{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T22:17:17Z","timestamp":1770761837496,"version":"3.50.0"},"reference-count":78,"publisher":"IGI Global","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,4]]},"abstract":"<jats:p>In this article, the author categorises the solid transportation problem (STP) under uncertain environments. He formulates the mixed and fully intuitionistic fuzzy solid transportation problems (FIFSTPs) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P. Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the mixed and type-4 IFSTP and the optimal objective value of mixed and type-4 IFSTP is obtained in terms of triangular intuitionistic fuzzy number (TIFN). The main advantage of this method is that the optimal solution of mixed and type-4 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. Finally, the procedure for the proposed method is illustrated with the help of numerical examples which is followed by graphical representation of the finding.<\/jats:p>","DOI":"10.4018\/ijoris.2019040102","type":"journal-article","created":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T17:15:05Z","timestamp":1553188505000},"page":"20-53","source":"Crossref","is-referenced-by-count":25,"title":["PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems"],"prefix":"10.4018","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4317-1021","authenticated-orcid":true,"given":"P. Senthil","family":"Kumar","sequence":"first","affiliation":[{"name":"Department of Humanities and Sciences, Navodaya Institute of Technology, Raichur, India"}]}],"member":"2432","reference":[{"key":"IJORIS.2019040102-0","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"issue":"1","key":"IJORIS.2019040102-1","first-page":"17","article-title":"Ideas for intuitionistic fuzzy equations, inequalities and optimization.","volume":"1","author":"K. T.Atanassov","year":"1995","journal-title":"Notes on Intuitionistic Fuzzy Sets"},{"key":"IJORIS.2019040102-2","doi-asserted-by":"publisher","DOI":"10.1080\/02331939408844023"},{"key":"IJORIS.2019040102-3","doi-asserted-by":"crossref","unstructured":"Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17(B), 141-164.","DOI":"10.1287\/mnsc.17.4.B141"},{"key":"IJORIS.2019040102-4","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90158-E"},{"key":"IJORIS.2019040102-5","first-page":"53","article-title":"Some definitions of intuitionistic fuzzy number-first properties.","author":"P.Burillo","year":"1994","journal-title":"Proceedings of the First Workshop on Fuzzy Based Expert System"},{"issue":"1","key":"IJORIS.2019040102-6","first-page":"1","article-title":"Multi-objective multi-item solid transportation problem with fuzzy inequality constraints.","author":"D.Chakraborty","year":"2014","journal-title":"Journal of Inequalities and Applications"},{"key":"IJORIS.2019040102-7","doi-asserted-by":"publisher","DOI":"10.1515\/9781400884179"},{"key":"IJORIS.2019040102-8","doi-asserted-by":"publisher","DOI":"10.12720\/jiii.1.2.107-110"},{"key":"IJORIS.2019040102-9","doi-asserted-by":"publisher","DOI":"10.1080\/18756891.2010.9727719"},{"key":"IJORIS.2019040102-10","unstructured":"Dinagar, D. S., & Palanivel, K. (2009). The transportation problem in fuzzy environment. Int. Journal of Algorithm, computing and mathematics, 2(3),65-71."},{"key":"IJORIS.2019040102-11","doi-asserted-by":"publisher","DOI":"10.1016\/0360-8352(95)00130-S"},{"key":"IJORIS.2019040102-12","first-page":"223","article-title":"Distance and orderings in a family of intuitionistic fuzzy numbers.","author":"P.Grzegorzewski","year":"2003","journal-title":"Proceedings of the Third Conference of the European Society for Fuzzy Logic and Technology"},{"key":"IJORIS.2019040102-13","doi-asserted-by":"crossref","unstructured":"Guha, D., & Chakraborty, D. (2010). A theoretical development of distance measure for intuitionistic fuzzy numbers. International Journal of Mathematics and Mathematical Sciences.","DOI":"10.1155\/2010\/949143"},{"key":"IJORIS.2019040102-14","doi-asserted-by":"publisher","DOI":"10.1287\/opre.10.4.448"},{"key":"IJORIS.2019040102-15","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1941201224"},{"issue":"4","key":"IJORIS.2019040102-16","first-page":"411","article-title":"The