A multi-criteria decision making approach for strategy formulation using Pythagorean fuzzy logic

The objective of this paper is to develop Pythagorean fuzzy (PF) multi-objective optimization by ratio analysis (PF-MOORA) plus full MULTIplicative form (PF-MULTIMOORA) method for solving multicriteria decision making (MCDM) problems with completely unknown information of criteria weights. In the model formulation process, a new distance measure is defined to quantify the difference between PF sets by combining Hamming distance and Hausdorff metric. This distance measure is, subsequently, implemented in entropy weight model for determining unknown weights of criteria, and also in reference point approach for obtaining preference indices of alternatives. To overcome the deficiencies occurred in existing MULTIMOORA method, like multiple comparisons, circular reasoning, and so on, an aggregation-based approach is recommended in the proposed PF-MULTIMOORA. To demonstrate the feasibility and practicality of the proposed method, an example concerning strategy prioritization of a tiles manufacturing company is presented. In the strategy evaluation process, at first, the judgement values provided by the decision maker are expressed in linguistic terms, and then those are converted into PF numbers through a PF weighting scale. The sensitivity of the proposed model is validated by changing of weights of criteria which impact on the ranks of the strategies. To show robustness of the developed method, the result attained by applying PF-MULTIMOORA is compared with existing techniques, not only in crisp and fuzzy quantitative strategic planning matrix context, but also using four other MCDM methods, namely, modified PF-MOORA, as a particular case of the proposed PF-MULTIMOORA technique, PF weighted sum, PF-TOPSIS and PF-VIKOR.     

A hybrid decision making approach to prevent chatter vibrations

In this paper, the optimum cutting conditions without chatter vibrations have been determined during turning operations. Chatter vibrations are detrimental and cause poor surface properties. In this study, chatter vibration prevention has been discussed in a different way using a multi-criteria decision making approach. Regression-multi-criteria decision making hybrid models have been developed and applied to the problem of chatter vibrations. First, regression models have been used to determine the criteria weights for TOPSIS (technique for order preference by similarity to ideal solution) model. Then, TOPSIS models have been developed. Three different hybrid models have been studied. The results of these three models are the same. It has been seen from the results that the number of revolutions and the workpiece hardness are the most effective parameters. The models are developed to help operators in different manufacturing environments.     

A hybrid fuzzy multiple criteria group decision making approach for sustainable project selection

In this paper, a new hybrid fuzzy multiple criteria group decision making (FMCGDM) approach has been proposed for sustainable project selection. First, a comprehensive framework, including economic, social, and environmental effects of an investment, strategic alliance, organizational readiness, and risk of investment has been proposed for sustainable project selection. As the relative importance of the criteria of the proposed framework are hard to find through several conflictive preferences of a group of Decision Makers (DMs) so, a goal programming (GP) has been supplied to this aim considering multiplicative and fuzzy preference relation. Then, a fuzzy TOPSIS method has been developed to assess the fitness of investment chances. It is based on Preference Ratio (PR), which is known as an efficient ranking method for fuzzy numbers, and a fuzzy distance measurement. The properties of proposed hybrid approach make it robust for modeling real case of uncertain group decision making problems. The FMCGDM has been developed through a linkage between Lingo 11.0, MS-Excel 12.0, and Visual Basic 6.0. The proposed hybrid approach has been applied in a real case study called Iranian financial and credit institute for sustainable project selection.     

A fuzzy constraint satisfaction approach for electronic shopping assistance

The Internet and World Wide Web offer an additional channel for consumers to find, select, and buy products. However, unlike shopping in the traditional store, consumers have no direct contact with human clerks to get the required information in the electronic store. The objective of this paper is to propose a fuzzy constraint satisfaction approach to help buyers find fully satisfactory or replacement products in electronic shopping. For the buyer who can give precise product requirements, the proposed approach can generate product-ranking lists based on the satisfaction degrees of each product to the given requirements. For the buyer who may not input accurate requirements, a similarity analysis approach is proposed to assess buyer requirements automatically during his browsing process. The proposed approach could help buyers find the preferred products on the top of the ranking list without further searching the remaining pages. The experimental results show the applicability of the proposed approach for electronic shopping assistance.     

