Research Paper
Fuzzy multisets and their variants
Mahdi Mollaei
Abstract
This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces via the notations ...
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This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces via the notations of KM-fuzzy metric spaces.This study, generalises the concept of fuzzy metric space to union and product of fuzzy metric spaces in classical logic and in this regard investigates the some product of fuzzy metric fuzzy manifold spaces. We apply the notation of valued-level subsets and make a relation between of topological space, Husdorff space, manifold space and fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space. In final, we extended the fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space to fuzzy metric topological space, fuzzy metric Husdorff space and fuzzy metric manifold spaceIndeed, this study analyses the notation of fuzzy metric manifold based on valued-level subset.
Short Communication
Fuzzy sets and their variants
Zanyar A. Ameen
Abstract
Thangaraj and Balasubramanian introduced the so-called somewhat fuzzy semicontinuous and somewhat fuzzy semiopen functions. Two years later, the same authors defined two other types of functions called somewhat fuzzy continuous and somewhat fuzzy open without indicating connections between them. At first ...
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Thangaraj and Balasubramanian introduced the so-called somewhat fuzzy semicontinuous and somewhat fuzzy semiopen functions. Two years later, the same authors defined two other types of functions called somewhat fuzzy continuous and somewhat fuzzy open without indicating connections between them. At first glance, we may easily conclude (from their definitions) that every somewhat fuzzy continuous (resp. open) function is somewhat fuzzy semicontinuous (resp. semiopen) but not conversely. In this note, we show that they are equivalent. We further prove that somewhat fuzzy continuous functions are weaker than fuzzy semicontinuous functions.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - -- - - - - - - - - - - - - - - - - - - - - - - - -
Review Paper
Pythagorean fuzzy sets and their variants
Amal Kumar Adak; Dheeraj Kumar
Abstract
Multiple criteria decision analysis (MCDA) has been widelyinvestigated and successfully applied to many fields, owingto its great capability of modeling the process of actualdecision-making problems and establishing proper evaluationand assessment mechanisms. With the developmentof management and economics, ...
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Multiple criteria decision analysis (MCDA) has been widelyinvestigated and successfully applied to many fields, owingto its great capability of modeling the process of actualdecision-making problems and establishing proper evaluationand assessment mechanisms. With the developmentof management and economics, real-world decision-makingproblems are becoming diversified and complicated to anincreasing extent, especially within a changeableand unpredictable environment. Multi-criteria decision making is a decision-making technique that explicitly evaluates numerous contradictory criteria. TOPSIS is a well-known multi-criteria decision-making process. The goal of this research is to use TOPSIS to solve MCDM problems in a Pythagorean fuzzy environment. The distance between two Pythagorean fuzzy numbers is utilised to create the model using the spherical distance measure. To construct a ranking order of alternatives and determine the best one, the revised index approach is utilised. Finally, we look at a set of MCDM problems to show how the proposed method and approach work in practise. In addition, it shows comparative data from the relative closeness and updated index methods.
Research Paper
Boolean-valued fuzzy sets and their variants
MANJUSHA O T
Abstract
Sambathkumar introduces the notion of global domination in graphs. According to him, a dominating set S of G is a global dominating set of G if S is also a dominating set of the complement of G.Nagoorgani and Jahir Hussain introduced the concept of global domination infuzzy graphs using effective arcs. ...
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Sambathkumar introduces the notion of global domination in graphs. According to him, a dominating set S of G is a global dominating set of G if S is also a dominating set of the complement of G.Nagoorgani and Jahir Hussain introduced the concept of global domination infuzzy graphs using effective arcs. This paper presents global domination infuzzy graphs using strong arcs. The strong global domination number of different classes of fuzzy graphs is obtained. An upper bound for the strong globaldomination number of fuzzy graphs is obtained. Strong global domination infuzzy trees is studied. It is established that every node of a strong global dominating set of a fuzzy tree is either a fuzzy cut node or a fuzzy end node. Itis proved that in a fuzzy tree each node of a strong global dominating set isincident on a fuzzy bridge. Also, the characteristic properties of the existenceof a strong global dominating set for a fuzzy graph and its complement areestablished
Research Paper
Abolfazl Rezaei; Mohammad Hemati
Abstract
Today, most manufacturing and service companies adopt a customer-oriented approach to take into account employee needs and expectations as a strategic principle for sustainability and success in a competitive market. Meanwhile, Sengeh argues that “many of the best ideas and strategies will not ...
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Today, most manufacturing and service companies adopt a customer-oriented approach to take into account employee needs and expectations as a strategic principle for sustainability and success in a competitive market. Meanwhile, Sengeh argues that “many of the best ideas and strategies will not be realized due to the conflict between new ideas and managers’ subjective model, rather than the management weakness”. On the other hand, managers’ decisions based on self-developed rules can suffer all kinds of biases . As Bierzman explains: “managers’ mental heuristic rules lead to weak analysis of information, inappropriate weighting of the various data, and an investigation of few alternatives for decision-making, which can lead to systematic errors and common biases in the decision”. Addressing the existing gap between managers’ subjective perceptions of employees and employees’ self-perceptions, the present study aims to present a new systematic approach with a combination of Delphi, Kano and AHP methods in an attempt to explain managers’ mental paradigms in Abadan Oil Refinary Company as one of the elading ones in the Middle East. The statistical population of the study consists of 18 experienced managers (using snowball method) and 203 employees at Abadan’s Oil Refinery (using the Cochran formula). The validity and reliability of the questionnaire were also confirmed using Kendall’s Correlation Coefficient, Cronbach’s Alpha coefficient, and Gogus and Butcher’s Incompatibility Rate. First, needs were determined from the views of the experts using the Fuzzy Delphi method, and then, Kano’s non-linear model and Alpha-cut (α-Cut) method were used to classify 21 components as basic, performance, and excitement needs. In the end, the needs have been ranked using the Fuzzy AHP method. The results indicated that the proposed method was effectively successful in reducing biases, vagueness, and possible inconsistencies in managers' decisions and judgments. Overall, the method presented insights on the significance of
Research Paper
Fuzzy sets and their variants
SUNDAY ADESINA ADEBISI
Abstract
Abstract The term fuzzy logic is generic as it can be used to describe the likes of fuzzy arithmetic, fuzzy mathematical programming, fuzzy topology, fuzzy graph theory ad fuzzy data analysis which are customarily called fuzzy set theory. The aspect of pure Mathematics has undergone a lot of dynamic ...
