Download Application of fuzzy logic to social choice theory by John N. Mordeson PDF

By John N. Mordeson

ISBN-10: 1482250993

ISBN-13: 9781482250992

Fuzzy social selection idea comes in handy for modeling the uncertainty and imprecision common in social existence but it's been scarcely utilized and studied within the social sciences. Filling this hole, Application of Fuzzy common sense to Social selection Theory presents a entire learn of fuzzy social selection theory.

The ebook explains the concept that of a fuzzy maximal subset of a collection of choices, fuzzy selection capabilities, the factorization of a fuzzy choice relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian effects, fuzzy types of Arrow’s theorem, and Black’s median voter theorem for fuzzy personal tastes. It examines how unambiguous and specific offerings are generated via fuzzy personal tastes and even if precise offerings triggered via fuzzy personal tastes fulfill convinced believable rationality relatives. The authors additionally expand identified Arrowian effects concerning fuzzy set conception to effects concerning intuitionistic fuzzy units in addition to the Gibbard–Satterthwaite theorem to the case of fuzzy susceptible choice family members. the ultimate bankruptcy discusses Georgescu’s measure of similarity of 2 fuzzy selection functions.

Show description

Read Online or Download Application of fuzzy logic to social choice theory PDF

Similar popular & elementary books

On The Foundations of Combinatorial Theory: Combinatorial Geometries

It's been transparent in the final ten years that combinatorial geometry, including its order-theoretic counterpart, the geometric lattice, can serve to catalyze the full box of combinatorial conception, and an enormous target of this ebook, now on hand in a initial variation, is to give the speculation in a kind obtainable to mathematicians operating in disparate matters.

Application of fuzzy logic to social choice theory

Fuzzy social selection thought turns out to be useful for modeling the uncertainty and imprecision usual in social existence but it's been scarcely utilized and studied within the social sciences. Filling this hole, software of Fuzzy common sense to Social selection idea presents a complete examine of fuzzy social selection concept.


Precalculus is meant for college-level precalculus scholars. for the reason that precalculus classes range from one establishment to the following, we've tried to fulfill the desires of as extensive an viewers as attainable, together with all the content material that would be lined in any specific path. the result's a complete e-book that covers extra flooring than an teacher may possibly most probably hide in a customary one- or two-semester direction; yet teachers may still locate, virtually with out fail, that the themes they want to incorporate of their syllabus are lined within the textual content.

Additional resources for Application of fuzzy logic to social choice theory

Example text

M. Larson, J. N. Mordeson, J. D. Potter, M. J. Wierman, Applying Fuzzy Mathematics to Formal Models in Comparative Politics, Springer-Verlag Berlin Heidelberg, Studies in Fuzziness and Soft Computing 225, 2008. 5. Georgescu, Fuzzy Choice Functions: A Revealed Preference Approach, Studies in Fuzziness and Soft Computing, Springer-Verlag Berlin Heidelberg 2007. 6. P. Hajek, Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998. 7. M. Koenig-Archibugi, Explaining government preferences for institutional change in EU foreign and security policy, International Organizations, 58 (2004) 137–174.

Then the following properties hold. (1) C satisfies condition γ for all (µ, ν) ∈ SC , where SC = {(µ, ν) | µ, ν ∈ FP ∗ (X), µ ∩ (µ ∪ ν) = 1∅ }. (2) ρC is partially transitive. 2. Consistency Conditions ✐ 35 Proof. (1) Let µ, ν ∈ FP ∗ (X). Suppose C(µ)∩C(ν) = 1∅ . Then condition γ clearly holds. Suppose C(µ)∩C(ν) = 1∅ . By condition α, C(µ∪ν)∩µ ⊆ C(µ). Let (µ, ν) ∈ SC . Then 1∅ = C(µ∪ν)∩µ = C(µ∪ν)∩C(µ). Hence by condition β, C(µ) ⊆ C(µ ∪ ν). Thus C(µ) ∩ C(ν) ⊆ C(µ ∪ ν). (2) Let x, y, z ∈ X be such that ρC (x, y) > 0, ρC (y, z) > 0.

13 Let C be a fuzzy choice function on X. Then C is said to satisfy path independence (PI) if ∀µ, ν ∈ F P ∗ (X), C(µ ∪ ν) = C(C(µ) ∪ C(ν)). 13 is a fuzzification of the crisp case which says that choices from µ ∪ ν are the same as those arrived at by first choosing from µ and from ν, and then choosing among these chosen alternatives. Path independence yields the following result: An alternative x ∈ Supp(C(µ ∪ ν)) if and only if x ∈ Supp(C(C(µ) ∪ C(ν))). Since x ∈ Supp(C(µ ∪ ν)) implies x ∈ Supp(µ ∪ ν) and also x ∈ Supp(C(C(µ) ∪ C(ν))) implies x ∈ Supp(C(µ) ∪ C(ν)) similar comments concerning decentralization as those in [2, p.

Download PDF sample

Rated 4.73 of 5 – based on 46 votes