A fuzzy multi-criteria decision making approach for solving a bi-objective personnel assignment problem

Effective personnel assignment is one of the most crucial tasks performed by the decision makers of a company. This paper proposes a systematic approach with a feedback mechanism in which the interdependences among positions and the differences among the selected employees are considered simultaneously. Unfortunately, the two combined considerations have rarely been discussed in the literature. The purpose of this approach is to obtain the best matching of candidates and positions in order to organize a collaboratively cross-functional team. In a fuzzy environment and, then, in the proposed approach, a bi-objective binary integer programming (BOBIP) model is formulated. Based on the weighted composite scores determined in the third step of the proposed procedure, the BOBIP model is transformed into a fuzzy bi-objective goal programming (FBOGP) model. An elaborately designed heuristic algorithm is developed to determine the appropriate values of several important parameters in the FBOGP model, which is solved using LINDO 8.0. An application example is illustrated, and two additional examples are tested. The results indicate that the proposed approach achieves the acceptable satisfaction level and requires less computation time than the brute force enumerative method.     

Pythagorean fuzzy TODIM approach to multi-criteria decision making

Recently, the TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) approach, which can characterize the decision makers’ psychological behaviours under risk, has been introduced to handle multi-criteria decision making (MCDM) problems. Moreover, Pythagorean fuzzy set is an effective tool for depicting uncertainty of the MCDM problems. In this paper, based on the prospect theory, we first extend the TODIM approach to solve the MCDM problems with Pythagorean fuzzy information. Then, we conduct simulation tests to analyze how the risk attitudes of the decision makers exert the influence on the results of MCDM under uncertainty. Finally, a case study on selecting the governor of Asian Infrastructure Investment Bank is made to show the applicability of the proposed approach.     

A fuzzy logic based approach to the SLAM problem using pseudolinear models with multiframe data association

This paper presents an alternative solution to simultaneous localization and mapping (SLAM) problem by applying a fuzzy Kalman filter using pseudolinear process and measurement models. Nonlinear process model and observation model are formulated as pseudo-linear models and rewritten with a composite model whose local models are linear according to Takagi-Sugeno (T-S) fuzzy model. Using the Kalman filter theory, each local T-S model is filtered to find the local estimates. The linear combination of these local estimates gives the global estimate for the complete system. Data association to correspond features to the observed measurement is proposed with two sensor frames obtained from two sensors. The above system is implemented and simulated with Matlab to claim that the proposed method yet finds a better solution to the SLAM problem, though nonlinearity is directly involved in the Kalman filter equations, compared to the conventional approach. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Multi-level decision making in reconfigurable machining systems using fuzzy logic

Reconfigurable machine tools (RMTs) are synthesised using the principles of modular design in order to achieve the required structural design for a particular part to be manufactured. In this paper, an effective method that uses multi-level fuzzy decisions to create dynamic optimal configurations of machine structures with respect to a given part geometry is presented. A system of modular machine configuration is utilised to arrive at machine configurations considering the fuzzy constraints that are pertinent in this process. With the utilisation of fuzzy decisions for the configuration system model, selection of optimal modular tool configurations is done. Decisions are made at a particular threshold level so as to verify the appropriateness of such decisions.     

An approach to fuzzy multiattribute decision making under uncertainty

It seems that there is little investigation on fuzzy multiattribute decision making (FMADM) problems under uncertainty, which are of important to scientific researches and real life applications. FMADM problems under uncertainty are investigated in this paper. Novel mathematical programming models are constructed for FMADM problems under uncertainty, and corresponding solving methods are proposed. The approach proposed in this paper may reflect both subjective judgment and objective information. Moreover, pairwise chain comparison methods for determination of relative membership degrees and weights are also proposed. Feasibility and effectiveness of the models and approach proposed in this paper are illustrated with a numerical example.     

Using fuzzy logic to implement decision policies in system dynamics models

This paper aims to show how the use of fuzzy systems can enhance the application of system dynamics (SD), with the construction of virtual worlds, for organizational learning. By doing so, the main contribution is to propose a fuzzy-SD integrated methodology that allows a natural language modeling of decision policies. At first it will be revised the recent literature with practical and theoretical fuzzy-SD integration showing that the motivation and purpose of this article have not been explored yet. Following, it will be scrutinized the origin of system dynamics to theoretically justify the proposed fuzzy-SD integration for organizational learning. Finally, it will be presented a hypothetical case study based on the balance scorecard model to illustrate the methodology in action.     

