Luis Garmendia

Measures of specificity of fuzzy sets under T-indistinguishabilities

The concept of measure of specificity of fuzzy sets is extended in this paper to measure of specificity under the knowledge of T-indistinguishabilities. Four axioms of measure of specificity under T-indistinguishabilities are given. An algorithm to compute the inference independent set Tfr from a fuzzy set and a T-indistinguishability is used to measure the specificity of fuzzy sets under T-indistinguishabilities satisfying the axioms

How to Make

Three ways to approximate a proximity relation <i>R</i> (i.e., a reflexive and symmetric fuzzy relation) by a <i>T</i> -transitive one where <i>T</i> is a continuous Archimedean <i>t</i>-norm are given. The first one aggregates the transitive closure <i>R</i> <i>macr</i> of <i>R</i> with a (maximal) <i>T</i>-transitive relation <i>B</i> contained in <i>R</i> . The second one computes the closest homotecy of <i>R</i> <i>macr</i> or <i>B</i> to better fit their entries with the ones of <i>R</i>. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for <i>T</i> the Lukasiewicz or the product <i>t</i>-norm. The previous methods do not apply for the minimum <i>t</i>-norm. An algorithm to approximate a given proximity relation by a min-transitive relation (a similarity) is given in the last section of the paper.

T

Since many complex decision making problems can be solved solely by means of an appropriate algorithm, checking the quality of such algorithm is a key issue, even more relevant in the presence of fuzzy uncertainty. In this paper we postulate that the design and formal specification of algorithms can be translated into a fuzzy framework introducing fuzzy first order logic and assert transformations. Following the classical crisp scheme we first formalize the concepts of a fuzzy algorithm specification and a fuzzy computing state, and then a new fuzzy computational logic is presented, so we can derive a computational reasoning for correctness of algorithms. A proposal for the evaluation and setting of suitable degrees of truth to computing states is also introduced.

-Transitive a Proximity Relation

Agent-based models are useful to study emergent behaviour in social systems. In general, existing agent models tend to be quite simple, but there are social problems that require the consideration of some aspects with uncertainty as human thinking does. Those characteristics can be addressed by using fuzzy sets theory in the specification of the attributes that describe agents representing individuals, and in the functions that model the evolution of individual change of mind, the relationships among individuals in a social network, the inheritance, and the similarity between individuals. This paper discusses the fuzzification of agent-based models and analyses experimentation results for a specific case of the study of the evolution of human values in a society.

SPECIFICATION AND COMPUTING STATES IN FUZZY ALGORITHMS

Simple models of agents have been used to study emergent behaviour in social systems. However, when considering the evolution of values in human societies, there is a need for the consideration of more complex agent models, which take into account uncertainty in human thinking. This characteristic can be addressed by using fuzzy logic in the specification of the attributes that describe agents representing individuals, the functions that model the evolution of individual change of mind, the relationships among individuals in a social network, the inheritance, and the similarity between individuals. The introduction of fuzzy logic in the models has improved the results of the simulation.

Introducing uncertainty into social simulation: using fuzzy logic for agent-based modelling

Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors? knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties.

Agent-Based Social Modeling and Simulation with Fuzzy Sets

This paper introduces some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of and L-fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations. Some properties and some examples is given for t-representable and t-pseudo representable generalized t-norms.

Computing a T-transitive lower approximation or opening of a proximity relation

An expression for measuring the specificity of fuzzy sets on continuous domains is introduced. This expression is based on t-norms, negations and the Choquet integral. It is also proved that the new expression satisfies the given axioms for measure of specificity. New examples are provided.

Transitive closure of L-fuzzy relations and interval-valued fuzzy relations

The expansible and recursively spreadable measures of specificity are introduced to improve the performance of computing measures of specificity of fuzzy sets when the universe of candidates is increased. The contractible measures of specificity and recursively reductible measures of specificity again improves the performance to compute the measure of specificity of a fuzzy set when the universe of candidates is decreased from the previous one. These kind of measures of specificity allows to compute very efficiently measures of specificity of fuzzy sets when a universe of discourse is variable.

A t-norm based specificity for fuzzy sets on compact domains

In this paper two methods are proposed to measure the μ-T-inconditionality character of any fuzzy relation for any continuous t-norm T, and it is studied when both methods result to be equivalent.