transportation problem in an intuitionistic fuzzy environment.","volume":"4","author":"R. J.Hussain","year":"2012","journal-title":"International Journal of Mathematics Research"},{"issue":"80","key":"IJORIS.2019040102-17","first-page":"3981","article-title":"Algorithmic approach for solving intuitionistic fuzzy transportation problem.","volume":"6","author":"R. J.Hussain","year":"2012","journal-title":"Applied Mathematical Sciences"},{"key":"IJORIS.2019040102-18","first-page":"819","article-title":"The transportation problem with the aid of triangular intuitionistic fuzzy numbers.","author":"R. J.Hussain","year":"2012","journal-title":"Proceedings in international conference on mathematical modeling and applied soft computing (MMASC-2012)"},{"key":"IJORIS.2019040102-19","doi-asserted-by":"publisher","DOI":"10.12988\/ijcms.2013.13056"},{"key":"IJORIS.2019040102-20","unstructured":"Jimenez, F., & Verdegay, J. L. (1996). Interval multiobjective solid transportation problem via genetic algorithms. In Management of Uncertainty in Knowledge-Based Systems (Vol. 2, pp. 787-792)."},{"key":"IJORIS.2019040102-21","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00164-4"},{"key":"IJORIS.2019040102-22","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(98)00083-6"},{"key":"IJORIS.2019040102-23","doi-asserted-by":"publisher","DOI":"10.4018\/IJFSA.2016100106"},{"key":"IJORIS.2019040102-24","doi-asserted-by":"publisher","DOI":"10.5391\/IJFIS.2016.16.4.225"},{"key":"IJORIS.2019040102-25","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-5225-1908-9.ch017"},{"key":"IJORIS.2019040102-26","unstructured":"Kumar, P. S. (2017b). Algorithmic approach for solving allocation problems under intuitionistic fuzzy environment [PhD thesis]. Jamal Mohamed College. Retrieved from http:\/\/hdl.handle.net\/10603\/209151"},{"key":"IJORIS.2019040102-27","doi-asserted-by":"publisher","DOI":"10.1504\/IJLSM.2018.088586"},{"key":"IJORIS.2019040102-28","doi-asserted-by":"publisher","DOI":"10.4018\/IJORIS.2018040104"},{"key":"IJORIS.2019040102-29","article-title":"Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem.","author":"P. S.Kumar","year":"2018","journal-title":"International Journal of Operational Research"},{"key":"IJORIS.2019040102-30","doi-asserted-by":"publisher","DOI":"10.4018\/IJORIS.2018070105"},{"key":"IJORIS.2019040102-31","doi-asserted-by":"publisher","DOI":"10.4018\/IJFSA.2018100104"},{"key":"IJORIS.2019040102-32","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-5225-5396-0.ch011"},{"key":"IJORIS.2019040102-33","article-title":"Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set.","author":"P. S.Kumar","year":"2018","journal-title":"International Journal of System Assurance Engineering and Management"},{"key":"IJORIS.2019040102-34","article-title":"Intuitionistic fuzzy solid assignment problems: A software-based approach.","author":"P. S.Kumar","year":"2018","journal-title":"International Journal of System Assurance Engineering and Management"},{"key":"IJORIS.2019040102-35","author":"P. S.Kumar","year":"2019","journal-title":"The PSK method for solving fully intuitionistic fuzzy assignment problems with some software tools (pp. -). Theoretical and Applied Mathematics in International Business"},{"issue":"1","key":"IJORIS.2019040102-36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4018\/IJFSA.2020010101","article-title":"Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment.","volume":"9","author":"P. S.Kumar","year":"2020","journal-title":"International Journal of Fuzzy System Applications"},{"issue":"3","key":"IJORIS.2019040102-37","first-page":"5","article-title":"Computationally Simple and Efficient Method for Solving Real-Life Mixed Intuitionistic Fuzzy Solid Assignment Problems.","volume":"9","author":"P. S.Kumar","year":"2020","journal-title":"International Journal of Fuzzy System Applications"},{"key":"IJORIS.2019040102-38","doi-asserted-by":"publisher","DOI":"10.12732\/ijpam.v92i2.4"},{"key":"IJORIS.2019040102-39","unstructured":"Kumar, P. S., & Hussain, R. J. (2014b). A method for finding an optimal solution of an assignment problem under mixed intuitionistic fuzzy environment. Proceedings in International Conference on Mathematical Sciences (ICMS-2014) (pp. 417-421). ELSEVIER."