A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets

In this paper we present a new approach to solve multi-attribute decision making problems in intuitionistic fuzzy environment. This approach is based on a new ranking method of intuitionistic fuzzy sets, in which the evaluated values (in the form of intervals) of the same alternative with different attributes are considered as one unified entity. According to people’s intuition, the ranking method proposed in this paper is mainly grounded on a revised score function and a revised accuracy function of intuitionistic fuzzy sets. Different from the traditional methods, in this new approach, the degree of membership, the degree of nonmembership and the degree of hesitation are considered with various importance in reflecting the true image of the respective alternative. Furthermore, an optimization model is established to estimate the relative degree of importance of each quantity. Finally, two practical examples are provided to illustrate our approach.     

A decision support system for coating selection based on fuzzy logic and multi-criteria decision making

Wear and corrosion are the most important factors that the surface of the engineering parts must confront. The need for protection and improvement of the mechanical characteristics of the surface of engineering parts can be to some extent satisfied by coatings. Coatings are considered as an excellent solution when resistance to corrosion, oxidation or low friction is demanded, but due the complexity of selecting the appropriate one, engineers often avoid them. The need for simultaneous consideration of qualitative and quantitative properties, render the use of classic material selection theories inadequate. An expert system for coating selection is presented in this paper, which can handle both qualitative and quantitative variables. The mathematical model used combines the multi-criteria decision making theories (MCDM) together with the fuzzy sets theory. The “Max-Min set” method is applied to calculate the ordering value of the alternatives while the TOPSIS method is used to rank them. A numerical example is provided to illustrate the method. Finally, the process presented can be easily computerized, to create the relative software.     

A new approach to partial constraint satisfaction problems

A finite binary Constraint Satisfaction Problem (CSPs) is defined as consisting of a set of n problem variables, a domain of d potential values for each variable and a set of m binary constraints involving only two variables at a time. A solution to such a CSP is specified by assignment of a value to each variable that does not violate any of the constraints. The CSPs belong to the class of NP-Complete Problems. Backtracking and its variants have been generally used for solving CSPs. The class of Partial Constraint Satisfaction Problems (PCSPs) is a subclass of CSPs that are either too difficult to solve or are unsolvable. Near optimal solutions are always desired to these problems.

In this article, we have considered only finite binary CSPs or PCSPs and developed a method of time complexity O(n ² d ²) to obtain a near optimal solution for them. The performance of the method in terms of the average number of consistency checks and the average number of constraint violations is measured on various randomly generated binary CSPs and compared with the Branch and Bound (BB) method used to obtain the same solution. The BB method is a widely used optimization technique that may be viewed as a variation of backtracking. Thus, it was a natural choice in seeking an analog of backtracking to find optimal partial solutions for PCSPs. The proposed method moves much faster to the solution. The performance results indicate that in terms of the number of consistency checks, the proposed method has much less consistency checks than BB whereas in terms of average number of constraint violations both methods are same. An upper bound on the distance of the solution from the optimal solution is obtained analytically as ?n(n???2)(d???2)/(d???1)?.     

A logic approach to fuzzy relational databases

A new definition of Fuzzy Relational Database is given by using logical concepts. With this definition it is possible to consider several kinds of fuzziness for the database attributes. A Domain Calculus-based query language is also established for the model. It allows us to formulate several types of queries with different lack of precision levels. © 1994 John Wiley & Sons, Inc.     

A hybrid constraint programming approach to a wood procurement problem with bucking decisions

In this article, we present a wood procurement problem that arises in Eastern Canada. We solve a multi-period wood supply planning problem, while taking into account bucking decisions. Furthermore, we present a new form of flexibility which allows the harvesting capacity to change from one time period to another. We study the impact of such flexibility upon the harvesting cost. We assess the performance of the problem by comparing it with a variant where the harvesting capacity is fixed during sites’ harvesting. To address this problem, we develop a hybrid approach based on both constraint and mathematical programming. In the first phase, we propose a constraint programming model dealing with forest sites harvesting and bucking problems. The result of this model is used as part of an initial solution for the whole problem formulated as a mixed integer model. We test the two versions of the problem on a set of different demand instances and we compare their results.     

