Ronald R. Yager

On ordered weighted averaging aggregation operators in multicriteria decisionmaking

The author is primarily concerned with the problem of aggregating multicriteria to form an overall decision function. He introduces a type of operator for aggregation called an ordered weighted aggregation (OWA) operator and investigates the properties of this operator. The OWAs performance is found to be between those obtained using the AND operator, which requires all criteria to be satisfied, and the OR operator, which requires at least one criteria to be satisfied. >

Some geometric aggregation operators based on intuitionistic fuzzy sets

The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.

A procedure for ordering fuzzy subsets of the unit interval

Abstract We introduce a function to help in the ordering of fuzzy subsets of the unit interval. This function is the integral of the mean of the level sets associated with the fuzzy subsets. Various properties of this function are studied.

Families of OWA operators

Abstract We introduce the ordered weighted averaging (OWA) operators. We look at some semantics and applications associated with these operators. We discuss the problem of obtaining the associated weighting parameters. We discuss the connection between OWA operators and linguistic quantifiers. We introduce a number of parametrized families of OWA operators; maximum entropy, S-OWA, step and window are among the most important of these families. We study the evaluation of quantified propositions using these operators. We introduce the idea of aggregate dependent weights.

On the Dempster-Shafer framework and new combination rules

Abstract We discuss the basic concepts of the Dempster-Shafer approach, basic probability assignments, belief functions, and probability functions. We discuss how to represent various types of knowledge in this framework. We discuss measures of entropy and specificity for belief structures. We discuss the combination and extension of belief structures. We introduce some concerns associated with the Dempster rule of combination inherent in the normalization due to conflict. We introduce two alternative techniques for combining belief structures. The first uses Dempsters rule, while the second is based upon a modification of this rule. We discuss the issue of credibility of a witness.

Quantifier guided aggregation using OWA operators

We consider multicriteria aggregation problems where, rather than requiring all the criteria be satisfied, we need only satisfy some portion of the criteria. The proportion of the critera required is specified in terms of a linguistic quantifier such as most. We use a fuzzy set representation of these linguistic quantifiers to obtain decision functions in the form of OWA aggregations. A methodology is suggested for including importances associated with the individual criteria. A procedure for determining the measure of “orness” directly from the quantifier is suggested. We introduce an extension of the OWA operators which involves the use of triangular norms.

On a general class of fuzzy connectives

Abstract A general class of conectives, intersection and union, are presented for fuzzy sets. The properties of this class are studied in comparison to the ordinary intersection and union.

Induced ordered weighted averaging operators

We briefly describe the Ordered Weighted Averaging (OWA) operator and discuss a methodology for learning the associated weighting vector from observational data. We then introduce a more general type of OWA operator called the Induced Ordered Weighted Averaging (IOWA) Operator. These operators take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are then aggregated. A number of different aggregation situations have been shown to be representable in this framework. We then show how this tool can be used to represent different types of aggregation models.

Uninorm aggregation operators

A generalization of the t-norm and t-conorm called the uni-norm is defined. These operators allow for an identity element lying anywhere in the unit interval rather than at one or zero as in the case of t-norms and t-conorms, respectively. Various important properties of these uni-norms are investigated. We next introduce two particular families of these uni-norms, R∗ and R∗, study their behavior and suggest some semantics. Finally, withdrawing the requirement of associativity, we introduce a class of operators called RQ-star aggregation operators which are useful for aggregations guided by imperatives such as “if most of the scores are above the identity take the Max else use the Min”.

Generation of Fuzzy Rules by Mountain Clustering

We develop, based upon the mountain clustering method, a procedure for learning fuzzy systems models from data. First we discuss the mountain clustering method. We then show how it could be used to obtain the structure of fuzzy systems models. The initial estimates of this model are obtained from the cluster centers. We then use a back propagation algorithm to tune the model.