The Journal of Fuzzy Mathematics
Volume 25, Number 4, December 2017
CONTENT
DETAILS
Extension of Extent Analysis Method in Intuitionistic Fuzzy Environment
Animesh Biswas
Department of Mathematics, University of Kalyani Kalyani-741235, West Bengal,
India E-mail: abiswaskln@rediffmail.com
Samir Kumar
Department of Mathematics, Acharya Jagadish Chandra Bose College Kolkata,
West Bengal, India. E-mail: kumarsamir2007@gmail.com
Abstract:
Analytic hierarchy process is one of the most important multiple criteria decision making methods. Extent analysis method was proposed for evaluating fuzzy pairwise comparison decision matrices resulting in crisp priority vectors. In this paper, the triangular intuitionistic fuzzy degree of possibility for comparing two or more triangular intuitionistic fuzzy numbers is defined and some related propositions are introduced resulting in intuitionistic fuzzy numbers as weights of criteria or performance scores of alternatives. A conversion scale for linguistic variables based on triangular intuitionistic fuzzy numbers is proposed and a new function is defined for ranking the intuitionistic fuzzy numbers. Finally, the extent analysis method is extended in intuitionistic fuzzy environment which is illustrated by an example.
Key words:
Intuitionistic fuzzy sets, triangular intuitionistic fuzzy number, analytic hierarchy process, extent analysis method, triangular intuitionistic fuzzy degree of possibility.
L-pre-separation Axioms in (2,L)-bitopologies via Complete Residuated Lattice-valued Logic
Wasim Akram Mandal
Beldanga D. H. Sr. Madrasah, Beldanga-742189, Murshidabad, WB, India. E-mail: wasim0018@gmail.com
Sahidul Islam
Department of Mathematics, University of kalyanl, kalyanl, W. B. India. E-mail: sahidul.math@gmail.com
Abstract:
Our aim in this paper is to obtain some applications of the results introduce [1, 2, 22] as a generalized and new consequences. We introduce and study the notions of five different symbols. Sometimes we need more conditions on such as the completely distributive law or that the ¡°^¡± is distributive over arbitrary joins or the double negation law as we illustrate through this paper. Some relations between these concepts are studied.
Key words:
(2,L) -bitopology; Complete residuated lattice; (i,j) -Pre-open set; L-pre strong symbol; separation axioms.
Solving Fuzzy Linear Programming Problems with Bell-shaped Membership Functions
Ritika Chopra
Department of Mathematics, Delhi University, Delhi, India. E-mail: ritikaritsin17@gmail.com
Ratnesh R. Saxenan
Department of Mathematics, Deen Dayal Upadhyay College, Delhi University, Delhi, India E-mail: ratnesh65@gmail.com
Abstract:
In this paper, we concentrate on the type of fuzzy linear programming problems(FLPP) in which the objective, the right hand side and the technological coefficients are all bell-shaped fuzzy numbers. The constraints are defuzzified using a ranking process and the FLPP is solved using the weighted multi-objective constrained linear programming problem by taking the Dombi-sum of the objective. It is also shown that the solution obtained is independent of the weights chosen in the weighted multi-objective problem. Finally, a numerical illustration is given to explain the method.
Key words:
Fuzzy linear programming, bell-shaped fuzzy numbers, weighted multi-objective constrained linear programming problem, Dombi-sum.
s-connectedness between Soft Sets
S. S. Thakur
Department of Applied Mathematics, Jabalpur Engineering College, postal code 482011, Jabalpur (M. P.)India
E-mail: samajh_singh@rediffmail.com
Alpa Singh Rajput
Department of Applied Mathematics , Jabalpur Engineering College, postal code 482011, Jabalpur (M. P.) India. E-mail:alpasinghrajput09@gmail.com
Abstract:
In the present paper the concepts of soft s -connectedness between soft sets and soft set-s -connected mappings in soft topological spaces have been introduced and studied.
