This paper extends a comparison measure called the statisfaction function(SF). The SF estimates the degree to which arithmetic comparisons between two fuzzy values are satissed. The previously proposed SF was deened on a discrete domain(SFD). So, in order to compare continuous fuzzy values, the fuzzy values should be converted into discrete ones. This paper deenes a satisfaction function on a c...

This paper extends a comparison measure called the statisfaction function(SF). The SF estimates the degree to which arithmetic comparisons between two fuzzy values are satissed. The previously proposed SF was deened on a discrete domain(SFD). So, in order to compare continuous fuzzy values, the fuzzy values should be converted into discrete ones. This paper deenes a satisfaction function on a c...

This paper provides an algebraic characterization of mathematical structures formed by cartesian products of fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom was given by G. Schmidt and T. Strohlein, and cartesian products of Boolean relation algebras were investigated by B. J onsson and A....

Introduction: As we know, an implementation of fuzzy inference can be done on general purpose computer architectures (including digital signal processors and microcontrollers) or on a special fuzzy hardware [1]. Analogous and digital techniques are used. Fuzzy controllers working on stochastic logic represent a special kind of fuzzy hardware [2], [3]. The stochastic logic uses binary random sig...

It is necessary and challenging to represent the probabilities of fuzzy events and make inferences between them based on a Bayesian network. Motivated by such real applications, in this paper, we first define the interval probabilities of type-2 fuzzy events. Then, we define weak interval conditional probabilities and the corresponding probabilistic description. The expanded multiplication rule...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

In this contribution we deal with the problem of doing computations with a Markov chain when the information about transition probabilities is expressed linguistically. This could be the case, for instance, if the process we are modeling is described by a human expert, for whom the use of linguistic labels is easier than being forced to give inexact numerical probabilities which, in turn, may y...

Atanassov (Fuzzy Sets and Systems 20 (1986) 87-96) defined basic operations over the intuitionistic fuzzy sets. Here we shall introduce two operations, subtraction and division, derived from the deconvolution for equations using addition and multiplication operations, respectively. In addition, we shall give some conditions to examine the correctness regarding the defined operations. The remark...

Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In additio...