Fuzzy concept
[9] Similarly, to the North, the Chinese Mars rover Zhurong used fuzzy logic algorithms to calculate its travel route in Utopia Planitia from sensor data.
[16] According to the Daoist thought of Laozi and Zhuang Zhou in ancient China, "vagueness is not regarded with suspicion, but is simply an acknowledged characteristic of the world around us" - a subject for meditation and a source of insight.
[17] The ancient Sorites paradox first raised the logical problem of how we could exactly define the threshold at which a change in quantitative gradation turns into a qualitative or categorical difference.
In Western civilization, the intellectual recognition of fuzzy concepts has been traced back to a diversity of famous and less well-known thinkers,[21] including (among many others) Eubulides,[22] Epicurus,[23] Plato,[24] Cicero,[25] Georg Wilhelm Friedrich Hegel,[26] Karl Marx and Friedrich Engels,[27] Friedrich Nietzsche,[28] William James,[29] Hugh MacColl,[30] Charles S. Peirce,[31] Carl Gustav Hempel,[32] Max Black,[33] Arto Salomaa,[34] Ludwig Wittgenstein,[35] Jan Łukasiewicz,[36] Emil Leon Post,[37] Alfred Tarski,[38] Georg Cantor,[39] Nicolai A. Vasiliev,[40] Kurt Gödel,[41] Stanisław Jaśkowski,[42] Willard Van Orman Quine,[43] Petr Hájek,[44] Joseph Goguen,[45] Jan Pavelka,[46] George J. Klir,[47] Didier Dubois,[48] and Donald Knuth.
[78] The "fuzzy area" can also refer simply to a residual number of cases which cannot be allocated to a known and identifiable group, class or set if strict criteria are used.
Fuzzy concept lattices are a useful programming tool for the exploratory analysis of big data, for example in cases where sets of linked behavioural responses are broadly similar, but can nevertheless vary in important ways, within certain limits.
[122] The basic programming techniques for this kind of fuzzy concept mapping and deep learning are by now well-established[123] and big data analytics had a strong influence on the US elections of 2016.
[127] However, NBC News reported in 2016 that the Anglo-American firm Cambridge Analytica which profiled voters for Donald Trump (Steve Bannon was a board member)[128] did not have 400, but 4,000 data points for each of 230 million US adults.
[133] This was confirmed by Kellyanne Conway, Donald Trump's campaign advisor and counselor in 2016, who emphasized the importance of human judgement and common sense in drawing conclusions from fuzzy data.
This was denied by Cambridge Analytica, which stated on its website that it legitimately "uses data to change audience behavior" among customers and voters (who choose to view and provide information).
[143] When Zuckerberg replied to his critics, he stated that because the revolutionary technology of Facebook (with 2.2 billion users worldwide, at that time) had ventured into previously unknown territory, it was unavoidable that mistakes would be made, despite the best of intentions.
"[144]In July 2018, Facebook and Instagram barred access from Crimson Hexagon, a company that advises corporations and governments using one trillion scraped social media posts, which it mined and processed with artificial intelligence and image analysis.
A clear, precise and logically rigorous conceptualization is no longer a necessary prerequisite, for carrying out a procedure, a project, or an inquiry, since "somewhat vague ideas" can always be accommodated, formalized and programmed with the aid of fuzzy expressions.
For example, if one starts off designing a procedure, not with well thought-out, precise concepts, but rather by using fuzzy or approximate expressions which conveniently patch up (or compensate for) badly formulated ideas, the ultimate result could be a complicated, malformed mess, that does not achieve the intended goal.
That point is obviously of great importance to computer programmers, educators and administrators seeking to code a process, activity, message or operation as simply as possible, according to logically consistent rules.
Central to ethics are theories of "value", what is "good" or "bad" for people and why that is, and the idea of "rule following" as a condition for moral integrity, consistency and non-arbitrary behaviour.
[209] Defending a cognitive realism, Scott Soames argues that the reason why this unsolvable conundrum has persisted, is because the ultimate constitution of the meaning of concepts and propositions was misconceived.
[214] For example, fuzzy set qualitative comparative analysis ("fsQCA") has been used by German researchers to study problems posed by ethnic diversity in Latin America.
[215] In New Zealand, Taiwan, Iran, Malaysia, the European Union and Croatia, economists have used fuzzy concepts to model and measure the underground economy of their country.
[218] Kron studies transnational terrorism and other contemporary phenomena using fuzzy logic, to understand conditions involving uncertainty, hybridity, violence and cultural systems.
For example, a New York Times journalist wrote that Prince Sihanouk "seems unable to differentiate between friends and enemies, a disturbing trait since it suggests that he stands for nothing beyond the fuzzy concept of peace and prosperity in Cambodia".
Lotfi A. Zadeh said in a 1994 interview that: "I expected people in the social sciences – economics, psychology, philosophy, linguistics, politics, sociology, religion and numerous other areas to pick up on it.
The semantic challenge of conveying meanings to an audience was explored in detail, and analyzed logically, by the British philosopher Paul Grice - using, among other things, the concept of implicature.
David Hilbert concluded that the existence of logical paradoxes tells us "that we must develop a meta-mathematical analysis of the notions of proof and of the axiomatic method; their importance is methodological as well as epistemological".
[241] According to fuzzy-trace theory, partly inspired by Gestalt psychology, human intuition is a non-arbitrary, reasonable and rational process of cognition; it literally "makes sense" (see also: Problem of multiple generality).
In interacting with the external world, the human mind may often encounter new, or partly new phenomena or relationships which cannot (yet) be sharply defined given the background knowledge available, and by known distinctions, associations or generalizations.
[276] Fuzzy concepts can be used as a practical method to describe something of which a complete description would be an unmanageably large undertaking, or very time-consuming; thus, a simplified indication of what is at issue is regarded as sufficient, although it is not exact.
The reason for using fuzzy concepts can therefore be purely pragmatic, if it is not feasible or desirable (for practical purposes) to provide "all the details" about the meaning of a shared symbol or sign.
Yet in many cases, fuzzy logic is used paradoxically to "imprecisiate what is precise", meaning that there is a deliberate tolerance for imprecision for the sake of simplicity of procedure and economy of expression.
Zadeh cited as example Takeshi Yamakawa's programming for an inverted pendulum, where differential equations are replaced by fuzzy if-then rules in which words are used in place of numbers.