Key words:
Soft semiopen sets ,soft semiclosed sets, soft semiconnectedness, soft s-connectedness between soft sets and soft set-s -connected mappings.
Triangular Fuzzy Matrix Norm and Its Properties
Madhumangal Pal and Rajkumar Pradhan
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721 102, India.
E-mail: math.rajkumar@gmail.com
Anti Fuzzy Gamma Near-algebras over Anti Fuzzy Fields
P. Narasimha Swamy
Department of Mathematics, GITAM University, Hyderabad-502 329, Telangana, India E-mail:swamy.pasham@gmail.com
K. Vijay Kumar
Department of Mathematics, Kakatiya University, Warangal-506 009,Telangana, India E-mail:nagaiah.phd4@gmail.com
T. Srinivas
Department of Mathematics, Kakatiya University, Warangal-506 009, Telangana, India. E-mail:swamy.pasham@gmail.com
K. Vijay Kumar
Department of Mathematics, Kakatiya University, Warangal-506 009,Telangana, India E-mail: thotasrinivas.srinivas@gmail.com
Abstract:
In this paper the notion of anti fuzzy gamma near-algebra over anti fuzzy field is introduced. Using this notion we have described some basic properties.
Key words:
tau- Near-algebra, Anti fuzzy tau - Near-algebra.
Fuzzy Weakly e-open and e-closed Functions
V. Chandrasekar
Department of Mathematics, Kandaswami Kandar¡¯s College, P-velur, Tamil Nadu-638 182. E-mail:vcsekar5@yahoo.co.in
S. Parimala
Research Scholar (Part Time), Department of Mathematics, Kandaswami Kandar¡¯s College, P-velur, Tamil Nadu-638 182. E-mail:pspmaths@gmail.com
Abstract:
In this paper, we introduce and characterize fuzzy weakly e-open (resp. fuzzy weakly e-closed) functions between fuzzy topological spaces and also study relations between this function with some other types of known functions.
Key words:
fuzzy e-open set, fuzzy e-closed set, fuzzy weakly e-open function, fuzzy weakly e-closed function.
Some Fixed Point Theorems in Intuitionistic Fuzzy2-metric Space Using Implicit Relation
A. Mohamed Ali
Department of Mathematics G.T.N Arts College,(Autonomous) G.T.N Nagar, Dindigul, . E-mail:mohamedali1128@gmail.com
Abstract:
In this paper, a class of implicit relation is introduced with suitable example and also some fixed point theorems in intuitionistic fuzzy 2-metric spaces using implicit relation are stated and proved.
Key words:
Intuitionsitic fuzzy 2-metric space, Implicit function.
Finite State Machine via Bipolar Neutrosophic Set Theory
S. Prabhu, R. Narmada Devi and D. Vidhya
Department of Mathematics, Lady Doak College, Madurai, Tamil Nadu, India. E-mail: narmadadevi23@gmail.com
Abstract:
In this paper, the concept of fuzzy finite state machine in bipolar neutrosophic set theory are introduced and discussed several basic properties. Also, the characterization of bipolar neutrosophic finite state So-compact machine, bipolar neutrosophic finite state Su-compact machine, bipolar neutrosophic finite state So-normal machine and bipolar neutrosophic finite state Su-normal machine are established.
Key words:
Bipolar neutrosophic finite state machine, Bipolar neutrosophic finite state sources, Bipolar neutrosophic finite state successor, bipolar neutrosophic finite state So-compact machine, bipolar neutrosophic finite state Su-compact machine, bipolar neutrosophic finite state So-normal machine and bipolar neutrosophic finite state Su-normal machine.
