{"title":"Tutorial on the uses of the interval type-2 fuzzy set’s Wavy Slice Representation Theorem","authors":"J. Mendel","doi":"10.1109/NAFIPS.2008.4531278","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531278","url":null,"abstract":"This tutorial paper demonstrates how the Wavy Slice Representation Theorem (RT) for a general type-2 fuzzy set (T2 FS), when specialized to an interval T2 FS (IT2 FS), can be used as the starting point to solve many diverse problems that involve IT2 FSs. The problems considered are: Set theoretic operations, centroid, uncertainty measures, similarity, inference engine computations for Mamdani IT2 fuzzy logic systems, and linguistic weighted average. Each solution obtained from the RT is a structural solution but is not a computational solution, however the latter are always found from the former. It is this author's recommendation that one should use the RT as a starting point whenever solving a new problem involving IT2 FSs, because it has had such great success in solving so many such problems in the past.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128259839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum computation techniques for gauging reliability of interval and fuzzy data","authors":"L. Longpré, C. Servin, V. Kreinovich","doi":"10.1080/03081079.2010.510247","DOIUrl":"https://doi.org/10.1080/03081079.2010.510247","url":null,"abstract":"In traditional interval computations, we assume that the interval data corresponds to guaranteed interval bounds, and that fuzzy estimates provided by experts are correct. In practice, measuring instruments are not 100% reliable, and experts are not 100% reliable, we may have estimates which are \"way off\", intervals which do not contain the actual values at all. Usually, we know the percentage of such outlier un-reliable measurements. However, it is desirable to check that the reliability of the actual data is indeed within the given percentage. The problem of checking (gauging) this reliability is, in general, NP-hard; in reasonable cases, there exist feasible algorithms for solving this problem. In this paper, we show that quantum computations techniques can drastically speed up the computation of reliability of given data.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128433844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"General interval type-2 Mamdani fuzzy systems are universal approximators","authors":"H. Ying","doi":"10.1109/NAFIPS.2008.4531255","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531255","url":null,"abstract":"Fuzzy systems using type-2 fuzzy sets and fuzzy logic are important and are indeed gaining increasing attention in the literature (e.g., type-2 fuzzy controllers and fuzzy models). A fundamental question is whether a type-2 fuzzy system is a universal approximator in that it is capable of uniformly approximating any real continuous function on a compact domain to any degree of accuracy. Up to date, no work addressing this issue can be found in the literature. In this paper, we constructively prove that a general class of Mamdani interval type-2 fuzzy systems is universal approximator. This result lays a theoretical foundation for the fuzzy systems development.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130514073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fuzziness in evolutionary biology","authors":"R. Seising","doi":"10.1109/NAFIPS.2008.4531318","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531318","url":null,"abstract":"The core of soft computing consists of fuzzy sets and systems (FSS) computing with words (CW) and the computational theory of perceptions (CTP). In the introduction of this paper we give a brief presentation of that subject. The second section of the paper focuses on a general view on fuzziness in evolutionary biology. The view on evolutionary biology is a meta-scientific reflection: The theory of FSS complemented by CW and CTP builds a stack of methodologies to help bridge the gap between systems and phenomena in the real world and scientific theories. Lotfi A. Zadeh established the theory of FSS to bridging this gap in the 1960s when he compared living systems that are very complex and man-made systems e.g. in electrical engineering. We use Zadeh's stack of soft computing methodologies in this tradition to reflect the field of evolutionary biology in the view of the evolutionary biologist, historian and philosopher of biology Ernst Mayr who emphasized that most theories in biology are based not on laws but on concepts.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125551646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Supplier selection in a multi-item/multi-supplier environment","authors":"S. Davari, M. Zarandi, I. Turksen","doi":"10.1109/NAFIPS.2008.4531232","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531232","url":null,"abstract":"Suppliers play a pivotal role in success of any organization. Supplier Selection is a complicated problem due to the vagueness of data and also its multi-criteria nature and the real world still observes a noticeable gap between its theory and practice. The aim of this paper is to present a fuzzy decision-making approach to address this problem in a way that facilitates the process of decision making while not deteriorating its comprehensiveness. The main contributions of the paper are twofold: first, a model is developed to consider multiple suppliers and multiple items. Moreover, a piecewise linear membership function (PLMF) is proposed for a specific criterion and is shown how it leads to better solutions. The model functions well in cases where decision maker is sensitive about a specific criterion, in other words, when there are some unequal weights for objectives of the problem. Although asymmetric methods proposed by Zimmerman are a way to tackle the above-mentioned situations; it is demonstrated that how the proposed model brings about both efficiency and simplicity for decision maker which is originated from the utilization of PLMF.