},{"key":"IJORIS.2019040102-40","first-page":"25971","article-title":"New algorithm for solving mixed intuitionistic fuzzy assignment problem.","volume":"73","author":"P. S.Kumar","year":"2014","journal-title":"Elixir Appl. Math"},{"issue":"3","key":"IJORIS.2019040102-41","first-page":"897","article-title":"A method for solving balanced intuitionistic fuzzy assignment problem.","volume":"4","author":"P. S.Kumar","year":"2014","journal-title":"International Journal of Engineering Research and Applications"},{"issue":"3","key":"IJORIS.2019040102-42","first-page":"54","article-title":"A method for solving unbalanced intuitionistic fuzzy transportation problems.","volume":"21","author":"P. S.Kumar","year":"2015","journal-title":"Notes on Intuitionistic Fuzzy Sets"},{"key":"IJORIS.2019040102-43","doi-asserted-by":"publisher","DOI":"10.1007\/s13198-014-0334-2"},{"key":"IJORIS.2019040102-44","doi-asserted-by":"publisher","DOI":"10.4018\/IJORIS.2016040103"},{"issue":"2","key":"IJORIS.2019040102-45","first-page":"289","article-title":"An algorithm for solving unbalanced intuitionistic fuzzy assignment problem using triangular intuitionistic fuzzy number.","volume":"24","author":"P. S.Kumar","year":"2016","journal-title":"The Journal of Fuzzy Mathematics"},{"key":"IJORIS.2019040102-46","doi-asserted-by":"publisher","DOI":"10.1063\/1.4990329"},{"key":"IJORIS.2019040102-47","doi-asserted-by":"publisher","DOI":"10.1016\/S0360-8352(97)00199-X"},{"key":"IJORIS.2019040102-48","doi-asserted-by":"publisher","DOI":"10.1016\/S0360-8352(97)00169-1"},{"key":"IJORIS.2019040102-49","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.05.018"},{"key":"IJORIS.2019040102-50","unstructured":"Mahapatra, B. S., & Mahapatra, G. S. (2010). Intuitionistic fuzzy fault tree analysis using intuitionistic fuzzy numbers. International Mathematical Forum, 5(21), 1015-1024."},{"issue":"2","key":"IJORIS.2019040102-51","first-page":"422","article-title":"Reliability evaluation using triangular intuitionistic fuzzy numbers, arithmetic operations.","volume":"3","author":"G. S.Mahapatra","year":"2009","journal-title":"International Scholarly and Scientific Research & Innovation"},{"issue":"2","key":"IJORIS.2019040102-52","first-page":"92","article-title":"Intuitionistic fuzzy number and its arithmetic operation with application on system failure.","volume":"7","author":"G. S.Mahapatra","year":"2013","journal-title":"Journal of Uncertain Systems"},{"issue":"1","key":"IJORIS.2019040102-53","first-page":"151","article-title":"A comparative study on transportation problem in fuzzy environment.","volume":"2","author":"S. I.Mohideen","year":"2010","journal-title":"International Journal of Mathematics Research"},{"issue":"2","key":"IJORIS.2019040102-54","first-page":"290","article-title":"A comparative study of the methods of solving intuitionistic fuzzy linear programming problem. International Journal of Advance Research","volume":"4","author":"A. L.Nachammai","year":"2018","journal-title":"Ideas and Innovations in Technology"},{"issue":"1","key":"IJORIS.2019040102-55","first-page":"24","article-title":"A generalized model for fuzzy linear programs with trapezoidal fuzzy numbers.","volume":"4","author":"H.Nasseri","year":"2017","journal-title":"Journal of Applied Research on Industrial Engineering"},{"key":"IJORIS.2019040102-56","doi-asserted-by":"publisher","DOI":"10.1109\/CFIS.2018.8336644"},{"key":"IJORIS.2019040102-57","unstructured":"Nayagam, G., Lakshmana, V., Venkateshwari, G., & Sivaraman, G. (2008, June). Ranking of intuitionistic fuzzy numbers. In IEEE International Conference onFuzzy Systems FUZZ-IEEE 2008 (pp. 1971-1974). IEEE."