Search

The essential goal of the manuscript is to initiate lattice ordered multi-fuzzy soft matrix ( ℒ ℳ ℱ S ℳ ) using lattice ordered multi-fuzzy soft set ( ℒ ℳ ℱ S S ) and discuss the operations and depict rudimentary properties on ℒ ℳ ℱ S ℳ . Moreover, we originate the various compositions of ℒ ℳ ℱ S ℳ and propose algorithm for medical diagnosis by applying score matrix which have been implemented with the numerical example. Finally, the comparitive analysis of three composition methods is also included for improved reasonability and reliability.

This article deals with a fuzzy hypercompositional structure called fuzzy hyperlattice ordered δ- group ( FHLO δ - G ) , the extension of the fuzzy hypercompositional structure namely fuzzy hyperlattice ordered group (FHLOG). Using FHLO δ - G , we can involve one additional non-empty set δ with FHLOG, which helps to develop new results and applications. The structural characteristics and properties of FHLO δ - G are analysed. Furthermore, an application of FHLO δ - G for ABO blood group system is proposed.

This paper introduces the concept of homomorphism on fuzzy hyperlattice ordered group ( FHLOG ) . It studies how the binary and the fuzzy hyperoperations of a FHLOG can be transformed into the binary and the fuzzy hyperoperations of another FHLOG . The notion of fuzzy hypercongruence relation on FHLOG is also defined. The paper also establishes the redox reaction of copper, gold and americium forms three FHLOG s. Besides, homomorphism and composition function of FHLOG s using the redox reactions are developed. Therefore, the paper develops a relation among three different metal’s redox reactions in which the binary and the fuzzy hyperoperations, are preserved.

Inspired by the analysis of soft sets and fuzzy sets, in this paper, we study the relevance and interrelationship of the equivalence and congruence relation of lattice ordered fuzzy soft groups(l-FSGs). Moreover, we analyze some of the innate algebraic results accrued out of it theoretically. We construct l-FSG congruence class and l-FSG quotient set on a group X. We analyze the relationship between l-FSG congruence relation and l-FSG normal subgroups. In particular, we prove that in a group X, l-FSG normal subgroups form a modular lattice.

In this paper, we introduce the concept of multiset implicative filter and multiset positive implicative filter of residuated lattice. Also, we discuss their characterizations and we show t...

Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced. The requirements for any function to be an entropy measure of plithogenic sets are outlined in the axiomatic definition of the plithogenic entropy using the axiomatic requirements of neutrosophic entropy. Several new formulae for the entropy measure of plithogenic sets are also introduced. The newly introduced entropy measures are then applied to a multi-attribute decision making problem related to the selection of locations. Web of Science 8 6 art. no. 965

Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.

In 2018, we have propounded the notion of lattice-ordered interval-valued hesitant fuzzy soft set and some of its basic properties were discussed. In this present work, we inherit some essential definitions such as \(\mathcal {L}\)-optimistic interval-valued fuzzy soft set, \(\mathcal {L}\)-pessimistic interval-valued fuzzy soft set, \(\mathcal {L}\)-neutral interval-valued fuzzy soft set, \(\mathcal {L}\)-threshold interval-valued fuzzy set and Contra-\(\mathcal {L}\)-threshold interval-valued fuzzy set. Also a new technique has been implemented to solve a real-life problem by applying these definitions over lattice-ordered interval-valued hesitant fuzzy soft set.

In this paper, the concepts of multiset Boolean filter, multiset Boolean pseudofilter, anti-multiset Boolean filter, and anti-multiset Boolean pseudofilter are introduced. Also, the relation between multiset Boolean filter(pseudofilter) and some other types of multiset filters(pseudofilters) are given.

In the online published article, the third author’s “A. Borumand Saeid” affiliation is updated as following “Dept. of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran”.

A naive concept of a multiset is the repetition of its elements that obtained from a set and the number of occurences of a particular element in a multiset is a finite positive integer. In this paper, we introduced the concepts of congruence relation on a residuated lattice induced by a multiset filter and cosets of multiset filter are established and we present several important characterizations of them.

The basic idea of triple representation of a structure is to associate two simpler structures and a connecting map. Triple representation was first introduced by Chen and Gratzer to Stone Lattices (2), (3). The concept was gen- eralised to distributive pseudo-complemented lattices and then to distributive pseudo-complemented semilattices by Katrinak. The triple representation for modular Pseudo Complemented semilattice was suceeded by W.H.Cornish(4). Now the triple representation was obtained for a supermodular semilattice and thereby the supermodular semilattices are characterised.