Analyzing the Problem of the Modeling of Periodic Normalized Behaviors in Multiagent-Based Simulation of Social Systems: The Case of the San Jerónimo Vegetable Garden of Seville, Spain

Bustince

et al. 2016

Fuzzy Sets and Systems

126

In this paper we introduce the notion of additive generator pair for overlap functions. We also study how some of the properties that can be demanded to an overlap function can be expressed in terms of its generator pair. In particular, given a continuous and positive t-norm T , we analyze the overlap functions which are obtained by the distortion of T by a pseudo-automorphism, showing that the additive generator pair of such overlap function may be given in terms of the considered pseudo-automorphism and the additive generator of T . Finally, we also consider the influence of the migrativity, homogeneity and idempotency properties for the overlap functions obtained by such distortion in terms of their respective additive generator pairs.

Section: Resultsmentioning

confidence: 99%

On additive generators of overlap functions

Bustince

et al. 2016

Fuzzy Sets and Systems

126

“…Then, we are also aiming at applications in the context of hybrid BDI-fuzzy [33] 3 agent models, commonly used in social simulation [35], [36], [37], where the evaluation of social values and exchanges are of a qualitative, subjective, vague nature [38], [39], [40]. We noticed that overlap functions can be used for dealing with indifference and incomparability when reasoning on the agent's fuzzy belief base, where a kind of weak preference relation may be defined.…”

Section: Moreover the Derivation Of An R O -Implication By An Overlamentioning

confidence: 99%

On the laws of contraposition for residual implications derived from overlap functions

2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

2015

Overlap functions are aggregation operators used in the overlap problem or when the associativity is not required. Residual implications derived from them (RO-implications) preserve the residuation property, and any overlap function O and the respective RO-implication form an adjoint pair, which is important in many applications. RO-implications are weaker than R-implications constructed from positive and continuous t-norms, since RO-implications do not necessarily satisfy certain properties, but only weaker versions of these properties. However, in general, such properties are not demanded for many applications.In this paper, we analyze the laws of contraposition for ROimplications with respect to a fuzzy negation.

“…Therefore, an interval fuzzy numberN is defined as a interval fuzzy set of R with the following characteristics: [9] If the functions LMF and UMF are both linear, thenN is called linear interval fuzzy number, which can be defined by an interval membership function µN , with supports lsuppN = (a l , b l ), 2 The continuity of interval functions was defined by Moore as an extension of the continuity of real functions. More information on this subject can be seen in [18,19,20].…”

Section: Interval Fuzzy Numbersmentioning

confidence: 99%

“…However, sometimes these probabilities are difficult to estimate precisely, such as problems in agent-based social simulation [1,2,3], which often have linguistic variables to define some parameters of the agents involved in the modeling [4,5,6] under vagueness, ambiguity and uncertainty.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Interval Fuzzy Probabilities

Asmus

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

2015

Fuzzy sets and logic have been largely used for the treatment of the uncertainty, vagueness and ambiguity found in the modeling of real problems. However, there may exist also the case when there is uncertainty related to the membership functions to be used in the modeling of fuzzy sets and fuzzy numbers, as there are many ways to define the shape of this kind of number. Thus, one can use, for example, the theory of interval fuzzy sets to address this uncertainty, considering different modelings of fuzzy numbers into a single interval fuzzy number. In this paper, we use interval fuzzy numbers to represent probabilities that are difficult to be estimated and where the modeling of fuzzy numbers is not trivial. To elaborate the calculation of interval fuzzy probabilities, we introduce an approach based on the one used by Buckley and Eslami for fuzzy probabilities, where the probabilities respect an arithmetic restriction. We discuss several properties of the proposed approach.