The uncovered set and indifference in spatial models: A fuzzy set approach

John N. Mordeson; Terry D. Clark; Nicholas R. Miller; Peter C. Casey; Michael B. Gibilisco

doi:10.1016/j.fss.2010.10.016

The uncovered set and indifference in spatial models: A fuzzy set approach

John N. Mordeson, Terry D. Clark, Nicholas R. Miller, Peter C. Casey, Michael B. Gibilisco

Department of Political Science and International Relations

Research output: Contribution to journal › Article

6 Scopus citations

Abstract

The uncovered set was developed in order to predict outcomes when spatial models result in an empty core. In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives. Hence, existing definitions of the covering relationship return differing results. We develop a definition for a fuzzy covering relation. Our definition results in an uncovered set that is, in most cases, contained within the Pareto set. We conclude by characterizing the exceptions.

Original language	English
Pages (from-to)	89-101
Number of pages	13
Journal	Fuzzy Sets and Systems
Volume	168
Issue number	1
DOIs	https://doi.org/10.1016/j.fss.2010.10.016
Publication status	Published - Apr 1 2011

Fingerprint

All Science Journal Classification (ASJC) codes

Artificial Intelligence
Logic

Cite this

Mordeson, J. N., Clark, T. D., Miller, N. R., Casey, P. C., & Gibilisco, M. B. (2011). The uncovered set and indifference in spatial models: A fuzzy set approach. Fuzzy Sets and Systems, 168(1), 89-101. https://doi.org/10.1016/j.fss.2010.10.016

@article{b0caccadf6174b75af0c2e12ba2c4667,

title = "The uncovered set and indifference in spatial models: A fuzzy set approach",

abstract = "The uncovered set was developed in order to predict outcomes when spatial models result in an empty core. In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives. Hence, existing definitions of the covering relationship return differing results. We develop a definition for a fuzzy covering relation. Our definition results in an uncovered set that is, in most cases, contained within the Pareto set. We conclude by characterizing the exceptions.",

author = "Mordeson, {John N.} and Clark, {Terry D.} and Miller, {Nicholas R.} and Casey, {Peter C.} and Gibilisco, {Michael B.}",

year = "2011",

month = "4",

day = "1",

doi = "10.1016/j.fss.2010.10.016",

language = "English",

volume = "168",

pages = "89--101",

journal = "Fuzzy Sets and Systems",

issn = "0165-0114",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - The uncovered set and indifference in spatial models

T2 - A fuzzy set approach

AU - Mordeson, John N.

AU - Clark, Terry D.

AU - Miller, Nicholas R.

AU - Casey, Peter C.

AU - Gibilisco, Michael B.

PY - 2011/4/1

Y1 - 2011/4/1

N2 - The uncovered set was developed in order to predict outcomes when spatial models result in an empty core. In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives. Hence, existing definitions of the covering relationship return differing results. We develop a definition for a fuzzy covering relation. Our definition results in an uncovered set that is, in most cases, contained within the Pareto set. We conclude by characterizing the exceptions.

AB - The uncovered set was developed in order to predict outcomes when spatial models result in an empty core. In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives. Hence, existing definitions of the covering relationship return differing results. We develop a definition for a fuzzy covering relation. Our definition results in an uncovered set that is, in most cases, contained within the Pareto set. We conclude by characterizing the exceptions.

UR - http://www.scopus.com/inward/record.url?scp=79551525395&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79551525395&partnerID=8YFLogxK

U2 - 10.1016/j.fss.2010.10.016

DO - 10.1016/j.fss.2010.10.016

M3 - Article

AN - SCOPUS:79551525395

VL - 168

SP - 89

EP - 101

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

SN - 0165-0114

IS - 1

ER -

Access to Document

10.1016/j.fss.2010.10.016