Edward Kofler
Encyclopedia
Edward Kofler was a mathematician
who made important contributions to game theory
and fuzzy logic
by working out the theory of linear partial information
.
He was born in Brzeżany, Imperial Russia (now Ukraine
) and graduated as a disciple of among others Hugo Steinhaus
and Stefan Banach
from the University of Lwów Poland (now Ukraine) and the University of Cracow, having studied game theory
. After the graduation in 1939 Kofler returned to his family in Kolomyia
(today Kolomea in Ukraine), where he taught mathematics in a Polish high school. After German attack
on the town 1 July 1941 he succeeded to flight to Kazakhstan
together with his wife. Here at Alma-Ata he managed a Polish school with orphanage in exile
and worked there as mathematics teacher. After the World War II was ended he returned home to Polen with the orphanage. He was accompanied by the wife and his baby son. The family settled in Poland. From 1959 he accepted the position of lecturer at the University of Warsaw
in the faculty of economics. In 1962 he gained a Ph.D.
with his thesis Economic Decisions, Applying Game Theory. Then in 1962 he became assistant professor at the faculty of social science in the same university, specializing in econometrics
.
In 1969 he migrated to Zürich
, Switzerland
, where he was employed at the Institute for Empirical Research in Economics at the University of Zürich
and scientific advisor at the Swiss National Science Foundation
(Schweizerische Nationalfonds zur Förderung der wissenschaftlichen Forschung). In Zürich in 1970 Kofler developed his linear partial information
(LPI) theory allowing qualified decisions to be made on the basis of fuzzy logic: incomplete or fuzzy a priori information
.
Kofler was visiting professor at the University of St Petersburg (former Leningrad
, Russia), University of Heidelberg (Germany), McMaster University
(Hamilton, Ontario
, Canada) and University of Leeds
(England). He collaborated with many well known specialists in information theory
, such as Oskar R. Lange in Poland, Nicolai Vorobiev in the Soviet Union, Günter Menges in Germany, and Heidi Schelbert and Peter Zweifel in Zürich. He was the author of many books and articles. He died in Zürich.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made important contributions to game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
and fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...
by working out the theory of linear partial information
Linear partial information
Linear partial information is a method of making decisions based on insufficient or fuzzy information. LPI was introduced in 1970 by Polish - Swiss mathematician Edward Kofler to simplify decision processes. Comparing to other methods the LPI-fuzziness is algorithmically simple and particularly...
.
He was born in Brzeżany, Imperial Russia (now Ukraine
Ukraine
Ukraine is a country in Eastern Europe. It has an area of 603,628 km², making it the second largest contiguous country on the European continent, after Russia...
) and graduated as a disciple of among others Hugo Steinhaus
Hugo Steinhaus
Władysław Hugo Dionizy Steinhaus was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics...
and Stefan Banach
Stefan Banach
Stefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
from the University of Lwów Poland (now Ukraine) and the University of Cracow, having studied game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
. After the graduation in 1939 Kofler returned to his family in Kolomyia
Kolomyia
Kolomyia or Kolomyya, formerly known as Kolomea , is a city located on the Prut River in the Ivano-Frankivsk Oblast , in western Ukraine. Serving as the administrative centre of the Kolomyia Raion , the city is also designated as a separate raion within the oblast...
(today Kolomea in Ukraine), where he taught mathematics in a Polish high school. After German attack
Operation Barbarossa
Operation Barbarossa was the code name for Germany's invasion of the Soviet Union during World War II that began on 22 June 1941. Over 4.5 million troops of the Axis powers invaded the USSR along a front., the largest invasion in the history of warfare...
on the town 1 July 1941 he succeeded to flight to Kazakhstan
Kazakhstan
Kazakhstan , officially the Republic of Kazakhstan, is a transcontinental country in Central Asia and Eastern Europe. Ranked as the ninth largest country in the world, it is also the world's largest landlocked country; its territory of is greater than Western Europe...
together with his wife. Here at Alma-Ata he managed a Polish school with orphanage in exile
Exile
Exile means to be away from one's home , while either being explicitly refused permission to return and/or being threatened with imprisonment or death upon return...
and worked there as mathematics teacher. After the World War II was ended he returned home to Polen with the orphanage. He was accompanied by the wife and his baby son. The family settled in Poland. From 1959 he accepted the position of lecturer at the University of Warsaw
University of Warsaw
The University of Warsaw is the largest university in Poland and one of the most prestigious, ranked as best Polish university in 2010 and 2011...
in the faculty of economics. In 1962 he gained a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
with his thesis Economic Decisions, Applying Game Theory. Then in 1962 he became assistant professor at the faculty of social science in the same university, specializing in econometrics
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
.
In 1969 he migrated to Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
, Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
, where he was employed at the Institute for Empirical Research in Economics at the University of Zürich
University of Zurich
The University of Zurich , located in the city of Zurich, is the largest university in Switzerland, with over 25,000 students. It was founded in 1833 from the existing colleges of theology, law, medicine and a new faculty of philosophy....
and scientific advisor at the Swiss National Science Foundation
Swiss National Science Foundation
The Swiss National Science Foundation is a science research support organization mandated by the Swiss Federal Government. The SNSF was established in 1952 as a foundation under private law. Its secretariat is based in Bern....
(Schweizerische Nationalfonds zur Förderung der wissenschaftlichen Forschung). In Zürich in 1970 Kofler developed his linear partial information
Linear partial information
Linear partial information is a method of making decisions based on insufficient or fuzzy information. LPI was introduced in 1970 by Polish - Swiss mathematician Edward Kofler to simplify decision processes. Comparing to other methods the LPI-fuzziness is algorithmically simple and particularly...
(LPI) theory allowing qualified decisions to be made on the basis of fuzzy logic: incomplete or fuzzy a priori information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
.
Kofler was visiting professor at the University of St Petersburg (former Leningrad
Leningrad
Leningrad is the former name of Saint Petersburg, Russia.Leningrad may also refer to:- Places :* Leningrad Oblast, a federal subject of Russia, around Saint Petersburg* Leningrad, Tajikistan, capital of Muminobod district in Khatlon Province...
, Russia), University of Heidelberg (Germany), McMaster University
McMaster University
McMaster University is a public research university whose main campus is located in Hamilton, Ontario, Canada. The main campus is located on of land in the residential neighbourhood of Westdale, adjacent to Hamilton's Royal Botanical Gardens...
(Hamilton, Ontario
Hamilton, Ontario
Hamilton is a port city in the Canadian province of Ontario. Conceived by George Hamilton when he purchased the Durand farm shortly after the War of 1812, Hamilton has become the centre of a densely populated and industrialized region at the west end of Lake Ontario known as the Golden Horseshoe...
, Canada) and University of Leeds
University of Leeds
The University of Leeds is a British Redbrick university located in the city of Leeds, West Yorkshire, England...
(England). He collaborated with many well known specialists in information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
, such as Oskar R. Lange in Poland, Nicolai Vorobiev in the Soviet Union, Günter Menges in Germany, and Heidi Schelbert and Peter Zweifel in Zürich. He was the author of many books and articles. He died in Zürich.
External links
- How to apply the Linear Partial Information (LPI)
- Linear Partial Information (LPI) theory and its applications
- Applying the Linear Partial Information (LPI) for USA's economy policy
- Practical decision making with the Linear Partial Information (LPI)
- Stochastic programming applying fuzzy Linear Partial Information (LPI)
- One-shot decisions applying the Linear Partial Information (LPI)