Elkan's theoretical argument, reconsidered

@article{Trillas2001ElkansTA,
  title={Elkan's theoretical argument, reconsidered},
  author={Enric Trillas and Claudi Alsina},
  journal={Int. J. Approx. Reason.},
  year={2001},
  volume={26},
  pages={145-152}
}
On Elkan's theorems: Clarifying their meaning via simple proofs
TLDR
This article deals with the claims that “a standard version of fuzzy logic collapses mathematically to two‐valued logic” made by Charles Elkan in two papers and presents alternative, considerably simpler proofs of Elkan's theorems and uses these proofs to argue thatElkan's claims are unwarranted.
Twenty years later: Remarks on a polemic
  • E. Trillas
  • Mathematics
    2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS)
  • 2013
This paper just deals with the starting point in the twenty years old paper [1] by Charles Elkan, with which he tried to puzzle fuzzy logic: That the formula 1-min (a,1-b) = max (b, min (1-a, 1-a))
Searching for the roots of non-contradiction and excluded-middle
This paper tries to obtain frameworks in which one can prove as theorems, and with few assumptions, the laws of non-contradiction (NC) and excluded-middle (EM), for a large class of very general
Comments to "Paradoxes of fuzzy logic, revisited"
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TLDR
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Clarifying Elkan's theoretical result
This paper is devoted to clarify the only theoretical result included in the controversial work of C. Elkan “The paradoxical success of fuzzy logic” (1994), by offering both a short proof of it and a
On contra‐symmetry and MPT conditionality in fuzzy logic
TLDR
The contra‐positive of S implications, R implications, Q implications, and Mamdani–Larsen operators, verifying either Modus Ponens or Modus Tollens inequalities or both, the conditionality's aspect on which lies the complementarity with Fodor is studied.
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TLDR
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TLDR
It is shown that the reasoning based on the truth qualification principle requires some modifications so that it naturally gives rise to type-2 fuzzy sets, in order to capture the uncertainty about selection of a solution for a set of self-referential statements.
How I would like to foresee the future of theoretic fuzzy logic
TLDR
By arguing on some aspects fuzzy sets and fuzzy logic research could follow to not only being a theoretic ground for Zadeh’s Computing with Words, but also for going towards a new experimental science dealing with the imprecision and non-random uncertainty permeating language and reasoning.
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