},{"issue":"1","key":"IJORIS.2019040102-58","first-page":"80","article-title":"A new ranking method for intuitionistic fuzzy numbers.","volume":"12","author":"H. M.Nehi","year":"2010","journal-title":"International Journal of Fuzzy Systems"},{"key":"IJORIS.2019040102-59","first-page":"1","article-title":"Intuitionistic fuzzy numbers and it\u2019s applications in fuzzy optimization problem.","author":"H. M.Nehi","year":"2005","journal-title":"Proceedings of the Ninth WSEAS International Conference on Systems"},{"key":"IJORIS.2019040102-60","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2009.04.010"},{"issue":"2","key":"IJORIS.2019040102-61","first-page":"79","article-title":"A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems.","volume":"4","author":"P.Pandian","year":"2010","journal-title":"Applied Mathematical Sciences"},{"issue":"5","key":"IJORIS.2019040102-62","first-page":"17","article-title":"The solid transportation problem and its variants.","volume":"5","author":"G.Patel","year":"1989","journal-title":"International Journal of Management and Systems"},{"issue":"11","key":"IJORIS.2019040102-63","first-page":"546","article-title":"Duality theory for intuitionistic fuzzy linear programming problems.","volume":"8","author":"K.Prabakaran","year":"2017","journal-title":"International Journal of Civil Engineering and Technology"},{"key":"IJORIS.2019040102-64","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-016-9233-0"},{"key":"IJORIS.2019040102-65","doi-asserted-by":"crossref","unstructured":"Roy, S. K., & Mahapatra, D. R. (2014). Solving solid transportation problems with multi-choice cost and stochastic supply and demand. In Handbook of Research on Organizational Transformations through Big Data Analytics (p. 397).","DOI":"10.4018\/978-1-4666-7272-7.ch023"},{"key":"IJORIS.2019040102-66","doi-asserted-by":"publisher","DOI":"10.5899\/2014\/jfsva-00199"},{"issue":"4","key":"IJORIS.2019040102-67","first-page":"363","article-title":"Some arithmetic operations on triangular intuitionistic fuzzy number and its application on reliability evaluation.","volume":"2","author":"A. K.Shaw","year":"2012","journal-title":"International Journal of Fuzzy Mathematics and Systems"},{"key":"IJORIS.2019040102-68","unstructured":"Shell, E. (1955). Distribution of a product by several properties. Directorate of Management Analysis. In Proceedings of the Second Symposium in Linear Programming (Vol. 2, pp. 615-642)."},{"key":"IJORIS.2019040102-69","doi-asserted-by":"publisher","DOI":"10.1007\/s13198-014-0274-x"},{"key":"IJORIS.2019040102-70","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-015-0108-2"},{"key":"IJORIS.2019040102-71","doi-asserted-by":"publisher","DOI":"10.1007\/s40819-015-0044-8"},{"issue":"3","key":"IJORIS.2019040102-72","first-page":"309","article-title":"Solving intuitionistic fuzzy linear programming problem based on ranking function. International Journal of Science","volume":"6","author":"G.Sudha","year":"2017","journal-title":"Engineering and Technology Research"},{"key":"IJORIS.2019040102-73","article-title":"Tracts in Operations Research.","author":"K.Swarup","year":"1997"},{"issue":"1","key":"IJORIS.2019040102-74","first-page":"19","article-title":"Centroid of an intuitionistic fuzzy number.","volume":"18","author":"A.Varghese","year":"2012","journal-title":"Notes on Intuitionistic Fuzzy Sets"},{"key":"IJORIS.2019040102-75","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/3049041"},{"key":"IJORIS.2019040102-76","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-5225-2990-3.ch032"},{"key":"IJORIS.2019040102-77","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["International Journal of Operations Research and Information Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.igi-global.com\/viewtitle.aspx?TitleId=225813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,5]],"date-time":"2022-05-05T22:04:42Z","timestamp":1651788282000},"score":1,"resource":{"primary":{"URL":"http:\/\/services.igi-global.com\/resolvedoi\/resolve.aspx?doi=10.4018\/IJORIS.2019040102"}},"subtitle":[""],"short-title":[],"issued":{"date-parts":[[2019,4]]},"references-count":78,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.4018\/ijoris.2019040102","relation":{},"ISSN":["1947-9328","1947-9336"],"issn-type":[{"value":"1947-9328","type":"print"},{"value":"1947-9336","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4]]}}}