In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the author...

In this paper we present several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Godel logic formulas. Based on different characterizations of necessity measures on fuzzy sets, a group of logics with Kripke style semantics are built over a restricted language, namely a two level language composed of nonmodal and modal formulas, the latter m...

With the desire to manage imprecise and vague information in evidential reasoning, several attempts have been made to generalize the Dempster–Shafer (D– S) theory to deal with fuzzy sets. However, the important principle of the D–S theory, that the belief and plausibility functions are treated as lower and upper probabilities, is no longer preserved in these generalizations. A generalization of...

This paper presents a design approach intended for the modeling and synthesis of discrete-event modules of hybrid controllers by combining a model of computation and a soft computing synthesis approach. The model of computation is based on coloured Petri nets (CPNs) and the soft computing method uses fuzzy logic. The design approach converts Petri net models into their equivalent fuzzy sets for...

in this note by considering a complete lattice l, we define thenotion of an l-fuzzy hyperrelation on a given non-empty set x. then wedefine the concepts of (pom)l-fuzzy graph, hypergraph and subhypergroupand obtain some related results. in particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (pom)l-fuzzy subhypergroups ...

the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...

In this paper, new definitions of $L$-fuzzy closure operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood spaces, the category of ...

In comparison to possibility theory, the Transferable Belief Model (TBM) – a nonproba-bilistic interpretation of Dempster-Shafer theory – enjoys little choice in terms of aggre-gation operators for the fusion of information. In this thesis, the problem of introducingsome flexibility for the combination of belief functions – the mathematical tool allowingthe representation of...

Possibility theory offers a qualitative framework for modeling decision under uncertainty. In this setting, pessimistic and optimistic decision criteria have been formally justified. The computation by means of possibilistic logic inference of optimal decisions according to such criteria has been proposed. This paper presents an Answer Set Programming (ASP)-based methodology for modeling decisi...