By I. Burhan Türksen
Fuzzy set and common sense concept recommend that every one usual language linguistic expressions are vague and has to be assessed as an issue of measure. yet typically club measure is an vague concept which calls for that sort 2 club levels be thought of in so much functions regarding human determination making schemas. whether the club features are limited to be Type1, their mixtures generate an period - valued variety 2 club. this is often a part of the final consequence that Classical equivalences breakdown in Fuzzy thought. therefore all classical formulation needs to be reassessed with an top and decrease expression which are generated by means of the breakdown of classical formulation.
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Additional info for An Ontological and Epistemological Perspective of Fuzzy Set Theory
Since we have argued all set and logic theories rest upon some philosophical assumptions, it is only consistent for us to argue that if these presuppositions are not dealt with explicitly in our writings, they must still be there implicitly. , to make the philosophical unconscious grounding more conscious. 2. Assessing Internal Consistency It is only when a multi-leveled overview of a complex theory is available that its internal consistency can be readily evaluated. While a given set of assumptions or hypotheses may appear to be coherently connected with each other at one level of inquiry, they may still be quite incompatible with positions assumed by the same theory on other levels of hierarchy.
Also with this conviction I raised the Conjunctive and Disjunctive Normal (Canonical) Form representations in the combination of concepts. In turn, it became to the forefront that linguistic connectives "AND". , are also imprecise and that they need to be precisiated in a graded manner and thus "AND" does not correspond to tnorm and "OR" does not correspond to a t-co-norm in a one-to-one isomorphic correspondence. Therefore, each combination of concepts has its own Conjunctive Normal (Canonical) Form that is not equivalent in general but larger in the set sense and greater in the membership sense or equal to its Disjunctive Normal (Canonical) Form for particular subclasses of t-norms and t-co-norms that are 32 Foundation isomorphic to Archimedean norms which are nilpotent or strict, and special cases of (Max-Min) and some ordinal sums.
Appendix 41 Secondly, his concern therefore with human decision-making processes in scientific thought brought him in contact and initially in conflict with the defenders of Probability theory and later with OR and MS. ) (A further personal note: T was introduced to Professor Zadeh in summer 1970 at NATO Conference on OR Education that was held in Istanbul, Turkey, by R. ) Let me next attempt to articulate Zadeh's scientific and philosophical contributions in a bit more detail. a continuum of grades of membership" along with the "complement", "containment", "union" and "intersection" operations with "Max-Min" and with "Algebraic sum and Product", as well as "convex combination of" fuzzy sets, "Fuzzy sets induced by mappings", and "separation of convex fuzzy sets".