly absorbing book. I tried to find all of papers from the list of references,and then I followed the references of papers that I have found and so on, and so on.I plunged into the world of fuzziness that was enigmatic and wonderful. I startedto work on several directions of research: entropy of fuzzy sets, fuzzy preferencerelations, fuzzy similarity relations and their applications in clustering and decisionmaking. It may be interesting that my first results in fuzziness have been presentedon October 1977 on Seminar on Applied Statistics led by Orlov A. I. in Central Eco-nomics and Mathematics Institute (CEMI) of Academy of Sciences of USSR andhave been published in a book on statistics [5]. It should be noted that in statisticscommunity of SU it was ambivalent attitude to fuzziness. Sometimes it was criticsof the fuzziness from researchers that could not find the rationale for the concept ofmembership function but some researchers tried to substantiate the concept of fuzzysets in terms of random sets [25]. In [5] I studied the possible axiomatizations ofmeasure of entropy of fuzzy set [17] and relationships between them and metricsand it was established one-to-one correspondence between (symmetric) metrics de-fined by positive valuations [13] and measures of fuzziness satisfying an axiom ofstrict monotonicity for “sharpened versions”. Further these results have been ex-tended on Kleene algebras and it was shown that a metric De Morgan algebra M willbe a Kleene algebra if and only if it can be defined a measure of entropy on M [8]. In

R. Seising et al. (Eds.): On Fuzziness: Volume 1, STUDFUZZ 298, pp. 31–38.DOI: 10.1007/978-3-642-35641-4_5 © Springer-Verlag Berlin Heidelberg 2013

32 5 A Retrospective Glance from Russia at Wonderland of Fuzziness

[6] I have studied transitivity properties of strict preference relations, for example, itwas shown that a fuzzy quasi-series satisfying transitivity in the form

if P(x,y)≥ 0 and P(y,z) ≥ 0 then P(x,z) = max(P(x,y),P(y,z))

defines a fuzzy quasi ordering and hence defines a hierarchy of ordered partitionson the set of alternatives. These results have been inspired by Zadeh’s paper [38]and [24]. The obtained results have been included later in my PhD dissertation [7].In this dissertation I have also proposed and studied a general scheme of hierar-chical clustering procedures invariant under numeration of objects and invariantunder monotone transformations of similarity values. They were many attemptsbefore in cluster analysis to develop clustering algorithms satisfying these proper-ties of invariance but only by means of the concepts of fuzzy equivalence relationand transitive closure studied by Zadeh in [38] it was possible to develop a schemeof hierarchical clustering procedures satisfying both invariance properties [10].

It should be noted that in Soviet Union (almost till today in Russia) the officiallanguage of scientific publications was Russian. The abstracts of almost all scien-tific papers published abroad were published in Russian in special abstract bulletins.Many good scientific books published in English have been translated into Russian.Interesting papers with new ideas were translated and published in Russian in spe-cial volumes or in periodical collections of papers like “Mathematics Today” thatdistributed by subscription for pennies. Before signing by Soviet Union the Univer-sal Copyright Convention in 1973 most of all foreign scientific journals have beencopied (I can suppose that without permission) and could be found in almost alluniversities and research centers of USSR. For example, I found the copy of thejournal Information and Control with Zadeh’s paper “Fuzzy Sets” [36] in the libraryof Kazan Institute of Chemical Technology. But later it was almost impossible tofind in the libraries of Soviet universities the foreign journals published after 1973because the universities had not dollars for paying for them. Only 2-3 central li-braries in Moscow and may be in Leningrad (now it is Saint Petersburg) had someof most important foreign journals in selected research areas. To find copies of thepapers on fuzzy logic I used all possibilities to go to Moscow and to work in StateScientific Technical Library (SSTL).

SSTL was located in the center of Moscow near metro station Kuznetskij Most.In one block from this metro station it resided my good friend Valery Tarassov. I methim on one of Soviet conferences on fuzzy sets and decision making when he wasthe PhD student of Moscow State Technical University n.a. N. E. Bauman (MSTU).He was (and till now he is) very hospitable and his apartment was something likepermanent center of fuzziness in Moscow during late 70’s-90’s. Many researchersin fuzziness coming to Moscow from different parts of SU found in his apartmentfriends and colleagues. The friendly conversations about fuzziness and other actualquestions usually accompanied by bottles of vine, cognac, liqueur or vodka broughtfrom all parts of SU often continued till the late night.

