Research Paper
Fuzzy sets and their variants
Eshetu Dadi Gurmu; Tagay Takele Fikadu
Abstract
In this study, we discussed a fuzzy programming approach to bi-level linear programming problems and their application. Bi-level linear programming is characterized as mathematical programming to solve decentralized problems with two decision-makers in the hierarchal organization. They become more important ...
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In this study, we discussed a fuzzy programming approach to bi-level linear programming problems and their application. Bi-level linear programming is characterized as mathematical programming to solve decentralized problems with two decision-makers in the hierarchal organization. They become more important for the contemporary decentralized organization where each unit seeks to optimize its own objective. In addition to this, we have considered Bi-Level Linear Programming (BLPP) and applied the Fuzzy Mathematical Programming (FMP) approach to get the solution of the system. We have suggested the FMP method for the minimization of the objectives in terms of the linear membership functions. FMP is a supervised search procedure (supervised by the upper Decision Maker (DM)). The upper-level decision-maker provides the preferred values of decision variables under his control (to enable the lower level DM to search for his optimum in a wider feasible space) and the bounds of his objective function (to direct the lower level DM to search for his solutions in the right direction).
Review Paper
Fuzzy sets and their variants
Fatemeh Zahra Montazeri
Abstract
One of the appropriate and efficient tools in the field of productivity measurement and evaluation is data envelopment analysis, which is used as a non-parametric method to calculate the efficiency of decision-making units. Today, the use of data envelopment analysis technique is expanding rapidly and ...
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One of the appropriate and efficient tools in the field of productivity measurement and evaluation is data envelopment analysis, which is used as a non-parametric method to calculate the efficiency of decision-making units. Today, the use of data envelopment analysis technique is expanding rapidly and is used in the evaluation of various organizations and industries such as banks, postal service, hospitals, training centers, power plants, refineries, etc.In real-world problems, the values observed from input and output data are often ambiguous and random. To solve this problem, data envelopment analysis in stochastic fuzzy environment was proposed. Although the DEA has many advantages, one of the disadvantages of this method is that the classic DEA does not actually give us a definitive conclusion and does not allow random changes in input and output. In this paper, we review some of the proposed models in data envelopment analysis with fuzzy and random inputs and outputs.
Research Paper
Intuitionistic fuzzy sets and their variants
Atiqe Ur Rahman; Muhammad Rayees Ahmad; Muhammad Saeed; Muhammad Ahsan; Muhammad Arshad; Muhammad Ihsan
Abstract
Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and ...
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Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and non-membership value. The meagerness regarding the allocation of a single membership and non-membership value to any object under consideration is addressed with this novel refinement. In this study, this novel idea is utilized to characterize the essential elements e.g. subset, equal set, null set, and complement set, for refined intuitionistic fuzzy set. Moreover, their basic set theoretic operations like union, intersection, extended intersection, restricted union, restricted intersection, and restricted difference, are conceptualized. Furthermore, some basic laws are also discussed with the help of an illustrative example in each case for vivid understanding.
Research Paper
Pythagorean fuzzy sets and their variants
Veerappan Chinnadurai; Arul Selvam
Abstract
In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, ...
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In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.
Research Paper
Pythagorean fuzzy sets and their variants
V. S. Subha; P. Dhanalakshmi
Abstract
In this paper, we expose cosine, jaccard and dice similarity measures and rough interval Pythagorean mean operator. Some of the important properties of the defined similarity measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, ...
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In this paper, we expose cosine, jaccard and dice similarity measures and rough interval Pythagorean mean operator. Some of the important properties of the defined similarity measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.
Research Paper
Spherical fuzzy sets
Chinnadurai Veerappan; Shakila Venkatesan
Abstract
In this paper we introduce the concept of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R and its some results. The union and intersection of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R is also a spherical interval-valued fuzzy bi-ideal of gamma near-ring R . Further ...
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In this paper we introduce the concept of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R and its some results. The union and intersection of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R is also a spherical interval-valued fuzzy bi-ideal of gamma near-ring R . Further we discuss about the relationship between bi-ideal and spherical interval-valued fuzzy bi-ideal of gamma near-ring R.
Research Paper
Neutrosophic sets and their variants
Mohanasundari Mohan; Mohana Krishnaswamy
Abstract
Abstract Quadripartitioned single valued neutrosophic (QSVN) set is a powerful structure where we have four components Truth-T, Falsity-F, Unknown-U and Contradiction-C. And also it generalizes the concept of fuzzy, initutionstic and single valued neutrosophic set. In this paper we have proposed the ...
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Abstract Quadripartitioned single valued neutrosophic (QSVN) set is a powerful structure where we have four components Truth-T, Falsity-F, Unknown-U and Contradiction-C. And also it generalizes the concept of fuzzy, initutionstic and single valued neutrosophic set. In this paper we have proposed the concept of K-algebras on QSVN, level subset of QSVN and studied some of the results. In addition to this we have also investigated the characteristics of QSVN Ksubalgebras under homomorphism.