delta-equalities of Fuzzy Soft Sets and Their Application in Decision Making
Xindong Peng and Jingguo Dai
School of Information Science and Engineering, Shaoguan University, Shaoguan 512005, China. E-mail:952518336@qq.com Yong Yang
College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China
Abstract:
There has been a rapid growth of interest in developing approaches that are capable of dealing with vagueness and indeterminacy. To this end, a fuzzy soft set theory has been proposed to handle vagueness and indeterminacy in applications such as decision making problems. However, there has been little focus on the rationality of decision values of the fuzzy soft sets, which is significant in decision making problems. In this paper, we introduce some new operations on fuzzy soft sets, such as product, Cartesian product, probabilistic sum, bold sum, bold intersection, bounded difference, symmetrical difference, symmetrical union, Dienes-Rescher. We then give a definition of the delta-equality of fuzzy soft sets, and derive some special properties using the new operations of fuzzy soft sets. Finally, an example of Chinese college entrance examination (CCEE ) demonstrates the usability of the concept of delta-equalities of fuzzy soft sets in practice.
Key words:
Fuzzy soft set, decision making, operations, delta-equality, .
Rough Ideal and Homomorphism and Their Applications to Lattice
Susanta Bera and Sankar Kumar Roy
Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore-721102, West Bengal, India. E-mail: sabbas73@yahoo.com , E-mail: ismail.ibedou@gmail.com
Abstract:
In this investigation, we analyze the rough ideal of rough lattice through rough set environment. The definition of rough ideal of rough lattice and the properties of lattice under an approximation space are studied. Besides, the concept of rough homomorphism in rough lattice under an approximation space is introduced. We consider the approximation space by means of an equivalence relation and also describe the rough set as pair of sets (lower and upper approximation sets). The objective of this paper is to study the properties of lattice under an approximation space based on Pawlak¡¯s notion of indiscernibility relation between the objects in a set. Several important results are established. Finally, we include various examples for usefulness and truthfulness of the proposed study of the paper.
Key words:
Lattice, Rough Set, Approximation Space, Rough Lattice, Rough Ideal, Homomorphism.
Fuzzy Soft e-open Sets and Their Applications
V. Chandrasekar
Department of Mathematics, Kandaswami Kandar¡¯s College, P-velur, Tamil Nadu-638 182. E-mail: vcsekar @yahoo.co.in, vckkc3895@gmail.com
S. Parimala
Research Scholar (Part Time), Department of Mathematics, Kandaswami Kandar¡¯s College, P-velur, Tamil Nadu-638 182. E-mail: pspmaths@gmail.com
Abstract:
In this paper, a new class of generalized fuzzy soft open sets in fuzzy soft topological spaces called fuzzy soft e-open(closed) sets, fuzzy soft e-interior(closure), fuzzy soft e-continuous(open) functions and fuzzy soft e-separation axioms are introduced and studied. Then discussed the relationships among fuzzy soft alpha-open sets, fuzzy soft semiopen sets, fuzzy soft preopen sets and fuzzy soft beta -open sets. We also investigated the concepts of fuzzy soft -open functions and fuzzy soft e-continuous functions and discussed their relation with fuzzy soft continuous and other weaker forms of fuzzy soft continuous functions. Moreover, we study the properties of fuzzy soft e-regular spaces and fuzzy soft e-normal spaces.
Key words:
Fuzzy soft e-open (closed) sets, fuzzy soft e-continuous functions, fuzzy soft e-separation axioms.
Image and Inverse Image of Refinement of Fuzzy Syntopogenougs Structures
Hong Wang
ollege of Science, Southwest University of Science and Technology Mianyang, Sichuan 621010, P. R. China
Abstract:
In this paper, the concept of fuzzy (semi-) topogenous order and fuzzy syntopogenous structure in the framework of fuzzy topologies, fuzzy proximities and fuzzy uniformities have been introduced. The refinement of a fuzzy syntopogenous structure has been researched. On this basis, firstly, image and inverse image of refinement of fuzzy (semi-)topogenous order have been defined by general order homomorphism(GOH). Secondly, the image and inverse image of refinement of fuzzy syntopogenous structure have been further researched. Some important properties of them have been obtained.
Key words:
Fuzzy (semi-) topogenous order, fuzzy syntopogenous structures, refinement, GOH, image and inverse image.