In one of such conversations it was arisen an idea to write a book on “almost all”topics of fuzziness. Several young researchers have been joined together for such

5 A Retrospective Glance from Russia at Wonderland of Fuzziness 33

ambitious project starting to write two-three chapters by each person [1]. At thistime I was already a PhD student of Department of Applied Mathematics of MoscowPower Engineering Institute, Alexey Averkin and Alexander Blishun have been withComputer Center of Soviet Academy of Sciences as researcher and PhD student andValery Tarassov was PhD student of MSTU. In one of my visits to SSTL I happenedto meet a young man holding in his hands a bright yellow volume of “Fuzzy Setsand Systems” journal. It was Valery Silov coming to Moscow from Sevastopol city,Ukraina, for several days and spending some time in the libraries looking for paperson fuzzy logic. We moved together from library to Tarassov apartment and afterseveral drinks he joined us with willingness to write some chapters of the book onfuzziness [1]. Note that further he wrote very interesting book on application offuzzy cognitive maps to modeling dynamic multi-objective fuzzy systems [33].

The idea of writing book [1] was supported by Prof. Dmitry Pospelov, editorof book series “Problems of Artificial Intelligence” in Nauka (“Science”) Publish-ing House where have been published later this book. Dmitry Pospelov was a headof Department of Problems of Artificial Intelligence of Computer Center of SovietAcademy of Sciences and at the same time a professor of MIPT. He served later as aPresident of Associations for Artificial Intelligence of USSR and Russia and Chair-man of Council of Soviet Association for Fuzzy Systems (SAFS). He served also asa chair of many workshops and conferences on artificial intelligence and fuzzinessin USSR and later in Russia. The book [1] contained the following chapters:

1. Methods of formalization of fuzziness.2. Fuzzy relations and their application in analysis of complex systems.3. Measures of fuzziness of fuzzy sets.4. Fuzzy measures and integrals.5. Fuzzy numbers, equations and approximation of linguistic values.6. Fuzzy logic and approximate reasoning.7. Generation and recognition of fuzzy languages.8. Fuzzy algorithms.9. Fuzzy models of optimization and decision making.

10. Methods of construction of membership functions.

The total list of references of all chapters contained about 600 works on fuzzinessand related topics. This book was published more than 25 years before but till nowit is a most referenced book on fuzziness in Russia.

From my subjective point of view, the researches on fuzziness in Soviet Unionand Russia can be divided on several periods:

1) 1965-1973: Initial period based on Zadeh’s paper “Shadows of fuzzy sets” pub-lished in Russian in 1966 [37] and on earlier works on fuzziness published inEnglish;

2) 1974-1991: A burst of works on fuzziness in Soviet Union after translationZadeh’s papers [12], [39], [40], [41] into Russian;

3) 1992- 2004: Fuzziness in new Russia;4) 2005-2012: Fuzziness and RAFSSoftCom.

34 5 A Retrospective Glance from Russia at Wonderland of Fuzziness

In 1965-1973 it was published only several papers on fuzziness in USSR, e.g. [18].After publishing in 1974 Zadeh’s paper [39], two other papers of Zadeh have beentranslated into Russian [12], [40] in 1976. The first paper [12] was published in theedited volume “Problems of Analysis and Procedures of Decision Making” contain-ing selected papers on decision making published in foreign journals and translatedinto Russian. Together with paper of Bellman and Zadeh this volume contained alsothe papers of Bernard Roy, Ralph L. Keeney and other well known researchers indecision making. Another paper [40] was published in Russian as a separate book.Later it was published Zadeh’s paper [41]. Publication of several papers of Zadehduring a short period caused in SU a burst of interest to the theory of fuzzy sets fromdifferent groups of researchers working in applied statistics, expert estimations, the-ory of measurements, Osgood’s semantic differential, linguistics, decision making,operations research, clustering, expert systems and artificial intelligence because theconcepts of fuzzy set, fuzzy relation and the problem of definition of degree of mem-bership were closely related with the problems studied in these research areas. Thetheory of fuzzy sets was a topic of interests of various seminars and workshops indifferent universities and research institutes. The Council of Artificial Intelligenceof Academy of Sciences of USSR organized two special interest groups related withapplications of fuzzy concepts in control, psycholinguistics, neurophysiology andartificial intelligence. The conferences on theory and application of fuzziness havebeen regularly organized in different parts of Soviet Union hosted by researchers andresearch groups actively working in fuzziness. Many books and surveys on fuzzi-ness and related topics [1–4],[14–16], [19–23], [25–27], [29–32], [34, 35],[42] havebeen published during 1974-1991. The authors of these works belonged to researchgroups from different cities: Moscow, Kazan, Kolomna, Sevastopol, Baku, Riga,Frunze, Taganrog, Kalinin, Tbilisi etc. Of course the list of references includes onlya small part of works on fuzziness in Soviet Union before its dissolution in Decemberof 1991.

