The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature.

Solving Fuzzy Job-Shop Scheduling Problem Using DE Algorithm Improved by a Selection Mechanism

A game is a situation which conceives and concludes through reality involving a set of players, may be two or more. Conclusions of such situations are not always very easy, e.g., if one wins other loses. Sometimes, when considering the totality, the outcome of game is not linguistically zero, and we utter the term non-zero-sum game. Prisoners’ dilemma game is one of most cited examples in non-zero-sum game literature. In this paper, human trafficking, one of the most rising problems of today’s society is viewed through Prisoners’ dilemma game using hesitant interval-valued intuitionistic fuzzy-linguistic term set, where linguistic terms in interval are expressed by linguistic semantics first, and then corresponding indices are used. Finally, Nash equilibrium is derived from the given definition, and the achieved result establishes a close contact with reality using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Dominance property of matrix game theory.

Hesitant interval-valued intuitionistic fuzzy-linguistic term set approach in Prisoners’ dilemma game theory using TOPSIS: a case study on Human-trafficking

The market competitiveness and sustainable operation of an enterprise are closely correlated with the support of high-tech core technologies in the enterprise. This study first discusses the basic knowledge of core competitiveness, introduces the components and evaluation methods of core competitiveness, and builds an evaluation index system for core competitiveness of high-tech enterprises. Then, the Analytic Hierarchy Process (AHP) is fully discussed, during which the steps, advantages, and disadvantages of the AHP evaluation method are introduced. Finally, the Fujian Province of China is taken as an example, the relevant data are collected and processed, the impact of indicators are analyzed, and a high-tech industry core technological capability analysis indicator system is built based on the AHP method. Thus, the influence of the core technological capabilities of the high-tech industry on the sustainable competitive advantage of the enterprise is obtained. This study puts forward suggestions for maintaining the competitiveness of high-tech industries, thereby improving the competitive advantage of enterprises and achieving the sustainable management of enterprises. The result finds that if the high-tech industries continue to carry out innovation and scientific research, enterprises will maintain their competitive advantages. In summary, exploring the impact of the core technological capabilities of high-tech industries on the sustainable competitive advantages of enterprises is greatly significant for improving their competitiveness and industrial status, which enables them to be invincible in a complex environment.

https://tspace.library.utoronto.ca/bitstream/1807/100197/1/sustainability-12-02980.pdf

The Impact of Core Technological Capabilities of High-Tech Industry on Sustainable Competitive Advantage

Type-2 intuitionistic fuzzy matrix games based on a new distance measure: Application to biogas-plant implementation problem

In real world, a typical decision-making problem in the medical field can be seen as an uncertain hesitant fuzzy multiattribute decision-making problem when existing experiences of decision-makers are insufficient. A three-way decision model is an effective tool to deal with uncertain decision-making problems, which can realize the classification of objects. However, different psychological behaviors of decision-makers are likely to affect decision-making results in actual decision-making processes. In order to address this challenge, we first propose a regret-theory-based three-way decision model in hesitant fuzzy environments, which mainly combines regret theory with hesitant fuzzy sets to calculate the perceived utility value of objects. Second, since one of the core ingredients for regret theory is the regret–rejoice function, we put forward a new regret–rejoice function that preserves the original indecisive uncertainty in hesitant fuzzy environments. In addition, according to the inherent relationship of the used data, this article provides a three-way classification method based on the preference ranking organization method for enrichment evaluations I method. Finally, the practicability, rationality, and superiority of the proposed method are shown via the case analysis and comparative analysis in the medical field.

Regret Theory-Based Three-Way Decision Model in Hesitant Fuzzy Environments and Its Application to Medical Decision

The dual hesitant fuzzy set is an effective mathematical approach to deal with the data which are imprecise, uncertain or incomplete information. Dual hesitant fuzzy set is an extension of hesitant fuzzy set which encloses fuzzy set, intuitionistic fuzzy set and hesitant fuzzy set as a special one. In this paper, the axiomatic definition of similarity measure between the dual hesitant fuzzy set is presented. A new similarity measure by considering membership and non-membership functions of dual hesitant fuzzy set is introduced. It is shown that the corresponding distance measure can be obtained from the proposed similarity measure. To check the utility, the proposed similarity measure is applied in a bidirectional approximate reasoning system into matrix game. Matrix game with precise data is hardly applicable in real-life decision-making problem. In view of more realistic sense, we choose the elements as dual hesitant fuzzy into the payoff of the matrix game, which is treated as dual hesitant fuzzy matrix game. Mathematical formulation of dual hesitant fuzzy matrix game with on restriction (DHFMGR) is described. Four algorithms are emerged on the proposed similarity measure, which are provoked to find the optimal value of the DHFMGR. A numerical example is incorporated to illustrate the applicability and feasibility of the proposed measure in dual hesitant fuzzy matrix game. The paper ends with the conclusions including an outlook for future study in this direction.

Dual hesitant fuzzy matrix games: based on new similarity measure

https://www.tandfonline.com/doi/pdf/10.1080/16168658.2018.1517975

Solution of Matrix Games with Generalised Trapezoidal Fuzzy Payoffs

Soft set theory has emerged recently as a new mathematical tool to handle uncertainty. Sometimes decision makers are not sure about the decision-making criteria, where soft set theory provides an i...

Soft Matrix Game: A Hesitant Fuzzy MCDM Approach

The hesitant fuzzy set (HFS) is a very fruitful mathematical approach to deal with uncertain or imprecise information. In this work, we consider a multi-objective linear production planning (MOLPP) problem in which multiple decision makers pool resources to make various products and analyze them with the help of cooperative game theory. It can be formulated as a mathematical programming problem with triangular hesitant fuzzy (THF) parameters. The main aim of this paper is to analyze the MOLPP problem in THF environment. In view of realistic sense we choose the coefficients of multi-objective linear production planning game (MOLPPG) as triangular hesitant fuzzy numbers (THFNs), and hereby it is referred to as THF-MOLPPG. The THF-MOLPPG is converted to fuzzy MOLPPG by taking an average aggregation operator (AAO) of the THFNs. Thereafter we consider $$\alpha $$
 -cut of a fuzzy number to obtain MOLPPG with interval parameters. Two approaches, namely weighted sum method (WSM) and extended technique for order preference by similarity to ideal solution (TOPSIS), are chosen to obtain the optimal strategy and payoff vectors of the players to the MOLPPG. For solving MOLPPG, we apply WSM and extended TOPSIS by considering the various values of $$\alpha $$
 for finding the value of the game in such a way that the total income is maximized. A comparison is drawn among the payoff vectors, which are determined from the approaches. Finally, the applicability and feasibility of the proposed methods are illustrated by a numerical example. WSM and extended TOPSIS provide better results at the values $$\alpha = 0.3$$
 and $$\alpha =0.9$$
 , respectively, for the proposed problem. From the results, we infer that TOPSIS is far better than WSM of the proposed problem. Also, the conclusions and outlooks of the paper are delineated.

Jishu Jana

Papers

Dual hesitant fuzzy matrix games: based on new similarity measure

Solution of Matrix Games with Generalised Trapezoidal Fuzzy Payoffs

Soft Matrix Game: A Hesitant Fuzzy MCDM Approach

The multi-objective linear production planning games in triangular hesitant fuzzy sets

Linguistic Pythagorean hesitant fuzzy matrix game and its application in multi-criteria decision making