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It is because of the concept and the use of infinity that much of the confusions, contradictions, and paradoxes have arisen in set theory.
Since the fuzzy set theory provides a mathematical formalism for vagueness and imprecision that is ever present in decision support systems in many areas, the fuzzy set theory is integrated with MAUT to increase its flexibility and sensitiveness in this paper.
Yang, "Data mining diagnosis system based on rough set theory for boilers in thermal power plants," Frontiers of Mechanical Engineering in China, Vol.
In this proposal folksonomies--human-made taxonomies--will be converted to machine-understandable ontologies adapted from fuzzy set theory.
True, they had decided to use the context of Axiomatic Set Theory, ZF, as developed by Zermelo and Fraenkel for their work.
It is feasible that a symbiosis of the proposed theory and Vdovin set theory [1, 2] will permit to formulate a (presumably) non-contradictory axiomatic set theory which will represent the core of Cantor set theory in a maximally full manner as to the essence and the contents.
Since set theory relies on the (according to my chosen premises, non-valid) modern logical axiom of identity, I infer that the premises of the WIE mathematical theory of sets violate the premises of non-Aristotelian systems-set theory does not and cannot survive general-semantics-based scrutiny.
The application of fuzzy set theory to decision-making and evaluation in different real estate issues has been well-documented, for instance in the geographical information system (GIS) for spatial analysis (Sui, 1992; Zeng and Zhou, 2001), as well as in housing sales performance predictions utilizing a computer-based decision support tool for investors and contractors (Perng et al.
These rules are based on the notion of triangular numbers from fuzzy set theory and are posited as "rules of thumb" type behaviors.
As Wapner informs us, the question was not laid to rest until Stanford University's Paul Cohen proved that the problem is Godel-undecidable within standard set theory.