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The objective of the paper is to introduce a new cross entropy measure in a neutrosophic cubic set (NCS) environment, which we call NC-cross entropy measure. We prove its basic properties. We also propose weighted NC-cross entropy...
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The objective of the paper is to introduce a new cross entropy measure in a neutrosophic cubic set (NCS) environment, which we call NC-cross entropy measure. We prove its basic properties. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision-making (MADM) strategy based on a weighted NC-cross entropy measure. To show the feasibility and applicability of the proposed multi attribute decision-making strategy, we solve an illustrative example of the multi attribute decision-making problem.
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The fuzzy linear fractional programming (FLFP) problem has always been a subject of keen interest, and a rigorous research has also been done on it. However, due to some limitation of these methods, they cannot be applied to solvi...
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The fuzzy linear fractional programming (FLFP) problem has always been a subject of keen interest, and a rigorous research has also been done on it. However, due to some limitation of these methods, they cannot be applied to solving multi-objective linear fractional programming (MOLFP)problem with fuzzy coefficients and fuzzy variables. To overcome these limitations, Taylor series approximation and normalisation technique is applied in this problem. In this paper, we deal with the concept of α-cuts which are employed to defuzzify the problem. We also formulate the membership function of each objective function is linearised using first order Taylor series approximation and normalisation technique. Normalisation technique is employed to ensure that the range of the reduced membership function belongs to. Then fuzzy goal programming is applied to solve the formulated problem so that the negative deviational variables are minimised. Finally, the fruitfulness of the proposed algorithm is illustrated through numerical examples as compared to other methods.
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This paper develops a goal programming (GP) algorithm to evaluate bi-level decentralised multi-objective linear programming problem (BLDMOLPP) in neutrosophic number (NN) environment. In a BLDMOLPP, a single decision maker (DM) is...
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This paper develops a goal programming (GP) algorithm to evaluate bi-level decentralised multi-objective linear programming problem (BLDMOLPP) in neutrosophic number (NN) environment. In a BLDMOLPP, a single decision maker (DM) is present at the upper level and multiple decision makers at the lower level. Here the parameters of the problem are considered to be NNs in the form of [ P + QI ], where P and Q are real numbers and indeterminacy is represented through the symbol I . I is expressed in the form of a real interval as agreed upon by the DMs. The BLDMOLPP with NNs then gets converted into an interval BLDMOLPP. Using interval programming, the target intervals for the objective functions are identified and subsequently, the goal achievement functions are constructed. The upper level DM provides some possible relaxation on the decision variables under his/her control to cooperate with the lower level DMs to attain a compromise optimal solution. Thereafter, goal programming (GP) models are formulated by minimising the deviational variables and thereby obtaining the most satisfactory solution for all DMs. Finally, a numerical example demonstrates the feasibility and simplicity of the proposed strategy.
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The objective of this paper is to present a technique for order preference by similarity to ideal solution (TOPSIS) algorithm to linear fractional bi-level multi-objective decision-making problem. TOPSIS is used to yield most appr...
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The objective of this paper is to present a technique for order preference by similarity to ideal solution (TOPSIS) algorithm to linear fractional bi-level multi-objective decision-making problem. TOPSIS is used to yield most appropriate alternative from a finite set of alternatives based upon simultaneous shortest distance from positive ideal solution (PIS) and furthest distance from negative ideal solution (NIS). In the proposed approach, first, the PIS and NIS for both levels are determined and the membership functions of distance functions from PIS and NIS of both levels are formulated. Linearization technique is used in order to transform the non-linear membership functions into equivalent linear membership functions and then normalize them. A possible relaxation on decision for both levels is considered for avoiding decision deadlock. Then fuzzy goal programming models are developed to achieve compromise solution of the problem by minimizing the negative deviational variables. Distance function is used to identify the optimal compromise solution. The paper presents a hybrid model of TOPSIS and fuzzy goal programming. An illustrative numerical example is solved to clarify the proposed approach. Finally, to demonstrate the efficiency of the proposed approach, the obtained solution is compared with the solution derived from existing methods in the literature.
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Many multi-attribute group decision-making (MAGDM) strategies have been introduced in the literature to deal with decision-making problems in uncertain environment. Many of them are based on fuzzy numbers and they are not able to ...
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Many multi-attribute group decision-making (MAGDM) strategies have been introduced in the literature to deal with decision-making problems in uncertain environment. Many of them are based on fuzzy numbers and they are not able to cope with indeterminacy and inconsistency involving in decision making. In recent years, some neutrosophic multi-attribute group decision-making strategies have been successfully developed to deal with uncertainty, indeterminacy, and inconsistency in decision making. Among them, TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) strategy based on prospect theory has received more attention due to its great performance in considering the bounded rationality of decision makers. In this paper, we develop a TODIM strategy to deal with multi-attribute group decision-making problem in trapezoidal neutrosophic numbers environment. To establish the TODIM strategy, we employ score function, accuracy function, and Hamming distance function for trapezoidal neutrosophic numbers. Lastly, we solve an illustrative numerical example to show the applicability and usefulness of the proposed strategy. A comparison analysis is also provided.