The Formalization of Group Theory Knowledge and Solving
Wan Li and Qinghua Liu
Southwest jiaotong University, School of Mathematics Verification Engineerng Lab of Sichuan Province, Sichuan, Chengdu, 610031, China.
Yang Xu
Southwest jiaotong University, School of Mathematics Verification Engineerng Lab of Sichuan Province, Sichuan, Chengdu, 610031, China.
Abstract:
The First-order logic formula is often used as a formal representation to represent and specify various objects and relationships among them, and it has a strong ability to express the problem. While, it is not a simple work to translate mathematical knowledge into logical formulas. To do the formalization correctly, I translate a lot of examples in Group theory into logical formulas, and then using the theorem proving tool to prove the attribute of these examples. In the process of experiment, I can gain experience from the practical transformation and test, and try to transform open problems and solve these problems.
This paper presents some definitions and theorems of my transformation about Group theory, and they have been verified by theorem prover, and then I select an open problem in Group theory. Those previous examples can help me understand the meaning of this open problem and formalize this problem. Finally, the open problem can be solved with the help of the theorem Prover9.
Key words:
Group theory, Formalization, Theorem Prover, Verify
Some Results on Fuzzy Normed Linear Spaces
Arindam Pal and T. Bag
Department of Mathematics, Visva-Bharati University, Santiniketan, INDIA. E-mail: arindambolpur3@gmail.com,, E-mail: tarapadavb@gmail.com
Abstract:
In this paper some examples are given and some basic properties are studied based on the definition of fuzzy normed linear space with general t-norm. Lastly idea of alpha-fuzzy equivalent norms is introduced.
Key words:
Fuzzy normed linear space, alpha-fuzzy equivalent norms, t-norm.
The Homomorphism of Fuzzy S-semipermutable Subgroups
Ganhua Yu, Lang Wang and Chengyi Zhang
Department of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
Abstract:
Based on the definition of fuzzy S-semipermutable subgroups given in [1]. In this paper, we further studied some properties of fuzzy S-semipermutable subgroups by using irreducible nested sets, and corresponding homomorphism and isomorphism properties were studied. And the corresponding conclusions are obtained in the fuzzy S-quasinormal subgroups.
Key words:
Irreducible Nested Sets; Fuzzy S-semipermutable Subgroups; Homomorphism; Isomorphism.
The Methods of Fuzzy Multi-attribute Decision Making Based on Fuzzy Structured Element
Liu Hai-tao and Guo Si-zong
College of Science, Liaoning Technical University, Liaoning Fuxin 123000, China. E-mail: haitao641@163.com
Abstract:
For the fuzzy multi-attribute decision making problems, many scholars have done research, and they put forward a set of methods. By analyzing, the main problem of the fuzzy multi-attribute decision making is the operation and sequencing of fuzzy numbers. Nowadays, in the research of fuzzy multi-attribute decision making problems, the operation of fuzzy numbers is based on the extension principle put forward by Zadeh and the sequencing of fuzzy numbers is based on the complex expression of membership function, which make the calculation of decision making very difficult. Some people also put forward the approximate computation methods of fuzzy numbers, which cannot be applied widely.
According to expression of structured element of fuzzy number and the homeomorphic property between the standard monotone function family with same monotonic form on [-1, 1] and the bounded fuzzy number, the author puts forward the methods of fuzzy multi-attribute decision making based on fuzzy structured element. In these methods, the operation of bounded fuzzy numbers is turned into that of the monotone functions on [-1, 1], and the ordered relationship between monotonous functions shows that between fuzzy numbers.
According to rules of classical multi-attribute decision making, we put forward three methods of fuzzy multi-attribute decision making based on fuzzy structured element theory. Making use of an example, we utilize these three methods to carry out the decision making, and compare these methods with the traditional ones. These methods are easy to understand, and the operation speed is much quicker than that of the traditional methods.
Key words:
Fuzzy operational research; Fuzzy multi-attribute decision making methods; Structured element; Decision making rules
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