There are two equivalent de nitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The rst one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the rst de nition. The pres...

This paper provides an improved decision making approach based on fuzzy numbers and the compositional rule of inference by Yao and Yao (2001). They claimed to have created a new method that combines statistical methods and fuzzy theory for medical diagnosis. Currently, numerous papers have cited that work. In this study, we show that if we follow their matrix multiplication operation approach, ...

The goal of this paper is to give a functional relationship between the membership functions of fuzzy intervals M1⊕...⊕Mn and M1 ... Mn, where Mi are positive LR fuzzy intervals of the same form Mi = M = (a, b, α, β)LR and the extended addition ⊕ and multiplication are defined in the sense of a triangular norm (i.e. via sup–t–norm convolution).

We consider linear equality systems where all the parameters may be fuzzy variables specified by their possibility distribution, the operations addition and multiplication by a real number of fuzzy parameters are defined via a suptriangular norm composition, and the equations are understood in possibilistic sense. We show that when the triangular norm defining the operations and equations is co...

EQ-algebras introduced by Novák are algebras of truth values for a higher-order fuzzy logic (fuzzy type theory). In this paper, the compatibility of multiplication w.r.t. the fuzzy equality in an arbitrary EQ-algebra is examined. Particularly, an example indicates that the compatibility axiom does not always hold, and then a class of EQ-algebras satisfying the compatibility axiom is characteriz...

Fuzzy arithmetic is a powerful tool in many engineering problems such as decision making , control theory, fuzzy systems and approximate reasoning. However, it is well known that the practical use of standard fuzzy arithmetic operators gives results more imprecise than necessary or in some cases, even incorrect. This problem is due to the overestimation effect induced by computing fuzzy arithme...

A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in va...

Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a⊕ b = max{a,b}, a⊗ b = min{a,b}. Fuzzy discrete dynamic systems can be introduced by fuzzy matrices and are useful for describing knowledge engineering, scheduling, cluster analysis, fuzzy logic programs, diagnosis of technical devices or medical diagnosis. The paper deals with...

In this paper, we develop to a new operator by using together IVBFS and Dombi operators. Also, the some properties of concept are introduced like addition, scalar multiplication, power, multiplication. The presented is Interval Valued Bipolar Fuzzy Prioritized Weighted Averaging (IVBFPWDA) various offered idempotency, monotoncity, boundedness. Then, present score function similar over (IVBFSs) ...

in this paper we continue development of formal theory of a special class offuzzy logics, called eq-logics. unlike fuzzy logics being extensions of themtl-logic in which the basic connective is implication, the basic connective ineq-logics is equivalence. therefore, a new algebra of truth values calledeq-algebra was developed. this is a lower semilattice with top element endowed with two binary...