New PDF release: Advanced Concepts in Fuzzy Logic and Systems with Membership

By Janusz T. Starczewski

ISBN-10: 3642295193

ISBN-13: 9783642295195

This booklet generalizes fuzzy good judgment platforms for various different types of uncertainty, together with - semantic ambiguity because of constrained conception or lack of understanding approximately certain club services - loss of attributes or granularity bobbing up from discretization of genuine information - vague description of club features - vagueness perceived as fuzzification of conditional attributes. as a result, the club uncertainty will be modeled by way of combining equipment of traditional and type-2 fuzzy common sense, tough set idea and chance idea.            specifically, this ebook presents a few formulae for imposing the operation prolonged on fuzzy-valued fuzzy units and provides a few uncomplicated constructions of generalized doubtful fuzzy good judgment platforms, in addition to introduces a number of of tips on how to generate fuzzy club uncertainty. it truly is fascinating as a reference publication for under-graduates in larger schooling, grasp and physician graduates within the classes of desktop technological know-how, computational intelligence, or fuzzy keep an eye on and category, and is mainly devoted to researchers and practitioners in undefined.  

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Additional info for Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty

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The extension of the Lukasiewicz tnorm partially leads to unexpected results. 2. Consider two fuzzy truth intervals with triangular membership F L mF +ΔF R −u and g (v) = , functions defined as, f (u) = min u−mΔFF+Δ ΔF R L min v−mG +ΔGL mG +ΔGR −v , ΔGL ΔGR . 36) w (μ) = max (0, − (ΔF R +ΔGR ) μ + mF + mG + ΔF R +ΔGR − 1) . 37) Consequently, the extended Lukasiewicz t-norm based on the minimum is characterized by the two following cases presented in Fig. 5. 5 Fig. 38) otherwise μT˜L min (F,G) (w) = 1 w=0 mF +mG −1+ΔF R +ΔGR −w ΔF R +ΔGR elsewhere.

Rα (A) (x) ≥ β ⇐⇒ ∀y : (x, y) ≥ Rα and μA (y) ≥ β. Note that the original definition of a fuzzy-rough set is valid for single fuzzy relation R. Extending this, many fuzzy equivalence relations Ri forms a fuzzy partition Φ on X, which is put up by fuzzy sets Fi . , inf max μFi (x) > 0 . 62) Therefore, a fuzzy-rough set may also be interpreted as a pair Φ (A) , Φ (A) of the lower and upper approximations of A by Φ which may be derived in the spirit of Nakamura’s definition. Now, fuzzy partition sets Fi can be decomposed into α-cuts allowing the fuzzy-rough set to be an α-composition of rough-fuzzy sets.

Semantic ambiguity may also apply to gradual properties. This type of uncertainty can be handled by type-2 fuzzy sets, and consequently, their use should follow from limited perception or lack of knowledge about the exact membership function. Fuzzy set of this type are characterized by ill-known memberships in the truth interval. Therefore the main source for type-2 fuzzy sets is an incomplete knowledge of the membership description. The particular kind of these type-2 fuzzy sets — an interval-valued fuzzy set is characterized by memberships of ill-known boundaries on the truth scale.

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Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty by Janusz T. Starczewski


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