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Formal fuzzy logic

Fuzzy logic is a relatively new chapter of formal logic whose aim is to formalize the reasonings involving predicates that are vague in nature (as an example small, near, similar). An example of such kind of reasoning is

If a tomato is red, then the tomato is ripe. Since this tomato is very red, this tomato is very ripe.

Further examples of reasonings involving vague predicates are in the item Paradoxes and fuzzy logic and in the section Fuzzy logic with no truth-functional semantics. The main tool for fuzzy logic is the notion of a fuzzy subset since a vague predicate is interpreted by a fuzzy subset. Notice that in literature the name "fuzzy logic" also denotes a large series of topics based on an informal usage of the notion of a fuzzy subset and which are usually devoted to applications.

As a matter of fact, fuzzy logic is an evolution and an enlargement of multi-valued logic since all the definitions and results in the literature on multi-valued logic are also considered in fuzzy logic. In particular, as in multi-valued logic, the starting point is a fixed valuation structure, i.e. a bounded lattice L equipped with suitable operations to interpret the logical connectives. The minimum 0 means 'False', the maximum 1 means 'True', the remaining elements are interpreted as intermediate truth values. The following is the main class of valuation structures (see Hájek 1998, Novák et al. 1999 and Gottwald 2005) corresponding to the connectives $\wedge$ and $\rightarrow$ .

.... (read more)

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-== '''[[Politics]]''' ==
+== '''[[Formal fuzzy logic]]''' ==
 ----
+'''Fuzzy logic''' is a relatively new chapter of formal logic whose aim is to formalize the reasonings involving predicates that are vague in nature (as an example ''small'', ''near'', ''similar''). An example of such kind of reasoning is
-'''Politics''' is about living together in communities. Its subject-matter includes the consideration of such  philosophical issues  as the extent to which individual conduct should be made subordinate to the will of the community,  and that of the proper rôle of the [[state]] as an expression of the will of the community. It also includes the consideration of such practical issues as the formulation and enforcement of rules governing the relations between the individual and the [[state]]. It encompasses the  sociological influences upon the resolution of those issues in various communities, including the collective beliefs (or[[ideology| ideologies]]) that are held by  their members. At the operational level, it includes prescriptive issues  such as the conditions governing the legitimacy of [[government]]; the extent to which collective decision-making should be determined by [[ethics|ethical]] considerations rather than by its intended consequences; and the consideration that should be given to the welfare of foreign nationals. The descriptive content of politics includes the taxonomy of political systems, of  institutional arrangements for the conduct of [[government]], and of the institutions governing the conduct of [[international relations]]. It also includes  accounts of the observed conduct of politicians in seeking to gain the approval of the community, and in their policy-making  and executive activities when in office.
+: ''If a tomato is red, then the tomato is ripe. Since this tomato is very red, this tomato is very ripe.''
-===Etymology===
+Further examples of reasonings involving vague predicates are in the item ''[[Paradoxes and fuzzy logic]]'' and in the section ''Fuzzy logic with no truth-functional semantics''. The main tool for fuzzy logic is the notion of a ''[[fuzzy subset]]'' since a vague predicate is interpreted by a fuzzy subset. Notice that in literature the name ''"fuzzy logic"'' also denotes a large series of topics based on an informal usage of the notion of a fuzzy subset and which are usually devoted to applications.
-The word politics comes from the Greek word Πολιτικά (politika), which was itself derived from πόλις (polis), "city". It was first used  to mean the art of living in a city, but it subsequently acquired the broader interpretation of the art of being a citizen. That broader interpretation was implicit in the use of the word "cosmopolitan" to denote a citizen of the cosmos by the [[Cynics]] of the 4th century BCE. Later derivations included the terms "politic", "policy" and "police", and "polity" (a word used by some academics to refer to particular forms of governmental organisation). The term politics itself has also been used colloquially to describe  (slightly discreditable) social conduct, as in "office politics" and, when extended to form a verb, in "politicking".
-''[[Politics|.... (read more)]]''
+As a matter of fact, fuzzy logic is an evolution and an enlargement of [[multi-valued logic]] since all the definitions and results in the literature on multi-valued logic are also considered in fuzzy logic. In particular, as in multi-valued logic, the starting point is a fixed ''valuation structure'', i.e. a bounded [[lattice (order)|lattice]] ''L'' equipped with suitable operations to interpret the logical connectives. The minimum 0 means ''''False'''', the maximum 1 means ''''True'''', the remaining elements are interpreted as intermediate truth values. The following is the main class of valuation structures (see Hájek 1998, Novák et al. 1999 and Gottwald 2005) corresponding to the connectives <math>\wedge</math> and <math>\rightarrow </math>.
+''[[Formal fuzzy logic|.... (read more)]]''
+<noinclude>
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+</noinclude>

CZ:Featured article/Current: Difference between revisions

Revision as of 01:02, 16 June 2012

Formal fuzzy logic

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