A Note on Prototypes,Convexity and Fuzzy Sets

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy.     

刻板印象的自动激活实验研究

本研究应用模糊主次评判方法配合语义启动技术进行实验。结果表明;在年龄刻板印象上存在自动激活,而且没有性别差异;用不同性质的启动词来激活与年龄有关的刻板印象,激活后的刻板印象对年龄的判断有不同的影响,而且被试没有一个人意识到这点,表明内隐刻板印象的存在;人的判断具有模糊性,模糊主次评判方法有助于社会认知领域的量化研究,这是一个全新的尝试。     

模糊分组的时间层次网络结构研究

本研究通过两个实验来对连续性的时间顺序标码的层次网络结构的性质进行了探讨。研究结果表明,连续性的时间顺序标码是按照层次网络的结构组织起来的,若干项目组成一个小组,若干小组组成更大的组。连续性的时间标码层次网络的形成具有自动性、内隐性的特点。连续性的时间顺序标码的层次网络结构是主观的、模糊的。两个相邻的小组的项目之间出现了距离效应,而两个相邻的大组的项目之间则出现了越界效应,由于两个大组的项目的平均距离大于两个小组的项目的平均距离,越界效应大于距离效应。     

Identifying and prioritizing factors influencing the selection of the top suppliers of e‐procurement using FDEMATEL and FANP

The aim of this study is to identify, rank, and determine the importance of factors influencing the selection of the top supplier of electronic procurement in organizations using a hybrid approach. This is a case study of Irancell Telecommunication Service Company in which fuzzy decision‐making trial and evaluation (FDEMATEL) and fuzzy analytical network process (FANP) were used. FDEMATEL was employed to determine the interaction and interrelationships among the identified criteria and subcriteria, while utilizing FANP to calculate the weights of the criteria and their relevant subcriteria to determine their priorities. Therefore, the research literature was first reviewed to identify the factors influencing the selection of suppliers. For this purpose, the experts on communication networks were interviewed to select 16 final factors as the most important subcriteria that were then categorized as 5 groups (technology, environmental, services, organizational, and commercial) on which the study was based. After extracting the criteria for ranking the suppliers, codifying evaluation questionnaire, and converting the opinions in the Likert scale, 16 criteria were finally chosen with scores above the mean. FDEMATEL was used to determine the weights of subcriteria. In the final step, FANP was employed for prioritization. Results indicate that the organizational criterion is the most influential factor; however, the criterion services is the most permeable factor. The greatest weights were obtained from production capacity and provisions and geographical situation which were weighted 0.097 and 0.039, respectively. They are also regarded as the most and least important criteria for the selection of the top supplier of e‐procurement by the experts.     

Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory.Our emphasis will be on various approaches toward (more or less naively formed)universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets. What we give is a (critical)survey of quite a lot of such approaches which have been offered in the last approximately 35 years. The present Part I is devoted to model based and to axiomatic approaches; the forth-coming Part II will be devoted to category theoretic approaches. This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005. Presented by Jacek Malinowski     

Philosophy for Computers: Some Explorations in Philosophical Modeling

Philosophical modeling has a long and distinguished history, but the computer offers new and powerful prospects for the creation and manipulation of models. It seems inevitable that the computer will become a major tool in future philosophical research. Here I offer an overview of explorations in philosophical computer modeling that we in the Group for Logic and Formal Semantics at SUNY Stony Brook have undertaken: explorations regarding (1) the potential emergence of cooperation in a society of egoists, (2) self-reference and paradox in fuzzy logic, (3) a fractal approach to formal systems, and (4) on-going explorations with models for the emergence of communication. The attempt is not to give a detailed report on any of these but to give a bird s-eye view of them all, emphasizing the general form that the models take, the philosophical motivations behind them, and the kinds of philosophical results that they may have to offer.     

Monadic Fuzzy Predicate Logics

Two variants of monadic fuzzy predicate logic are analyzed and compared with the full fuzzy predicate logic with respect to finite model property (properties) and arithmetical complexity of sets of tautologies, satisfiable formulas and of analogous notion restricted to finite models.     

Fuzzy Logic and Arithmetical Hierarchy III

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.     

Attribute Partitioning in Multiple Attribute Decision Making Problems for a Decision with a Purpose – a Fuzzy Approach

This work introduces a methodology to find solutions corresponding to different purposes in a multiple attribute decision‐making problem under fuzzy environment. The discernment of purpose‐based solutions becomes important when the problem is defined vaguely and solution is targeted to heterogeneous population. Depending on the purpose, for which the solution is sought, the attributes are identified and weighted in an appropriate proportion. The level of similarity between a pair of attributes plays an important role to determine the aggregated value of attributes specific to a purpose. Our work determines the similarity levels between a pair of attributes by calculating their maximum attainability in presence of each other. The achievement of an attribute in presence of another is represented as a fuzzy set in the unit interval. The crisp equivalents of the fuzzy sets in the unit interval are used to define their simultaneous satisfaction denoted as 1‐step relation. The 1‐step relation is extended to (m‐1)‐step relation to calculate the degree of attainability of the same pair of attributes in the presence of m (all) attributes. The different levels of (m‐1)‐step relations generate several partitions of the attributes corresponding to multiple purposes in the multiple attribute decision‐making problems. The degree of fulfilment of the purposes in the alternatives are numerically derived by first taking weighted average of attributes within the equivalence classes of a partition and then aggregating the values corresponding to equivalence classes through ordered weighted averaging. The methodology is illustrated with a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.