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This paper presents fuzzy goal programming approach for solving multi- objective quadratic programming problem. The problem deals with a decision- making unit with multiple objective functions, which are quadratic in nature and th...
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This paper presents fuzzy goal programming approach for solving multi- objective quadratic programming problem. The problem deals with a decision- making unit with multiple objective functions, which are quadratic in nature and the system constraints are linear functions. In the proposed approach, we first formulate the quadratic membership functions by determining best solution of the objective functions subject to the system constraints. The quadratic membership functions are then linearized into equivalent linear membership functions at the best solution point by using first order Taylor polynomial series. Then fuzzy goal programming technique is used for solving the problem by minimizing only the negative deviational variables. A multi-objective quadratic programming problem is solved to demonstrate the efficiency of the proposed approach.
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This paper deals with linear fractional bilevel programming problem. The goals of objective functions are determined by optimizing individual objective function subject to the system constraints. Then the fractional objective func...
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This paper deals with linear fractional bilevel programming problem. The goals of objective functions are determined by optimizing individual objective function subject to the system constraints. Then the fractional objective functions are transformed into equivalent linear functions at the optimal solution point by using first order Taylor polynomial series. Since the objectives of the decision makers are potentially conflicting in nature, decision makers consider relaxation on decision for avoiding decision deadlock. To demonstrate the efficiency of the proposed approach, a numerical example is solved and compared with other approaches.
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In this paper, we studied the problems faced by construction workers in West Bengal in order to find its solutions using neutrosophic cognitive maps, which is the generalization of fuzzy cognitive maps. Florentin Smarandache and V...
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In this paper, we studied the problems faced by construction workers in West Bengal in order to find its solutions using neutrosophic cognitive maps, which is the generalization of fuzzy cognitive maps. Florentin Smarandache and Vasantha Kandasamy studied neutrosophic cognitive map which is an extension of fuzzy cognitive map by incorporating indeterminacy. Construction sector plays a major role in which construction workers face many problems in their day-to-day life. Some of the problems are discussed in the present study. The major problems are working for more number of hours, staying away from home, bad habits, absence of social security, misunderstanding, arguments with partners, stress, skin problems, sexual behavior & sexual health problem, and physical health problems. Based on the expert’s opinion and the notion of indeterminacy, we formulate neutrosophic cognitive map. Then we studied the effect of two instantaneous state vectors separately on connection matrix E & neutrosophic adjacency matrix N(E).
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This paper presents the fuzzy goal programming approach for linear fractional bilevel decentralized programming problem based on Taylor series approximation. The bilevel decentralized programming problem is an extension of the con...
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This paper presents the fuzzy goal programming approach for linear fractional bilevel decentralized programming problem based on Taylor series approximation. The bilevel decentralized programming problem is an extension of the conventional bilevel programming problem. Bilevel decentralized programming problem consists of an upper level decision maker at the first level and multiple lower level decision makers at the second level. In the decision making situation, each decision maker controls a decision vector independently. The objective function of both level decision makers are linear fractional in nature. To formulate the fuzzy goal programming model of the proposed method, the fractional membership function of the fuzzy objective goals of both levels are transformed into linear membership function by first order Taylor polynomial series. The objectives of both level decision makers are potentially conflicting in nature, a possible relaxation of upper level decision is considered for avoiding decision deadlock. Then, the fuzzy goal programming approach due to Pramanik and Roy [9] is used for achieving highest degree of each of the membership goals by minimizing the negative deviational variables. To demonstrate the efficiency of the proposed method, a bilevel linear fractional decentralized programming is solved.
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The main purpose of this study is to bring in a new extension of multi-objective optimisation on the basis of ratio analysis plus full multiplicative form (MULTIMOORA) in trapezoidal neutrosophic number (TrNN) environment. MULTIMO...
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The main purpose of this study is to bring in a new extension of multi-objective optimisation on the basis of ratio analysis plus full multiplicative form (MULTIMOORA) in trapezoidal neutrosophic number (TrNN) environment. MULTIMOORA strategy provides high efficiency and effectiveness in problem-solving. The new MULTIMOORA strategy consists of three components. The components are ratio system approach, reference point approach, and full multiplicative form. To develop the proposed strategy, the authors find out three ranking order of alternatives using the three components. The final ranking order of the alternatives is based on dominance property. The study is original as it first develops the MULTIMOORA strategy in the TrNN environment, which they call TrNN- MULTIMOORA. They solve a realistic banking problem involving multi-attribute group decision making in the TrNN environment to reflect the applicability and proficiency of the developed strategy. They also present a comparison between the proposed strategy and the existing tomada de decisao interativa e multicritévio and VlseKriterijumska Optimizcija I Kaompromisno Resenje strategies.
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