Logical connectives on fuzzy sets arise from those on the unit interval. The basic theory of these connectives is cast in an algebraic spirit with an emphasis on equivalence between the various systems that arise. Special attention is given to De Morgan systems with strict Archimedean t-norms and strong negations. A typical result is that any De Morgan system with strict t-norm and strong negat...

This paper analyzes the performance of some fuzzy implications proposed in the bibliography together with the operators needed for their definition and for the fuzzy inference process, Examining the specialized literature, it is clear that the selection of the best fuzzy implication operator has become one of the main question in the design of a fuzzy system, being occasionally contradictory (a...

Since the discovery of fuzzy sets, the arithmetic operations of fuzzy numbers (Zadeh [7, 8]) which may be viewed as a generalization of interval arithmetic (Moore [5]) have emerged as an important area of research within the theory of fuzzy sets (Mizumoto and Tanaka [4], Dubois and Prade [2]). The arithmetic operations of fuzzy numbers have been performed either by extension principle [7, 8] or...

In this paper a new parallel version of finding the Fuzzy Reasoning Path (FRP) using the knowledge representation model, introduced by Chandwani & Chaudhari [1] known as Fuzzy Deduction Graph (FDG) is presented. In an FDG, a systematic method of finding the Fuzzy Reasoning Path (FRP) already exists, which is based on Dijkstra's shortest path framework [2]. Our FRP algorithm is conglomerati...

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations meet, multiplication, fuzzy equality and a unit element. They open the door to an alternative development of fuzzy (manyvalued) logic with the basic connective being fuzzy e...

Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation o...

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...

In the past, mathematicians actively used the ability of some people to perform calculations unusually fast. With the advent of computers, there is no longer need for human calculators – even fast ones. However, recently, it was discovered that there exist, e.g., multiplication algorithms which are much faster than standard multiplication. Because of this discovery, it is possible than even fas...

Abstract The aim of this paper is to introduce the notion cornets, which form a particular subclass ordered semigroups also equipped with multiplication by natural numbers. most important standard examples for cornets are families nonempty subsets and fuzzy vector space. In cornet, convexity, nonnegativity, Archimedean property, boundedness, closedness an element can be defined naturally. basic...

One of the most fundamental concepts in fuzzy set theory is extension principle. It gives a generic way dealing with quantities by extending non-fuzzy mathematical concepts. There are few examples, including concept distance between sets. The approach then methodically applied to real algebra, considerable development number operations. These operations computationally appealing and generalized...