Arrow Index of Fuzzy Choice Function

The Arrow index of a fuzzy choice function C is a measure of the degree to which C satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that A(C) characterizes the degree to which C is full rational. We also obtain a method for computing A(C). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality. Thus, if for solving a decision problem several fuzzy choice functions are proposed, by the Arrow index the most rational one will be chosen.Fuzzy choice function, revealed preference indicator, congruence indicator, similarity

Fuzzy ART Choice Functions

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic intersection (∩) with the fuzzy intersection(∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (∨), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare peformance of fuzzy ARTMAP systems that use different choice functions.Advanced Research Projects Agency (ONR N00014-92-J-4015); National Science Foundation (IRI-90-00530); Office of Naval Research (N00014-91-J-4100

A new fuzzy set merging technique using inclusion-based fuzzy clustering

This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets

Parents Preference for Students’ Choice of Urban Schools in Benin City, Nigeria: Integrated AHP Intuitionistic Fuzzy Topsis

The paper examines the attributes considered by parents for school choice enrolment for their children and wards. Four classes of school alternatives with twelve attributes were considered in this work. A survey was randomly carried out in the three Local government areas in Benin City. The Analytical Hierarchy Process (AHP) was adopted  in evaluating the attributes, while intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) was applied in the ranking of the alternatives. In adopting the method two metric functions were used with both producing same result indicating consistency and correctness of results. The Missionary schools (A4) is the most preferred of the 4 alternative schools, closely followed by private schools for middle class (A2) as second best preferred and the premier private schools for the elite (A3) is third best preferred. While, the Public (government) schools (A1) is bracing the rear as least preferred of all the 4 alternatives. It is concluded that adopting scientific approach to humanistic system is appropriate and produces accuracy in results.Keyword: School choice, intuitionistic fuzzy TOPSIS and attribute

A kernel-based framework for learning graded relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl