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

By I. Burhan Türksen

Fuzzy set and common sense idea recommend that every one ordinary language linguistic expressions are obscure and needs to be assessed as an issue of measure. yet mostly club measure is an vague proposal which calls for that variety 2 club levels be thought of in such a lot functions with regards to human choice making schemas. no matter if the club features are constrained to be Type1, their combos generate an period - valued sort 2 club. this is often a part of the final outcome that Classical equivalences breakdown in Fuzzy conception. therefore all classical formulation has to be reassessed with an top and decrease expression which are generated through the breakdown of classical formulation.

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Example text

In this paper, we are introduced to "the concept of a possibility distribution", "possibility measure", truth qualification", "probability qualification", etc. " It is stated that "Given our veneration for what is precise, rigorous and quantitative, and our disdain for what is fuzzy, unrigorous and qualitative, it is not surprising that the advent of digital computers... have proved highly effective in dealing with mechanistic systems, that is, with inanimate systems whose behavior is governed by the laws of mechanics, physics, chemistry, and electromagnetism.

And introduce "Meta-Linguistic Axioms" as a foundation for CWW. 5. , |IA- X ^ - [ O J ] , M'A(x)=ae[0,l], xeX, where |IA(X) is the membership assignment of an element XGX to a concept class A in a proposition. Most of all concepts are definable to be true to a degree. , |LIA:X^^[0,1] is not reducible to |LIA:X^^{0,1}. , jiv-M^A -^ {T,F} absolutely in Descriptive fuzzy set theory, where V{T,F}? or V{o,i}, is the veristic assignment which is the atomic building block of the two-valued logic. , jay: [jayijaA -^ [0,1]]^'{0,1} where V[o,i] is a partial veristic truth assignment but V'|o,i} is a secondary absolute veristic assignment which is once again the atomic building block of the two-valued logic!

This approach opens the potential of fuzzy theory by exposing the uncertainty entailed in fuzzy reasoning. We all know that in the acquisition of memberships, we are confronted with Type 2 fuzzy sets represented either simply as Interval-Valued Type 2 fuzzy sets or full Type 2 fuzzy sets that exposes the distribution of membership values between the upper and lower membership values by second order fuzzy sets. Naturally, there is much work required to expose all the assumptions that are made in the development and analysis of Type 2 fuzzy sets.

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