Fuzzy Prime Ideal Theorem in Residuated Lattices

This paper mainly focuses on building the fuzzy prime ideal theorem of residuated lattices. Firstly, we introduce the notion of fuzzy ideal generated by a fuzzy subset of a residuated lattice and we give a characterization. Also, we introduce different types of fuzzy prime ideals and establish existing relationships between them. We prove that any fuzzy maximal ideal is a fuzzy prime ideal in residuated lattice. Finally, we give and prove the fuzzy prime ideal theorem in residuated lattice.

ANTI SUBGRUP α-FUZZY

The concept of fuzzy subgroups is a combination of the group structure with the fuzzy set, which was first introduced by Rosenfeld (1971). This concept became the basic concept in other the fuzzy algebra fields such as fuzzy normal subgroups, anti fuzzy subgroups and anti fuzzy normal subgroups. The development in the area of fuzzy algebra is characterized by the continual emergence of new concepts, one of which is the α-anti fuzzy subgroup concept. The idea of α-anti fuzzy subgroups is a combination between the α-anti fuzzy subset and anti fuzzy subgroups. The α-anti subset fuzzy which is an anti fuzzy subgroup is called as α-anti fuzzy subgroup. The purpose of this study is to prove that the α-anti fuzzy subset is an anti fuzzy subgroup, examine the relationship between α-anti fuzzy subgroups with anti fuzzy subgroups and α-fuzzy normal subgroups with anti fuzzy subgroups. The results of this study are, if A is an anti fuzzy subgroup (an anti fuzzy normal subgroup), then an α-anti subset fuzzy of A is an anti fuzzy subgroup (an anti fuzzy normal subgroup). However, this does not apply otherwise. Furthermore, this study also provides sufficient and necessary conditions for an α-anti fuzzy subset of any group to be an α-anti fuzzy subgroup and the formation of a group of factors that are built from an α-anti fuzzy normal subgroup.Keywords : Anti Fuzzy Subgroup, Anti Fuzzy Normal Subgroup, α-Anti Fuzzy Subgroup and α-Anti Fuzzy Normal Subgroup.

ω – SUBSEMIRING FUZZY

Mapping ρ is called a fuzzy subset of an empty set of S if ρ is the mapping from S to the closed interval [0,1]. A fuzzy subset ρ introduced into this paper is a fuzzy subset of semiring S, defined byρ(a+d)≥ρ(a)∧ρ(d) and ρ(ad)≥ρ(a)∧ρ(d),for each a,d∈S so that a fuzzy subset ρ is called a fuzzy subsemiring from a semiring S.In this paper, Investigated the basic nature of subsemi-ring fuzzy ρ from a semiring S, which includes intersecting with two or more fuzzy subsemiring from a semiring S, is always a fuzzy subsemiring from a semiring S. Moreover, it was introduced to the concept of ω – fuzzy subsemiring from a semiring S which is denoted by ρω. Finally, investigated the minimal conditions that guarantee the existence of ω – fuzzy subsemiring ρω and the intersection of two or more ω – fuzzy subsemiring ρω of a semiring, S is always an ω – fuzzy subsemiring ρω of a semiring S.

Weighted Fuzzy Sets

The weighted fuzzy subset is to describe the importance of each element in the set through the characteristi3c function. In this paper, we study how an element and its presence in the set, namely, the degree of belongingness plays a role in determining the characteristic level of the set. Presence of an element in the set strengthens the set to a greater extent. Set gets its weightage, because of its elements and its association with the other elements. Association depicts the internal and external factors influencing over an element. In other words, the proposed weighted fuzzy subset has 3-tuple representation such as elements in a set, degree of presence of an elements and degree of impact of the set because of each elements presence.

