Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Abstract

Abstract. Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Fuzzy sets have become popular in every branch of mathematics such as analysis, topology, algebra, applied mathematics etc. Thus fuzzy sets triggered the creation of a wide range of research topics in all areas of science in a short time. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.Key words: fuzzy numbers, integrated matrix, differentiated matrix, real duals.AMS Mathematics Subject Classification: 03E72, 46A45, 40C05. IntroductionFuzziness has revolutionized many areas such as mathematics, science, engineering, medicine. This concept was initiated by Zadeh [17]. Not only Zadeh discovered this concept, but he also developed the infrastructure of today's popular forms of use such as relations of similarity, decision making, and fuzzy programming in a short time.Just like in the theory of sets, fuzzy sets(FS) also have led to the emergence of new mathematical concepts, research topics, and the design of engineering applications. Therefore, the nature of the classical set theory must be well known and understood. In particular, consider the two fundamental laws of Boolean algebra the law of excluded middle and law of contradiction. In logic, the proposition every proposition is either true or falseť excludes any third, or middle, possibility, which gave this principle the name of the law of excluded middle. When look at the principles of Boolean algebra, there are two items as prediction: "True" or "False". Whether classical, Unauthenticated Download Date | 5/9/18 6:25 PM 76Murat Kirişci Boolean or crisp, set theory can be defined as a characteristic function of the membership of an element x in a set A. For each elements of universal set X, the function that generates the values 0 and 1 is called the characteristic function.Today, the studies and applications related to the fuzziness are increasing rapidly and this concept is finding in every scientific areas. Zadeh's FS theory succeeded in attracting mathematicians as well as other scientists and was adopted. The most important feature of FS is to generalize the values of "true" and "false" in traditional logic and to produce a logic that can use multi-valued results.Any change or transition in real life takes place between membership and non-membership. This transition is clear, well-defined. Despite this certainty in classical sets, this is somewhat different in FS. This difference arises because the transition is gradual. The uncertainty of the boundaries of the FS implies that this transition will vary from one membership to another. In that case, membership of an element from the universe in this set is measured by a function that attempts to describe vagueness and ambiguity.Matlok...

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