An automatic approach to reaching consensus in multiple attribute group decision making

In this work, we consider the problem of consensus of multiple attribute group decision making, and develop an automatic approach to reaching consensus among group opinions. In the process of group decision making, each expert provides his/her preferences over the alternatives with respect to each attribute, and constructs an individual decision matrix. The developed approach first aggregates these individual decision matrices into a group decision matrix by using the additive weighted aggregation (AWA) operator, and then establishes a convergent iterative algorithm to gain a consentaneous group decision matrix. Then based on the consentaneous group decision matrix, the approach utilizes the AWA operator to derive the overall attribute values of alternatives, by which the most desirable alternative can be found out. Finally, we detailedly expound the implementation process of the approach with a practical example.     

A hybrid data envelopment analysis and multi-attribute decision making approach to sustainability assessment

The concept of sustainability consists of three main dimensions: environmental, techno-economic, and social. Measuring the sustainability status of a system or technology is a significant challenge, especially when it needs to consider a large number of attributes in each dimension of sustainability. In this study, we first propose a hybrid approach, involving data envelopment analysis (DEA) and a multi-attribute decision making (MADM) methodologies, for computing an index for each dimension of sustainability, and then we define the overall sustainability index as the mean of the three measured indexes. Towards this end, we define new concepts of efficiency and cross-efficiency of order (p, q) where p and q are the number of inputs and outputs, respectively. For a given (p, q) , we address the problem of finding efficiency of order (p, q) by developing a novel DEA-based selecting method. Finally, we define the sustainability index as a weighted sum of all possible cross-efficiencies of order (p, q) . Form a computational viewpoint, the proposed selecting model significantly decreases the computational burden in comparison with the successive solving of traditional DEA models. A case study of the electricity-generation technologies in the United Kingdom is taken as a real-world example to illustrate the potential application of our method.     

A new method selection approach for fuzzy group multicriteria decision making

Fuzzy multicriteria decision making (MCDM) has been widely used in ranking a finite number of decision alternatives characterized by fuzzy assessments with respect to multiple criteria. In group decision settings, different fuzzy group MCDM methods often produce inconsistent ranking outcomes for the same problem. To address the ranking inconsistency problem in fuzzy group MCDM, this paper develops a new method selection approach for selecting a fuzzy group MCDM method that produces the most preferred group ranking outcome for a given problem. Based on two group averaging methods, three aggregation procedures and three defuzzification methods, 18 fuzzy group MCDM methods are developed as an illustration to solve the general fuzzy MCDM problem that requires cardinal ranking of the decision alternatives. The approach selects the group ranking outcome of a fuzzy MCDM method which has the highest consistency degree with its corresponding ranking outcomes of individual decision makers. An empirical study on the green bus fuel technology selection problem is used to illustrate how the approach works. The approach is applicable to large-scale group multicriteria decision problems where inconsistent ranking outcomes often exist between different fuzzy MCDM methods.     

Novel intuitionistic fuzzy decision making models in the framework of decision field theory

The intuitionistic fuzzy decision making problems have gained great popularity recently. Most of the current methods depend on various aggregation operators that provide collective intuitionistic fuzzy values of alternatives to be ranked. Such collective information only depicts the overall characteristics of the alternatives but ignores the detailed contrasts among them. Most important of all, the current decision making procedure is not in accordance with the way that the decision makers (DMs) think about the decision making problems. In this paper, we develop a novel intuitionistic fuzzy decision making model in the framework of decision field theory. The decision making model emphasizes the contrasts among alternatives with respect to each attribute that competes and influences each other, and thus, the preferences for alternatives can dynamically evolve and provide the final optimal result. After that, we develop an intuitionistic fuzzy group decision making model based on decision field theory, and then make a practical case study on the application of the developed models to the “one belt, one road” investment decision making problems. Finally, we point out the characteristics and the limitations of our models in detail.     

Approach to decision making in fuzzy environment

A general approach to solving a wide class of optimization problems with fuzzy coefficients in objective functions and constraints is described. It is based on a modification of traditional mathematical programming methods and consists in formulating and solving one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective function alone. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The approach is applied within the context of fuzzy discrete optimization models, that is based on a modification of discrete optimization algorithms. The results of the paper are of a universal character and are already being used to solve problems of the design and control of power systems and subsystems.