I. Burhan Turksen

Portfolio selection based on fuzzy probabilities and possibility distributions

Abstract In this paper, two kinds of portfolio selection models are proposed based on fuzzy probabilities and possibility distributions, respectively, rather than conventional probability distributions in Markowitzs model. Since fuzzy probabilities and possibility distributions are obtained depending on possibility grades of security data offered by experts, investment experts’ knowledge can be reflected. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches.

Measurement of Membership Functions: Theoretical and Empirical Work

This chapter presents a review of various interpretations of the fuzzy membership function together with ways of obtaining a membership function. We emphasize that different interpretations of the membership function call for different elicitation methods. We try to make this distinction clear using techniques from measurement theory.

Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm

Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.

Fuzzy functions with support vector machines

A new fuzzy system modeling (FSM) approach that identifies the fuzzy functions using support vector machines (SVM) is proposed. This new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods. It is a new alternate version of the earlier FSM with fuzzy functions approaches. SVM is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c-means (FCM) clustering algorithm. Original input variables, the membership values obtained from the FCM together with their transformations form a new augmented set of input variables. The performance of the proposed system modeling approach is compared to previous fuzzy functions approaches, standard SVM, LSE methods using an artificial sparse dataset and a real-life non-sparse dataset. The results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods.

A fuzzy neural network for pattern classification and feature selection

A fuzzy neural network with memory connections for classification, and weight connections for selection is introduced, thereby solving simultaneously two major problems in pattern recognition: pattern classification and feature selection. The proposed network attempts to select important features from among the originally given plausible features, while maintaining the maximum recognition rate. The resulting value of weight connection represents the degree of importance of feature. Moreover, the knowledge acquired by the network can be described as a set of interpretable rules. The effectiveness of this new method has been validated by using Andersons IRIS data. The results are: first, the use of two features selected by our method from among the original four in the proposed network results in virtually identical classifier performance; and second, the constructed classifier is described by three simple rules that are of if-then form.

A new class of fuzzy implications, axioms of fuzzy implication revisited

Abstract Many different fuzzy implication operators have been proposed; most of them fit into one of the two classes: implication operations that are based on an explicit representation of implication A → B in terms of &, ∨, and ¬ (e.g., S-implications that are based on the formula B ∨ ¬ A), and R-implications that are based on an implicit representation of implication A → B as the weakest C for which C&B implies A. However, some fuzzy implication operations (such as ba) cannot be naturally represented in this form. To describe such operations, we propose a new (third) class of implication operations called A-implications whose relation to &, ∨, and ¬ is described by (implicit) axioms.

Type I and type II fuzzy system modeling

Abstract Two system modeling approaches are proposed with a unification of fuzzy methodologies. Type I and Type II knowledge representation are reviewed together with their proposed approximate reasoning schemes. Type I representation and inference are based on Boolean normal forms. Type I models are myopic because, in these models, either the disjunctive or the conjunctive Boolean normal forms are selected rather arbitrarily for knowledge representation and inference and then they are fuzzified. Whereas in Type II models, representation and inference are based on fuzzy disjunctive and conjunctive normal forms which are derived from the fuzzy truth tables.

Fuzzy pharmacology: theory and applications.

Fuzzy pharmacology is a term coined to represent the application of fuzzy logic and fuzzy set theory to pharmacological problems. Fuzzy logic is the science of reasoning, thinking and inference that recognizes and uses the real world phenomenon that everything is a matter of degree. It is an extension of binary logic that is able to deal with complex systems because it does not require crisp definitions and distinctions for the system components. In pharmacology, fuzzy modeling has been used for the mechanical control of drug delivery in surgical settings, and work has begun evaluating its use in other pharmacokinetic and pharmacodynamic applications. Fuzzy pharmacology is an emerging field that, based on these initial explorations, warrants further investigation.

Capacitated location-routing problem with time windows under uncertainty

This paper puts forward a location-routing problem with time windows (LRPTW) under uncertainty. It has been assumed that demands of customers and travel times are fuzzy variables. A fuzzy chance constrained programming (CCP) model has been designed using credibility theory and a simulation-embedded simulated annealing (SA) algorithm is presented in order to solve the problem. To initialize solutions of SA, a heuristic method based on fuzzy c-means (FCM) clustering with Mahalanobis distance and sweep method have been employed. The numerical experiments clearly attest that the proposed solution approach is both effective and robust in solving problems with up to 100 demand nodes in reasonable times.

A fuzzy set preference model for consumer choice

Abstract A fuzzy set model for predicting consumer choice is developed by combining the vector conjoint model with fuzzy measurement in a new model that requires only ordinal data. Fuzzy set measurement of consumer preferences is examined by testing alternative set representations and an interactive set definition method. A comparison test of predictive validity using identical data from 139 subjects showed large improvements in rank order prediction validity compared to a non-fuzzy approach. Prediction improvements of 83% are attributable to the use of fuzzy set definitions for subject ratings, with the first two of six ordered ranking predicted on average.