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126531125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Using fuzzy logic based evidence for Bulgarian winery market competitiveness","authors":"D. Olson, A. Korvin","doi":"10.1109/NAFIPS.2008.4531212","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531212","url":null,"abstract":"A fuzzy set based evidence set methodology is developed in this paper to address a wine management decision about whether or not to undertake a product introduction, and if so, in what cost range. The basis for this decision is competitiveness of the marketplace and cost based on the perception of related selling price and profitability. The paper presents an application utilizing simulated results and expert opinions acquired through collaboration with Bulgarian institutions of higher education.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121504413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identification of Takagi-Sugeno (TS) fuzzy model with Evolutionary Parallel Gradient Search","authors":"Zhao Zhongyu, W. Xie, H. Hong","doi":"10.1109/NAFIPS.2008.4531203","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531203","url":null,"abstract":"In this paper the modeling of nonlinear system with TS fuzzy model is discussed. The identification of TS fuzzy model is first posed as an optimization problem and a new hybrid optimization algorithm- referred to as evolutionary parallel gradient search (EPGS) is applied to find the optimal values of the parameters in the fuzzy model. The main feature of EPGS is its ability to deal with the local minima problem in global optimization. By using the gradient information of cost function, EPGS combines gradient-based algorithm and evolutionary algorithm (EA) in an innovative way such that EA is used to keep the best searches at every step in the optimization process and the gradient descent method is used to update these best searches. The application of EPGS in the parameter estimation problem of TS fuzzy models shows excellent performance in terms of modeling accuracy.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122518451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Perfect and precisely perfect fuzzy graphs","authors":"P. Nair","doi":"10.1109/NAFIPS.2008.4531246","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531246","url":null,"abstract":"In this paper, we consider two different definitions of adjacency in fuzzy graph. Thus any graph theory concept that can be defined through adjacency can have two different variations in fuzzy graph theory. We demonstrate this fact through perfect graph and perfect graph theorem. Thus in the case of fuzzy graphs we have two independent concepts: perfect fuzzy graphs and precise perfect fuzzy graphs.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131382061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Axioms for uncertainty measures on belief functions and credal sets","authors":"A. Bronevich, G. Klir","doi":"10.1109/NAFIPS.2008.4531311","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531311","url":null,"abstract":"In this paper we present a system of axioms for total uncertainty measures, which can be equivalently defined for belief functions and credal sets. This system of axioms provides that a measure of total uncertainty coincides with Shannon entropy on the set of probability measures and it is the Hartley measure on the set of {0,1}-valued belief measures. We check this system of axioms for the well-known candidates for total uncertainty measures; in particular, the upper entropy obeys all the necessary requirements. Some properties of such measures of total uncertainty allow us to propose ways for disaggregation of these measures into two parts, which correspond to measures of conflict and measures of nonspecificity.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127957054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Handling disjunctions in open world relational databases","authors":"N. Viswanath, Rajshekhar Sunderraman","doi":"10.1109/NAFIPS.2008.4531248","DOIUrl":"https://doi.org/10.1109/NAFIPS.2008.4531248","url":null,"abstract":"Incomplete information is usually present in a database in the form of null values. Several other forms of incompleteness such as fuzzy information, partial values and disjunctive information have been studied extensively. Most of the research on indefinite information has been carried out under the Closed World Assumption(CWA). In this paper, we present a data structure that supports the opposite view, the Open World Assumption(OWA), where negative information is explicitly represented in a relation. We allow disjunctions at the tuple level to appear in two forms: A or B and notA or notB, thus obtaining a gain in expressivity. Wenot define a generalization of the relational algebra that handles this kind of information.","PeriodicalId":430770,"journal":{"name":"NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132117485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}