An Ontological and Epistemological Perspective of Fuzzy Set by I. Burhan Türksen

By I. Burhan Türksen

Fuzzy set and good judgment idea recommend that every one average language linguistic expressions are obscure and needs to be assessed as a question of measure. yet more often than not club measure is an vague suggestion which calls for that style 2 club levels be thought of in such a lot functions regarding human determination making schemas. no matter if the club services are constrained to be Type1, their combos generate an period - valued variety 2 club. this is often a part of the overall end result that Classical equivalences breakdown in Fuzzy idea. therefore all classical formulation has to be reassessed with an top and decrease expression which are generated by way of the breakdown of classical formulation.

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For example, particular consequences that we receive are:(l) FDCF(A OR NOT A)cFCCF(A OR NOT A) which is the realization of the law of "Fuzzy Middle" as opposed to the Law of Excluded Middle and (2) the Law of "Fuzzy Contradiction, FDCF(A AND NOT A) cFCCF(A AND NOT A) as opposed to the Law of Crisp Contradiction. As a consequence of these, we obtain new Laws of Conservation as: |i[FDCF(A AND c(A))] + ^l[FCCF(A OR c(A))] = 1; (well known but re-interpreted for fuzzy sets) and |i[FDCF(A OR c(A))] + ^[FCCF(A AND c(A))] = 1.

Therefore system models so developed are assumed to be universally valid representations of domain specific object world that is captured by measurement based data only! , V{o,i}, by measurements only. On level 5 of the hierarchy, dealing with the Domain-Specific Epistemology, for a particular investigation, the scientists appear to find limits to knowledge only on the subjective side of the Cartesian split. Tt is assumed that such subjective distortions may originate in the (system) analyst, but the "untruths" are all seen as coming from the s-or subject- side of the sRo split.

On the other hand, the subject matter rests more precisely on the "subjectivity" side in all its richness for the human decisionmaking systems. Thus for the objectivism, it is no wonder that their mechanistic meta-physical explanations demanded revisions. Nor is it surprising that their critical writing have quite a different tone as well and perhaps even a different implicit epistemological leaning. For all these reasons and more, we have proposed that at the very foundation of the Ontological level, we need to consider the " S < > O " paradigm to push to the surface the integrated subjective-objective stand that is investigated by most fuzzy set and logic theory researchers in many different directions.

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