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Abstract The term fuzzy logic is generic as it can be used to describe the likes of fuzzy arithmetic, fuzzy mathematical programming, fuzzy topology, fuzzy graph theory ad fuzzy data analysis which are customarily called fuzzy set theory. The aspect of pure Mathematics has undergone a lot of dynamic developments over the years. Since inception , the study has been extended to some other important classes of finite abelian and nonabelian groups such as the dihedral , quaternion, semidihedral, and hamiltonian groups. Other different approaches have been so far, applied for the classification. Every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. Efforts are carefully being intensified to calculate , in this paper, the explicit formulae for the number of distinct fuzzy subgroups of the Cartesian product of the dihedral group of order 25 with a cyclic group of order of an n power of two for, which n ≥ 5.
Research Paper
Neutrosophic sets and their variants
Sarannya Kumari R
Abstract
Many advances have been made in the field of research since Chang created fuzzy topological space. The goal of this study is to incorporate topological space into the realm of n- cylindrical fuzzy neutrosophic sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper we ...
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Many advances have been made in the field of research since Chang created fuzzy topological space. The goal of this study is to incorporate topological space into the realm of n- cylindrical fuzzy neutrosophic sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper we define n-cylindrical fuzzy neutrosophic topological spaces (n-CyFNTS), n-CyFN Open sets and n-CyFN Closed sets. Also we put forward definition of n-CyFN base and a characterization for the base of an n-CyFNTS.
Research Paper
Fuzzy sets and their variants
SUNDAY ADESINA ADEBISI; Florentin Smarandache
Abstract
Abstract The neutrosophic interval statistical number (NISN) has been known to be very useful in expressing the interval values under indeterminate environments. One of the essential and so important useful as tools for measuring the degree of similarity between sets of given objects is the similarity ...
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Abstract The neutrosophic interval statistical number (NISN) has been known to be very useful in expressing the interval values under indeterminate environments. One of the essential and so important useful as tools for measuring the degree of similarity between sets of given objects is the similarity measure . In this paper, neutrosophic numbers as well as the generalized Dice similarity measure for neutrosophic numbers for two sets are defined after which the axioms of fuzziness similarity and symmetry satisfying the NISN the properties were proved.
Research Paper
Neutrosophic sets and their variants
Sunday Adesina Adebisi; Florentin Smarandache
Abstract
Abstract. The neutrosophic automorphisms of a neutrosophic groups G(I), denoted by Aut(G(I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G(I) which is also a neutrosophichomomorphism. Moreover, suppose that X1 = X(G(I)) is the neutrosophic group of Inner neutrosophic ...
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Abstract. The neutrosophic automorphisms of a neutrosophic groups G(I), denoted by Aut(G(I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G(I) which is also a neutrosophichomomorphism. Moreover, suppose that X1 = X(G(I)) is the neutrosophic group of Inner neutrosophic auto-morphisms of a neutrosophic group G(I) and Xn the neutrosophic group of Inner neutrosophic automorphismsof Xn1. In this paper, we show that if any neutrosophic group of the sequence G(I);X1;X2; : : : is the identity,then G(I) is nilpotent.
Research Paper
Intuitionistic fuzzy sets and their variants
Behnam Talaee; Mehrnoosh Sobhani; Bijan Davvaz
Abstract
In this paper, we discuss the structure of intuitionistic fuzzy projec- tive modules and investigate some properties of them. Also we study about intuitionistic fuzzy homomorphisms between intuitionistic fuzzy modules.We study about exact sequences, products and co-products, func- tors and relating topics ...
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In this paper, we discuss the structure of intuitionistic fuzzy projec- tive modules and investigate some properties of them. Also we study about intuitionistic fuzzy homomorphisms between intuitionistic fuzzy modules.We study about exact sequences, products and co-products, func- tors and relating topics in IFR − Mod and investigate the relationship between them, where IFR − Mod is category whose objects are intu- itionidtic fuzzy modules and morphisms are intuitionistic fuzzy homo-morphisms.For a commutative ring R and two intuitionistic fuzzy R- modulesA = (μA, νA) ≤IF M, B = (μB, νB) ≤IF N we show thatHomIF −R (A, B) = (α, β) is an intuitionistic fuzzy R-module.Also for a commutative ring R, if0⟶𝐴𝑓~→ B 𝑔~→ C is an exact sequence in IFR-Mod, where f˜ is IF split homomorphism, thenwe show that HomIF −R(D,-) preserves the sequence, for every D ∈ IFR − Mod.
Review Paper
Plithogenic sets and their variants
Florentin Smarandache
Abstract
This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of ...
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This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.