The Measure of Fuzzy Filters on BL-Algebras

The new concept of the fuzzy filter degree was given by means of the implication operator, which enables to measure a degree to which a fuzzy subset of a BL-algebra is a fuzzy filter. In this paper, we put forward several equivalent characterizations of the fuzzy filter degree by studying its properties and the relationship with level cut sets. Furthermore, we study the fuzzy filter degrees of the intersection and fuzzy direct products of fuzzy subsets and investigate the fuzzy filter degrees of the image and the preimage of a fuzzy subset under a homomorphism.

Interval Valued Fuzzy Soft Sets and Fuzzy Connectives

The Article, We Learning A Few Operations Of Interval Valued Fuzzy Soft Sets Of Connectives And Give Elementary Properties Of Interval Valued Fuzzy Soft Sets Of Principal Disjunctive Normal Form And Principal Conjunctive Normal Form. 2000 Ams Subject Classification: 03f55, 08a72, 20n25. Keywords: Interval Valued Fuzzy Subset, Interval Valued Fuzzy Soft Set, And Principal Conjunctive Normal Form And Principal Disjunctive Normal Form Interval Valued Fuzzy Soft Set ‘’∧ ‘’ Operator And ‘’∨’’ Operator.

Some Topological and Algebraic Properties of α-level Subsets’ Topology of a Fuzzy Subset

The theory of fuzzy sets, since its foundation, has advanced in a wide range of means and in many fields. One of the areas to which fuzzy set theory has been applied extensively is mathematical programming. Nevertheless, the applications of fuzzy theory can be found in e.g. logic, decision theory, artificial intelligence, computer science, control engineering, expert systems, management science, operations research, robotics, and others. Theoretical improvements have been made in many directions. Nowadays it has a lot of applications also on possibility theory, actuarial credibility theory, fuzzy logic and approximate reasoning, fuzzy control, fuzzy data analysis, fuzzy set models in operations research, etc. The aim of this paper is to investigate some topological properties of a set X when the topology defined on it is the collection of all the α-level subsets of a fuzzy subset A of X.We have been able to establish some results regarding fuzzy cluster level subsets, convergence of level subsets and quasicompactness among others.

Generalization of (∈,∈∨q_k )-fuzzy subnear-rings and (∈,∈∨q_k )-fuzzy ideals of near-rings

In this paper, we introduce the notions of (∈, ∈∨q_δ^k)-fuzzy subnear-ring and (∈, ∈∨q_δ^k)-fuzzy ideal of a near-ring which are generalization of (∈, ∈∨q_k)-fuzzy subnear-ring and (∈, ∈∨q_k)-fuzzy ideal respectively. We provide the characterizations of (∈, ∈∨q_δ^k)-fuzzy subnear-ring (resp. ideal) of a near-ring and deal with some related properties. Further, we introduce the notion of ∈∨q_δ^k-level subset of a fuzzy subset and obtain some related results.

Relationship the Fuzzy P-Ideal with Some Fuzzy Subset of BH-Algebra

This work involved some studying ,we study and prove some theorems and a propositions which determine the relationships among the notion of fuzzy p-ideal with the intersection, union, image of function, inverse function and with some other fuzzy subsets of BH-algebra, also we gave some properties of this ideal of a BH-algebra.

Design and Application of a Fuzzy Evaluation Algorithm for Stroke Force in Calligraphy Teaching

To solve the problem that the existing electronic word learning device only had a single character writing exercise function, the interaction structure and the stroke force analysis algorithm of Chinese characters were studied from aspects such easy use, smart technology and writing paper simulation. In re-sponse to the problems in the writing process and the limitations of smart guidance, the writing problems occurred the resistive touch screen were ana-lyzed, and a fuzzy evaluation method for Chinese strokes was proposed. The main contents included membership template construction, fuzzy subset se-lection, template parameter generation and evaluation. The experimental re-sult showed that the interaction structure can inherit the advantages of paper writing and exert the advantages of electronic devices. It is concluded that human-computer interaction based on interactive structures can better apply the intelligent machine to character practitioner.