In January of 1990 in Kazan city it was held a founding convention of SovietAssociation for Fuzzy Systems (SAFS). The founding members of SAFS are pre-sented in Fig. 5.1, first line (from left to right): Ildar Batyrshin, Alla Zaboleeva-Zotova, Dmitry Pospelov, V. Chernyaev; second line (from left to right): ValeryTarassov, Alexander Yazenin, Alexey Averkin, Askold Melikhov, Arkady Borisov;upper line (from right to left): Alexander Blishun, Alexander Shostak. The otherpersons were from research groups of Alexander Blishun. Askold Melikhov and laterAlexey Averkin have been elected as the first and the second presidents of SAFS.

In 1989-1991, in the last years of “Perestroyka” in USSR, and in the first yearsof new Russia, when it was an economic collapse, research in fuzziness in Russiacould survive for several reasons. In 1989-1992, research in artificial intelligenceand fuzziness have been supported partially by State Research and DevelopmentProgram “Perspective Information Technologies”. Since 1992 these researches havebeen supported also by grants of Russian Foundation of Basic Research (RFBR). Iused these possibilities to work actively in the area of fuzzy intelligent systems andclustering and obtained results have been included in 1996 in my Dr. Sci. (Habili-tation) Dissertation [9]. It was developed, for example, a method of construction of

5 A Retrospective Glance from Russia at Wonderland of Fuzziness 35

strict monotonic conjunctions and disjunctions for processing in expert systems ex-pert evaluations of truth measured in finite ordinal scale L. It is impossible to definesuch operations on L and the solution of the problem was consisted in embeddingof L in the linearly ordered set of uncertainties with memory (lexicographic valua-tions) [11]. This problem could not be resolved in the theory of measurements [28]but was resolved in fuzzy logic. Obtained results were implemented in fuzzy expertsystems shell LEXICO and in fuzzy decision support system SMOPLEX used foroptimization of polymerization process in simulator of chemical reactor [11]. Thelast one used the knowledge-base based on the concept of fuzzy algorithm proposedby Zadeh [39].

Fig. 5.1. The founding members of Soviet Association for Fuzzy Systems, January 1990

In new Russia, in 2005, it was organized Russian Association for Fuzzy Sys-tems and Soft Computing (RAFSSoftCom), Presidents: Ildar Batyrshin (2005-2006),Alexander Yazenin (2006-2008), Nadezhda Yarushkina (2008-2011), Sergey Ko-valev (2011-2013). RAFSSoftCom is a member of IFSA, publishes the journal FuzzySystems and Soft Computing (Editor in Chief Alexander Yazenin), organizes bian-nual conferences on Fuzzy Systems and Soft Computing. Another biannual con-ference “Integrated Models and Soft Computing in Artificial Intelligence” (chairValery Tarassov) is organized in Kolomna near Moscow by RAFSSoftCom togetherwith Russian Association for Artificial Intelligence. Members of association actively

36 References

participate in biannual conferences of Russian Association for Artificial Intelligenceand in many other conferences on intelligent systems in Russia and abroad.

I met Lotfi Zadeh first time in Aachen, on EUFIT 1993, and after this we meton many conferences: in Zittau, in Antalya on ICSCCW’ 2001 (Fig. 5.2), in SanFrancisco in 2011 etc. It was honor for me to be invited by him in Berkeley in 2002on the meeting “State of the Art Assessment and New Directions for Research” andin 2005 on BISC-2005. I always admired his kindness, cordiality, willingness tohelp, activity and ability to generate new ideas.

Fig. 5.2. On ICSCCW’ 2001, Antalya, Turkey, June 6-8, 2001

References

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2. Aliev, R.A., Abdikeev, N.M., Shakhnazarov, M.M.: Industrial Systems with ArtificialIntelligence. Radio and Communication Publisher, Moscow (1990) (in Russian)

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References 37

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